Graphene NEGF examples
浅谈锂离子电池石墨负极材料的改性研究进展
112AUTO TIMENEW ENERGY AUTOMOBILE | 新能源汽车现代化社会，各种人工智能技术、大数据平台或者是电力能源的全面发展，都在不断的提高各行业内部运行设备所需要的电能，而对于目前使用广泛的电力能源储存设备锂离子电池，怎样在保障自身效益扩大的同时，满足不同消费群体的需求，还需要作出全面改革，例如：如何扩充储锂容量、提高倍率性能及循环稳定性等，而对锂离子电池关键构件进行分析，起到核心作用的就是石墨负极材料。
对此，石墨负极材料的性能，对锂离子电池后期发展和使用效益有着决定性作用。
再加上石墨导电效率优良，还具备良好的锂离子嵌入、脱出性能，多种优势条件也最终使得石墨变成锂离子电池体系当中使用率为最高、商业化程度为最广泛的负极材料。
但是由于受石墨微观结构客观因素影响，造成石墨理论储锂容量只能达到372mA.h/g，从而出现了电解液兼容性较差、体积膨胀率过高等问题，最终严重影响到了电极能量的密度以及循环稳定性。
对此，意识到问题的严重性，若是要想让实现石墨负极材料性能综合性提升，目前已有诸多国内外重量级研究人员投入到对石墨负极材料改性研究工作当中，也做到了多角度、多层面的研究分析，同时也取得了一定的成果。
1 锂离子电池的电化学机理及石墨嵌锂机制作为一种正常锂离子浓差电池，锂离子电池可分为正极、负极、隔膜、电解液等。
设置石墨负极、LiCoO 2正极，然后综合以上因素，研究锂离子电池的工作机制，可以看出，在对其进行充电期间，清晰看到锂离子在正极LiCoO 2晶格中顺利脱出，而后锂离子循序渐进扩散到电解液中，并在最后穿过隔膜而进入到石墨负极层。
整个过程中，为充分保障电荷之间平衡度，会有同等数量的电子在正极中释放出来，并从外电流路流到石墨负极中，此时会构建出一个回路整体[1]。
而在放电过程中，负极石墨层间的锂离子又开始慢慢脱出，再经电解液，最后返回并嵌入到LiCoO 2晶格中，此时电子会经外电流路传输到正极，这样就可以实现以此充电、放电循环。
inequalities for graph eigenvalues
1
Introduction
We consider the Laplacian and eigenvalues of graphs and induced subgraphs. Although an induceas a graph in its own right, it is natural to consider an induced subgraph S as having a boundary (formed by edges joining vertices in S and vertices not in S but in the “ host ” graph). The host graph then can be regarded as a special case of a subgraph with no boundary. This paper consists of three parts. In the first part (Section 2-5), we give definitions and describe basic properties for the Laplacian of graphs. We introduce the Neumann eigenvalues for induced subgraphs and the heat kernel for graphs and induced subgraphs. Then we establish the following lower bound for the Neumann eigenvalues of induced subgraphs. 1
Abstract For an induced subgraph S of a graph, we show that its Neumann eigenvalue λS can be lower-bounded by using the heat kernel Ht (x, y ) of the subgraph. Namely, √ 1 Ht (x, y ) dx λS ≥ inf y ∈S 2t dy x ∈S where dx denotes the degree of the vertex x. In particular, we derive lower bounds of eigenvalues for convex subgraphs which consist of lattice points in an d-dimensional Riemannian manifolds M with convex boundary. The techniques involve both the (discrete) heat kernels of graphs and improved estimates of the (continuous) heat kernels of Riemannian manifolds. We prove eigenvalue lower bounds for convex subgraphs of the form cǫ2 /(dD(M ))2 where ǫ denotes the distance between two closest lattice points, D(M ) denotes the diameter of the manifold M and c is a constant (independent of the dimension d and the number of vertices in S , but depending on the how “dense” the lattice points are). This eigenvalue bound is useful for bounding the rates of convergence for various random walk problems. Since many enumeration problems can be approximated by considering random walks in convex subgraphs of some appropriate host graph, the eigenvalue inequalities here have many applications.
诺贝尔石墨烯得奖者Grem2011文章
RANDOM WALK TO GRAPHENENobel Lecture, December 8, 2010byANDRE K. GEIMSchool of Phys i cs and Astronomy, The Un i vers i ty of Manchester, Oxford Road, Manchester M13 9PL, Un i ted K i ngdom.If one wants to understand the beaut i ful phys i cs of graphene, they w i ll be spo i led for cho i ce w i th so many rev i ews and popular sc i ence art i cles now ava i lable. I hope that the reader w i ll excuse me i f on th i s occas i on I recommend my own wr i t i ngs [1–3]. Instead of repeat i ng myself here, I have chosen to descr i be my tw i sty sc i ent ific road that eventually led to the Nobel Pr i ze. Most parts of th i s story are not descr i bed anywhere else, and i ts t i me-l i ne covers the per i od from my PhD i n 1987 to the moment when our 2004 paper, recogn i sed by the Nobel Comm i ttee, was accepted for publ i cat i on. The story naturally gets denser i n events and explanat i ons towards the end. Also, i t prov i des a deta i led rev i ew of pre-2004 l i terature and, w i th the benefit of h i nds i ght, attempts to analyse why graphene has attracted so much i nter-est. I have tr i ed my best to make th i s art i cle not only i nformat i ve but also easy to read, even for non-phys i c i sts.ZOMBIE MANAGEMENTMy PhD thes i s was called “Invest i gat i on of mechan i sms of transport relaxa-t i on i n metals by a hel i con resonance method”. All I can say i s that the stuff was as i nterest i ng at that t i me as i t sounds to the reader today. I publ i shed five journal papers and fin i shed the thes i s i n five years, the offic i al durat i on for a PhD at my i nst i tut i on, the Inst i tute of Sol i d State Phys i cs.Web of Sc i ence so-berly reveals that the papers were c i ted tw i ce, by co-authors only. The subject was dead a decade before I even started my PhD. However, every cloud has i ts s i lver l i n i ng, and what I un i quely learned from that exper i ence was that I should never torture research students by offer i ng them “zomb i e” projects. After my PhD, I worked as a staff sc i ent i st at the Inst i tute of M i cro-electron i cs Technology, Chernogolovka, wh i ch belongs to the Russ i an Academy of Sc i ences. The Sov i et system allowed and even encouraged jun i or staff to choose the i r own l i ne of research. After a year of pok i ng i n d i fferent d i rect i ons, I separated research-w i se from my former PhD superv i sor, V i ctor Petrashov, and started develop i ng my own n i che. It was an exper i mental system that was both new and doable, wh i ch was nearly an oxymoron, tak i ng i nto account the scarce resources ava i lable at the t i me at Sov i et researchi nst i tutes. I fabr i cated a sandw i ch cons i st i ng of a th i n metal film and a super-conductor separated by a th i n i nsulator. The superconductor served only to condense an external magnet i c field i nto an array of vort i ces, and th i s h i ghly i nhomogeneous magnet i c field was projected onto the film under i nvest i ga-t i on. Electron transport i n such a m i croscop i cally i nhomogeneous field (vary i ng on a subm i cron scale) was new research terr i tory, and I publ i shed the first exper i mental report on the subject [4], wh i ch was closely followed by an i ndependent paper from S i mon Bend i ng [5]. It was an i nterest i ng and reasonably i mportant n i che, and I cont i nued study i ng the subject for the next few years, i nclud i ng a spell at the Un i vers i ty of Bath i n 1991 as a postdoctoral researcher work i ng w i th S i mon.Th i s exper i ence taught me an i mportant lesson: that i ntroduc i ng a new exper i mental system i s generally more reward i ng than try i ng to find new phenomena w i th i n crowded areas. The chances of success are much h i gher where the field i s new. Of course, the fantast i c results one or i g i nally hopes for are unl i kely to mater i al i se, but, i n the process of study i ng any new system, someth i ng or i g i nal i nev i tably shows up.ONE MAN’S JUNK, ANOTHER MAN’S GOLDIn 1990, thanks to V i taly Ar i stov, d i rector of my Inst i tute i n Chernogolovka at the t i me, I rece i ved a s i x month v i s i t i ng fellowsh i p from the Br i t i sh Royal Soc i ety. Laurence Eaves and Peter Ma i n from Nott i ngham Un i vers i ty k i ndly agreed to accept me as a v i s i tor. S i x months i s a very short per i od for exper i mental work, and c i rcumstances d i ctated that I could only study de-v i ces read i ly ava i lable i n the host laboratory. Ava i lable were subm i cron GaAs w i res left over from prev i ous exper i ments, all done and dusted a few years earl i er. Under the c i rcumstances, my exper i ence of work i ng i n a poverty-str i cken Sov i et academy was helpful. The samples that my hosts cons i dered pract i cally exhausted looked l i ke a gold ve i n to me, and I started work i ng 100 hours per week to explo i t i t. Th i s short v i s i t led to two Phys. Rev. Letters of decent qual i ty [6,7], and I often use th i s exper i ence to tease my younger colleagues. When th i ngs do not go as planned and people start compla i n i ng, I provoke them by procla i m i ng ‘there i s no such th i ng as bad samples; there are only bad postdocs/students’. Search carefully and you w i ll always find someth i ng new. Of course, i t i s better to avo i d such exper i ences and explore new terr i tor i es, but even i f one i s fortunate enough to find an exper i mental system as new and exc i t i ng as graphene, met i culousness and perseverance allow one to progress much further.The pace of research at Nott i ngham was so relentless and, at the same t i me so i nsp i r i ng, that a return to Russ i a was not an opt i on. Sw i mm i ng through Sov i et treacle seemed no less than wast i ng the rest of my l i fe. So at the age of th i rty-three and w i th an h-i ndex of 1 (latest papers not yet publ i shed), I entered the Western job market for postdocs. Dur i ng the next four years I moved between d i fferent un i vers i t i es, from Nott i ngham to Copenhagen to Bath and back to Nott i ngham. Each move allowed me to get acqua i nted w i thyet another top i c or two, s i gn ificantly broaden i ng my research hor i zons. The phys i cs I stud i ed i n those years could be broadly descr i bed as mesoscop i c and i nvolved such systems and phenomena as two-d i mens i onal electron gases (2DEGs), quantum po i nt contacts, resonant tunnell i ng and the quantum Hall effect (QHE), to name but a few. In add i t i on, I became fam i l i ar w i th GaAlAs heterostructures grown by molecular beam ep i taxy (MBE) and i mproved my expert i se i n m i crofabr i cat i on and electron-beam l i thography, technolog i es I had started learn i ng i n Russ i a. All these elements came together to form the foundat i on for the successful work on graphene a decade later.DUTCH COMFORTBy 1994 I had publ i shed enough qual i ty papers and attended enough con-ferences to hope for a permanent academ i c pos i t i on. When I was offered an assoc i ate professorsh i p at the Un i vers i ty of N i jmegen, I i nstantly se i zed upon the chance of hav i ng some secur i ty i n my new post-Sov i et l i fe. The first task i n N i jmegen was of course to establ i sh myself. To th i s end, there was no start-up and no m i crofabr i cat i on to cont i nue any of my prev i ous l i nes of re-search. As resources, I was offered access to magnets, cryostats and electron i c equ i pment ava i lable at N i jmegen’s H i gh F i eld Magnet Laboratory, led by Jan Kees Maan. He was also my formal boss and i n charge of all the money. Even when I was awarded grants as the pr i nc i pal i nvest i gator (the Dutch fund i ng agency FOM was generous dur i ng my stay i n N i jmegen), I could not spend the money as I w i shed. All funds were d i str i buted through so-called ‘work i ng groups’ led by full professors. In add i t i on, PhD students i n the Netherlands could formally be superv i sed only by full professors. Although th i s probably sounds strange to many, th i s was the Dutch academ i c system of the 1990s. It was tough for me then. For a couple of years, I really struggled to adjust to the system, wh i ch was such a contrast to my joyful and product i ve years at Nott i ngham. In add i t i on, the s i tuat i on was a b i t surreal because outs i de the un i vers i ty walls I rece i ved a warm-hearted welcome from everyone around, i nclud i ng Jan Kees and other academ i cs.St i ll, the research opportun i t i es i n N i jmegen were much better than i n Russ i a and, eventually, I managed to surv i ve sc i ent ifically, thanks to help from abroad. Nott i ngham colleagues (i n part i cular Mohamed Hen i n i) prov i ded me w i th 2DEGs that were sent to Chernogolovka, where Sergey Dubonos, a close colleague and fr i end from the 1980s, m i crofabr i cated requested dev i ces. The research top i c I eventually found and later focused on can be referred to as mesoscop i c superconduct i v i ty. Sergey and I used m i cron-s i zed Hall bars made from a 2DEG as local probes of the magnet i c field around small superconduct i ng samples. Th i s allowed measurements of the i r magnet i sat i on w i th accuracy suffic i ent to detect not only the entry and ex i t of i nd i v i dual vort i ces but also much more subtle changes. Th i s was a new exper i mental n i che, made poss i ble by the development of an or i g i nal techn i que of ball i st i c Hall m i cromagnetometry [8]. Dur i ng the next fewyears, we explo i ted th i s n i che area and publ i shed several papers i n Nature and Phys. Rev. Letters wh i ch reported a paramagnet i c Me i ssner effect, vort i ces carry i ng fract i onal flux, vortex configurat i ons i n confined geometr i es and so on. My w i fe Ir i na Gr i gor i eva, an expert i n vortex phys i cs [9], could not find a job i n the Netherlands and therefore had plenty of t i me to help me w i th conquer i ng the subject and wr i t i ng papers. Also, Sergey not only made the dev i ces but also v i s i ted N i jmegen to help w i th measurements. We establ i shed a very product i ve modus operand i where he collected data and I analysed them w i th i n an hour on my computer next door to dec i de what should be done next.A SPELL OF LEVITYThe first results on mesoscop i c superconduct i v i ty started emerg i ng i n 1996, wh i ch made me feel safer w i th i n the Dutch system and also more i nqu i s i-t i ve. I started look i ng around for new areas to explore. The major fac i l i ty at N i jmegen’s H i gh F i eld Lab was powerful electromagnets. They were a major headache, too. These magnets could prov i de fields up to 20 T, wh i ch was somewhat h i gher than 16 to 18 T ava i lable w i th the superconduct i ng magnets that many of our compet i tors had. On the other hand, the elec-tromagnets were so expens i ve to run that we could use them only for a few hours at n i ght, when electr i c i ty was cheaper. My work on mesoscop i c super-conduct i v i ty requ i red only t i ny fields (< 0.01T), and I d i d not use the electro-magnets. Th i s made me feel gu i lty as well as respons i ble for com i ng up w i th exper i ments that would just i fy the fac i l i ty’s ex i stence. The only compet i t i ve edge I could see i n the electromagnets was the i r room temperature (T) bore. Th i s was often cons i dered as an extra d i sadvantage because research i n condensed matter phys i cs typ i cally requ i res low, l i qu i d-hel i um T. The con-trad i ct i on prompted me, as well as other researchers work i ng i n the lab, to ponder on h i gh-field phenomena at room T. Unfortunately, there were few to choose from.Eventually, I stumbled across the mystery of so-called magnet i c water. It i s cla i med that putt i ng a small magnet around a hot water p i pe prevents format i on of scale i ns i de the p i pe. Or i nstall such a magnet on a water tap, and your kettle w i ll never suffer from chalky depos i ts. These magnets are ava i lable i n a great var i ety i n many shops and on the i nternet. There are also hundreds of art i cles wr i tten on th i s phenomenon, but the phys i cs beh i nd i t rema i ns unclear, and many researchers are scept i cal about the very ex i stence of the effect [10]. Over the last fifteen years I have made several attempts to i nvest i gate “magnet i c water” but they were i nconclus i ve, and I st i ll have noth i ng to add to the argument. However, the ava i lab i l i ty of ultra-h i gh fields i n a room T env i ronment i nv i ted lateral th i nk i ng about water. Bas i cally, i f magnet i c water ex i sted, I thought, then the effect should be clearer i n 20 T rather than i n typ i cal fields of <0.1 T created by standard magnets.W i th th i s i dea i n m i nd and, allegedly, on a Fr i day n i ght, I poured water i ns i de the lab’s electromagnet when i t was at i ts max i mum power. Pour i ngwater i n one's equ i pment i s certa i nly not a standard sc i ent ific approach, and I cannot recall why I behaved so ‘unprofess i onally’. Apparently, no one had tr i ed such a s i lly th i ng before, although s i m i lar fac i l i t i es ex i sted i n several places around the world for decades. To my surpr i se, water d i d not end up on the floor but got stuck i n the vert i cal bore of the magnet. Humberto Carmona, a v i s i t i ng student from Nott i ngham, and I played for an hour w i th the water by break i ng the blockage w i th a wooden st i ck and chang i ng the field strength. As a result, we saw balls of lev i tat i ng water (F i gure 1). Th i s was awesome. It took l i ttle t i me to real i se that the phys i cs beh i nd was good old d i amagnet i sm. It took much longer to adjust my i ntu i t i on to the fact that the feeble magnet i c response of water (~10–5), b i ll i ons of t i mes weaker than that of i ron, was suffic i ent to compensate the earth’s grav i ty. Many colleagues, i nclud i ng those who worked w i th h i gh magnet i c fields all the i r l i ves, were flabbergasted, and some of them even argued that th i s was a hoax.I spent the next few months demonstrat i ng magnet i c lev i tat i on to colleagues and v i s i tors, as well as try i ng to make a ‘non-boffin’i llustrat i on for th i s beaut i ful phenomenon. Out of the many objects that we had float i ng i ns i de the magnet, i t was the i mage of a lev i tat i ng frog (F i gure 1) that started the med i a hype. More i mportantly, though, beh i nd all the med i a no i se, th i s i mage found i ts way i nto many textbooks. However qu i rky, i t has become a beaut i ful symbol of ever-present d i amagnet i sm, wh i ch i s no longer perce i ved to be extremely feeble. Somet i mes I am stopped at conferences by people excla i m i ng “I know you! Sorry, i t i s not about graphene. I start my lectures w i th show i ng your frog. Students always want to learn how i t could fly.” The frog story, w i th some i ntr i cate phys i cs beh i nd the stab i l i ty of d i amagnet i c lev i tat i on, i s descr i bed i n my rev i ew i n Phys i cs Today [11].F i gure 1. Lev i tat i ng moments i n N i jmegen. Left – Ball of water (about 5 cm i n d i ameter) freely floats i ns i de the vert i cal bore of an electromagnet. R i ght – The frog that learned to fly. Th i s i mage cont i nues to serve as a symbol show i ng that magnet i sm of ‘nonmagnet i c th i ngs’, i nclud i ng humans, i s not so negl i g i ble. Th i s exper i ment earned M i chael Berry and me the 2000 Ig Nobel Pr i ze. We were asked first whether we dared to accept th i s pr i ze, and I take pr i de i n our sense of humour and self-deprecat i on that we d i d.FRIDAY NIGHT EXPERIMENTSThe lev i tat i on exper i ence was both i nterest i ng and add i ct i ve. It taught me the i mportant lesson that pok i ng i n d i rect i ons far away from my i mmed i ate area of expert i se could lead to i nterest i ng results, even i f the i n i t i al i deas were extremely bas i c. Th i s i n turn i nfluenced my research style, as I started mak i ng s i m i lar exploratory detours that somehow acqu i red the name ‘Fr i day n i ght exper i ments’. The term i s of course i naccurate. No ser i ous work can be accompl i shed i n just one n i ght. It usually requ i res many months of lateral th i nk i ng and d i gg i ng through i rrelevant l i terature w i thout any clear i dea i n s i ght. Eventually, you get a feel i ng – rather than an i dea – about what could be i nterest i ng to explore. Next, you g i ve i t a try, and normally you fa i l. Then, you may or may not try aga i n. In any case, at some moment you must dec i de (and th i s i s the most d i fficult part) whether to cont i nue further efforts or cut losses and start th i nk i ng of another exper i ment. All th i s happens aga i nst the backdrop of your ma i n research and occup i es only a small part of your t i me and bra i n.Already i n N i jmegen, I started us i ng lateral i deas as under- and post-graduate projects, and students were always exc i ted to buy a p i g i n a poke. Kostya Novoselov, who came to N i jmegen as a PhD student i n 1999, took part i n many of these projects. They never lasted for more than a few months, i n order not to jeopard i se a thes i s or career progress i on. Although the enthus i asm i nev i tably van i shed towards the end, when the pred i ctable fa i lures mater i al i sed, some students later confided that those exploratory detours were i nvaluable exper i ences.Most surpr i s i ngly, fa i lures somet i mes fa i led to mater i al i se. Gecko tape i s one such example. Acc i dentally or not, I read a paper descr i b i ng the mechan i sm beh i nd the amaz i ng cl i mb i ng ab i l i ty of geckos [12]. The phys i cs i s rather stra i ghtforward. Gecko’s toes are covered w i th t i ny ha i rs. Each ha i r attaches to the oppos i te surface w i th a m i nute van der Waals force (i n the nN range), but b i ll i ons of ha i rs work together to create a form i dable attract i on suffic i ent to keep geckos attached to any surface, even a glass ce i l i ng. In part i cular, my attent i on was attracted by the spat i al scale of the i r ha i rs. They were subm i cron i n d i ameter, the standard s i ze i n research on mesoscop i c phys i cs. After toy i ng w i th the i dea for a year or so, Sergey Dubonos and I came up w i th procedures to make a mater i al that m i m i cked a gecko’s ha i ry feet. He fabr i cated a square cm of th i s tape, and i t exh i b i ted notable adhes i on [13]. Unfortunately, the mater i al d i d not work as well as a gecko’s feet, deter i orat i ng completely after a couple of attachments. St i ll, i t was an i mportant proof-of-concept exper i ment that i nsp i red further work i n the field. Hopefully, one day someone w i ll develop a way to repl i cate the h i erarch i cal structure of gecko’s setae and i ts self-clean i ng mechan i sm. Then gecko tape can go on sale.BETTER TO BE WRONG THAN BORINGWh i le prepar i ng for my lecture i n Stockholm, I comp i led a l i st of my Fr i day n i ght exper i ments. Only then d i d I real i se a stunn i ng fact. There were two dozen or so exper i ments over a per i od of approx i mately fifteen years and, as expected, most of them fa i led m i serably. But there were three h i ts: lev i tat i on, gecko tape and graphene. Th i s i mpl i es an extraord i nary success rate: more than 10%. Moreover, there were probably near-m i sses, too. For example, I once read a paper [14] about g i ant d i amagnet i sm i n FeGeSeAs alloys, wh i ch was i nterpreted as a s i gn of h i gh-T superconduct i v i ty. I asked Lamarches for samples and got them. Kostya and I employed ball i st i c Hall magnetometry to check for g i ant d i amagnet i sm but found noth i ng, even at 1 K. Th i s happened i n 2003, well before the d i scovery of i ron pn i ct i de superconduct i v-i ty, and I st i ll wonder whether there were any small i nclus i ons of a supercon-duct i ng mater i al wh i ch we m i ssed w i th our approach. Another m i ss was an attempt to detect “heartbeats” of i nd i v i dual l i v i ng cells. The i dea was to use 2DEG Hall crosses as ultrasens i t i ve electrometers to detect electr i cal s i gnals due to phys i olog i cal act i v i ty of i nd i v i dual cells. Even though no heartbeats were detected wh i le a cell was al i ve, our sensor recorded huge voltage sp i kes at i ts “last gasp” when the cell was treated w i th excess alcohol [15]. Now I attr i bute th i s near-m i ss to the unw i se use of yeast, a very dormant m i cro-organ i sm. Four years later, s i m i lar exper i ments were done us i ng embryon i c heart cells and – what a surpr i se – graphene sensors, and they were successful i n detect i ng such b i oelectr i cal act i v i ty [16].Frankly, I do not bel i eve that the above success rate can be expla i ned by my lateral i deas be i ng part i cularly good. More l i kely, th i s tells us that pok i ng i n new d i rect i ons, even randomly, i s more reward i ng than i s generally perce i ved. We are probably d i gg i ng too deep w i th i n establ i shed areas, leav i ng plenty of unexplored stuff under the surface, just one poke away. When one dares to try, rewards are not guaranteed, but at least i t i s an adventure.THE MANCUNIAN WAYBy 2000, w i th mesoscop i c superconduct i v i ty, d i amagnet i c lev i tat i on and four Nature papers under my belt, I was well placed to apply for a full professorsh i p. Colleagues were rather surpr i sed when I chose the Un i vers i ty of Manchester, decl i n i ng a number of seem i ngly more prest i g i ous offers. The reason was s i mple.M i ke Moore, cha i rman of the search comm i ttee, knew my w i fe Ir i na when she was a very successful postdoc i n Br i stol rather than my co-author and a part-t i me teach i ng lab techn i c i an i n N i jmegen. He suggested that Ir i na could apply for the lecturesh i p that was there to support the professorsh i p. After s i x years i n the Netherlands, the i dea that a husband and w i fe could offic i ally work together had not even crossed my m i nd. Th i s was the dec i s i ve factor. We apprec i ated not only the poss i b i l i ty of sort i ng out our dual career problems but also felttouched that our future colleagues cared. We have never regretted the move.So i n early 2001, I took charge of several d i lap i dated rooms stor i ng anc i ent equ i pment of no value, and a start-up grant of £100K. There were no central fac i l i t i es that I could explo i t, except for a hel i um l i quefier. No problem. I followed the same rout i ne as i n N i jmegen, comb i n i ng help from other places, espec i ally Sergey Dubonos. The lab started shap i ng up surpr i s i ngly qu i ckly. W i th i n half a year, I rece i ved my first grant of £500K, wh i ch allowed us to acqu i re essent i al equ i pment. Desp i te be i ng consumed w i th our one year old daughter, Ir i na also got her start i ng grant a few months later. We i nv i ted Kostya to jo i n us as a research fellow (he cont i nued to be offic i ally reg i stered i n N i jmegen as a PhD student unt i l 2004 when he defended h i s thes i s there). And our group started generat i ng results that led to more grants that i n turn led to more results.By 2003 we publ i shed several good-qual i ty papers i nclud i ng Nature, Nature Mater i als and Phys. Rev. Letters, and we cont i nued beefing up the labora-tory w i th new equ i pment. Moreover, thanks to a grant of £1.4M (research i nfrastructure fund i ng scheme masterm i nded by the then sc i ence m i n i ster Dav i d Sa i nsbury), Ern i e H i ll from the Department of Computer Sc i ences and I managed to set up the Manchester Centre for Mesosc i ence and Nanotechnology. Instead of pour i ng the w i ndfall money i nto br i cks-and-mortar, we ut i l i sed the ex i st i ng clean room areas (~250 m2) i n Computer Sc i ences. Those rooms conta i ned obsolete equ i pment, and i t was thrown away and replaced w i th state-of-the-art m i crofabr i cat i on fac i l i t i es, i nclud i ng a new electron-beam l i thography system. The fact that Ern i e and I are most proud of i s that many groups around the world have more expens i ve fac i l i t i es but our Centre has cont i nuously, s i nce 2003, been produc i ng new structures and dev i ces. We do not have a posh horse here that i s for show, but rather a draft horse that has been work i ng really hard.Whenever I descr i be th i s exper i ence to my colleagues abroad, they find i t d i fficult to bel i eve that i t i s poss i ble to establ i sh a fully funct i onal labora-tory and a m i crofabr i cat i on fac i l i ty i n less than three years and w i thout an astronom i cal start-up grant. If not for my own exper i ence, I would not bel i eve i t e i ther. Th i ngs progressed unbel i evably qu i ckly. The Un i vers i ty was support i ve, but my greatest thanks are reserved spec ifically for the respons i ve mode of the UK Eng i neer i ng and Phys i cal Sc i ences Research Counc i l (EPSRC). The fund i ng system i s democrat i c and non-xenophob i c. Your pos i t i on i n an academ i c h i erarchy or an old-boys network counts for l i ttle. Also, ‘v i s i onary i deas’ and grand prom i ses to ‘address soc i al and econom i c needs’ play l i ttle role when i t comes to the peer rev i ew. In truth, the respons i ve mode d i str i butes i ts money on the bas i s of a recent track record, whatever that means i n d i fferent subjects, and the fund i ng normally goes to researchers who work both effic i ently and hard. Of course, no system i s perfect, and one can always hope for a better one. However, paraphras i ng W i nston Church i ll, the UK has the worst research fund i ng system, except for all the others that I am aware of.THREE LITTLE CLOUDSAs our laboratory and Nanotech Centre were shap i ng up, I got some spare t i me for th i nk i ng of new research detours. Gecko tape and the fa i led attempts w i th yeast and quas i-pn i ct i des took place dur i ng that t i me. Also, Serge Morozov, a sen i or fellow from Chernogolovka, who later became a regular v i s i-tor and i nvaluable collaborator, wasted h i s first two v i s i ts on study i ng magnet i c water. In the autumn of 2002, our first Manchester PhD student, Da J i ang, arr i ved, and I needed to i nvent a PhD project for h i m. It was clear that for the first few months he needed to spend h i s t i me learn i ng Engl i sh and gett i ng acqua i nted w i th the lab. Accord i ngly, as a starter, I suggested to h i m a new lateral exper i ment. It was to make films of graph i te ‘as th i n as poss i ble’ and, i f successful, I prom i sed we would then study the i r ‘mesoscop i c’ propert i es. Recently, try i ng to analyse how th i s i dea emerged, I recalled three badly shaped thought clouds.One cloud was a concept of ‘metall i c electron i cs’. If an external electr i c field i s appl i ed to a metal, the number of charge carr i ers near i ts surface changes, so that one may expect that i ts surface propert i es change, too. Th i s i s how modern sem i conductor electron i cs works. Why not use a metal i nstead of s i l i con? As an undergraduate student, I wanted to use electr i c field effect (EFE) and X-ray analys i s to i nduce and detect changes i n the latt i ce constant. It was naïve because s i mple est i mates show that the effect would be negl i g i ble. Indeed, no d i electr i c allows fields much h i gher than 1V/nm, wh i ch translates i nto max i mum changes i n charge carr i er concentrat i on n at the metal surface of about 1014 per cm2. In compar i son, a typ i cal metal (e.g., Au) conta i ns ~1023 electrons per cm3 and, even for a 1 nm th i ck film, th i s y i elds relat i ve changes i n n and conduct i v i ty of ~1%, leav i ng as i de much smaller changes i n the latt i ce constant.Prev i ously, many researchers asp i red to detect the field effect i n metals. The first ment i on i s as far back as 1902, shortly after the d i scovery of the electron. J. J. Thomson (1906 Nobel Pr i ze i n Phys i cs) suggested to Charles Mott, the father of Nev i ll Mott (1977 Nobel Pr i ze i n Phys i cs), to look for the EFE i n a th i n metal film, but noth i ng was found [17]. The first attempt to measure the EFE i n a metal was recorded i n sc i ent ific l i terature i n 1906 [18]. Instead of a normal metal, one could also th i nk of sem i metals such as b i smuth, graph i te or ant i mony wh i ch have a lot fewer carr i ers. Over the last century, many researchers used B i films (n ~1018 cm–3) but observed only small changes i n the i r conduct i v i ty [19,20]. Aware of th i s research area and w i th exper i ence i n GaAlAs heterostructures, I was cont i nuously, albe i t casually, look i ng for other cand i dates, espec i ally ultra-th i n films of superconductors i n wh i ch the field effect can be ampl ified i n prox i m i ty to the superconduct i ng trans i t i on [21,22]. In N i jmegen, my enthus i asm was once sparked by learn i ng about nm-th i ck Al films grown by MBE on top of GaAlAs heterostructures but, after est i mat i ng poss i ble effects, I dec i ded that the chances of success were so poor i t was not worth try i ng.Carbon nanotubes were the second cloud hang i ng around i n the late。
line graph 例题和范文
line graph 例题和范文以下是一个关于人口增长的line graph 例题和范文：Line Graph Example: Population Growth题目：The line graph below represents the population growth in a city from the year 2000 to 2010. Analyze the data and write a report summarizing the trends.范文：Population Growth Trends in City (2000-2010)The line graph illustrates the population growth of a city over the span of a decade, from 2000 to 2010. The vertical axis represents the population in thousands, while the horizontal axis denotes the years.In the year 2000, the population stood at approximately 250,000, marking the starting point of the observed period. Over the next three years, there was a steady and gradual increase in population, reaching around 280,000 by 2003. However, the most significant surge in population occurred between 2003 and 2007, where the numbers nearly doubled, peaking at 520,000 residents.Following this period of rapid growth, there was a noticeable decline in population from 2007 to 2009. By 2009, the population had decreased to approximately 430,000. The last year of the observed period, 2010, witnessed a slight recovery, with the population rising to around450,000.Key Observations:Steady Growth (2000-2003): The city experienced a steady population growth in the initial years, with a modest increase from 250,000 to 280,000.Exponential Growth (2003-2007): The most remarkable phase of the decade was the period from 2003 to 2007, where the population nearly doubled, reaching its peak at 520,000.Population Decline (2007-2009): Subsequently, there was a noticeable decline in population, possibly attributed to external factors or migration trends, bringing the population down to 430,000 by 2009.Slight Recovery (2009-2010): The last year of the observation period saw a slight recovery, with the population increasing to 450,000.In conclusion, the line graph illustrates significant fluctuations in the population of the city over the decade, reflecting periods of both growth and decline. Understanding these trends is crucial for urban planners and policymakers to address the challenges and opportunities associated with population dynamics.。
Two-Dimensional Gas of Massless Dirac Fermions in Graphene
Two-Dimensional Gas of Massless Dirac Fermions in Graphene K.S. Novoselov1, A.K. Geim1, S.V. Morozov2, D. Jiang1, M.I. Katsnelson3, I.V. Grigorieva1, S.V. Dubonos2, A.A. Firsov21Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester, M13 9PL, UK2Institute for Microelectronics Technology, 142432, Chernogolovka, Russia3Institute for Molecules and Materials, Radboud University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, the NetherlandsElectronic properties of materials are commonly described by quasiparticles that behave as nonrelativistic electrons with a finite mass and obey the Schrödinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective “speed of light” c∗ ≈106m/s. Our studies of graphene – a single atomic layer of carbon – have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at halfinteger filling factors; b) graphene’s conductivity never falls below a minimum value corresponding to the conductance quantum e2/h, even when carrier concentrations tend to zero; c) the cyclotron mass mc of massless carriers with energy E in graphene is described by equation E =mcc∗2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of π due to Berry’s phase.Graphene is a monolayer of carbon atoms packed into a dense honeycomb crystal structure that can be viewed as either an individual atomic plane extracted from graphite or unrolled single-wall carbon nanotubes or as a giant flat fullerene molecule. This material was not studied experimentally before and, until recently [1,2], presumed not to exist. To obtain graphene samples, we used the original procedures described in [1], which involve micromechanical cleavage of graphite followed by identification and selection of monolayers using a combination of optical, scanning-electron and atomic-force microscopies. The selected graphene films were further processed into multi-terminal devices such as the one shown in Fig. 1, following standard microfabrication procedures [2]. Despite being only one atom thick and unprotected from the environment, our graphene devices remain stable under ambient conditions and exhibit high mobility of charge carriers. Below we focus on the physics of “ideal” (single-layer) graphene which has a different electronic structure and exhibits properties qualitatively different from those characteristic of either ultra-thin graphite films (which are semimetals and whose material properties were studied recently [2-5]) or even of our other devices consisting of just two layers of graphene (see further). Figure 1 shows the electric field effect [2-4] in graphene. Its conductivity σ increases linearly with increasing gate voltage Vg for both polarities and the Hall effect changes its sign at Vg ≈0. This behaviour shows that substantial concentrations of electrons (holes) are induced by positive (negative) gate voltages. Away from the transition region Vg ≈0, Hall coefficient RH = 1/ne varies as 1/Vg where n is the concentration of electrons or holes and e the electron charge. The linear dependence 1/RH ∝Vg yields n =α·Vg with α ≈7.3·1010cm-2/V, in agreement with the theoretical estimate n/Vg ≈7.2·1010cm-2/V for the surface charge density induced by the field effect (see Fig. 1’s caption). The agreement indicates that all the induced carriers are mobile and there are no trapped charges in graphene. From the linear dependence σ(Vg) we found carrier mobilities µ =σ/ne, whichreached up to 5,000 cm2/Vs for both electrons and holes, were independent of temperature T between 10 and 100K and probably still limited by defects in parent graphite. To characterise graphene further, we studied Shubnikov-de Haas oscillations (SdHO). Figure 2 shows examples of these oscillations for different magnetic fields B, gate voltages and temperatures. Unlike ultra-thin graphite [2], graphene exhibits only one set of SdHO for both electrons and holes. By using standard fan diagrams [2,3], we have determined the fundamental SdHO frequency BF for various Vg. The resulting dependence of BF as a function of n is plotted in Fig. 3a. Both carriers exhibit the same linear dependence BF = β·n with β ≈1.04·10-15 T·m2 (±2%). Theoretically, for any 2D system β is defined only by its degeneracy f so that BF =φ0n/f, where φ0 =4.14·10-15 T·m2 is the flux quantum. Comparison with the experiment yields f =4, in agreement with the double-spin and double-valley degeneracy expected for graphene [6,7] (cf. caption of Fig. 2). Note however an anomalous feature of SdHO in graphene, which is their phase. In contrast to conventional metals, graphene’s longitudinal resistance ρxx(B) exhibits maxima rather than minima at integer values of the Landau filling factor ν (Fig. 2a). Fig. 3b emphasizes this fact by comparing the phase of SdHO in graphene with that in a thin graphite film [2]. The origin of the “odd” phase is explained below. Another unusual feature of 2D transport in graphene clearly reveals itself in the T-dependence of SdHO (Fig. 2b). Indeed, with increasing T the oscillations at high Vg (high n) decay more rapidly. One can see that the last oscillation (Vg ≈100V) becomes practically invisible already at 80K whereas the first one (Vg <10V) clearly survives at 140K and, in fact, remains notable even at room temperature. To quantify this behaviour we measured the T-dependence of SdHO’s amplitude at various gate voltages and magnetic fields. The results could be fitted accurately (Fig. 3c) by the standard expression T/sinh(2π2kBTmc/heB), which yielded mc varying between ≈ 0.02 and 0.07m0 (m0 is the free electron mass). Changes in mc are well described by a square-root dependence mc ∝n1/2 (Fig. 3d). To explain the observed behaviour of mc, we refer to the semiclassical expressions BF = (h/2πe)S(E) and mc =(h2/2π)∂S(E)/∂E where S(E) =πk2 is the area in k-space of the orbits at the Fermi energy E(k) [8]. Combining these expressions with the experimentally-found dependences mc ∝n1/2 and BF =(h/4e)n it is straightforward to show that S must be proportional to E2 which yields E ∝k. Hence, the data in Fig. 3 unambiguously prove the linear dispersion E =hkc∗ for both electrons and holes with a common origin at E =0 [6,7]. Furthermore, the above equations also imply mc =E/c∗2 =(h2n/4πc∗2)1/2 and the best fit to our data yields c∗ ≈1⋅106 m/s, in agreement with band structure calculations [6,7]. The employed semiclassical model is fully justified by a recent theory for graphene [9], which shows that SdHO’s amplitude can indeed be described by the above expression T/sinh(2π2kBTmc/heB) with mc =E/c∗2. Note that, even though the linear spectrum of fermions in graphene (Fig. 3e) implies zero rest mass, their cyclotron mass is not zero. The unusual response of massless fermions to magnetic field is highlighted further by their behaviour in the high-field limit where SdHO evolve into the quantum Hall effect (QHE). Figure 4 shows Hall conductivity σxy of graphene plotted as a function of electron and hole concentrations in a constant field B. Pronounced QHE plateaux are clearly seen but, surprisingly, they do not occur in the expected sequence σxy =(4e2/h)N where N is integer. On the contrary, the plateaux correspond to half-integer ν so that the first plateau occurs at 2e2/h and the sequence is (4e2/h)(N + ½). Note that the transition from the lowest hole (ν =–½) to lowest electron (ν =+½) Landau level (LL) in graphene requires the same number of carriers (∆n =4B/φ0 ≈1.2·1012cm-2) as the transition between other nearest levels (cf. distances between minima in ρxx). This results in a ladder of equidistant steps in σxy which are not interrupted when passing through zero. To emphasize this highly unusual behaviour, Fig. 4 also shows σxy for a graphite film consisting of only two graphene layers where the sequence of plateaux returns to normal and the first plateau is at 4e2/h, as in the conventional QHE. We attribute this qualitative transition between graphene and its two-layer counterpart to the fact that fermions in the latter exhibit a finite mass near n ≈0 (as found experimentally; to be published elsewhere) and can no longer be described as massless Dirac particles. 2The half-integer QHE in graphene has recently been suggested by two theory groups [10,11], stimulated by our work on thin graphite films [2] but unaware of the present experiment. The effect is single-particle and intimately related to subtle properties of massless Dirac fermions, in particular, to the existence of both electron- and hole-like Landau states at exactly zero energy [912]. The latter can be viewed as a direct consequence of the Atiyah-Singer index theorem that plays an important role in quantum field theory and the theory of superstrings [13,14]. For the case of 2D massless Dirac fermions, the theorem guarantees the existence of Landau states at E=0 by relating the difference in the number of such states with opposite chiralities to the total flux through the system (note that magnetic field can also be inhomogeneous). To explain the half-integer QHE qualitatively, we invoke the formal expression [9-12] for the energy of massless relativistic fermions in quantized fields, EN =[2ehc∗2B(N +½ ±½)]1/2. In QED, sign ± describes two spins whereas in the case of graphene it refers to “pseudospins”. The latter have nothing to do with the real spin but are “built in” the Dirac-like spectrum of graphene, and their origin can be traced to the presence of two carbon sublattices. The above formula shows that the lowest LL (N =0) appears at E =0 (in agreement with the index theorem) and accommodates fermions with only one (minus) projection of the pseudospin. All other levels N ≥1 are occupied by fermions with both (±) pseudospins. This implies that for N =0 the degeneracy is half of that for any other N. Alternatively, one can say that all LL have the same “compound” degeneracy but zeroenergy LL is shared equally by electrons and holes. As a result the first Hall plateau occurs at half the normal filling and, oddly, both ν = –½ and +½ correspond to the same LL (N =0). All other levels have normal degeneracy 4B/φ0 and, therefore, remain shifted by the same ½ from the standard sequence. This explains the QHE at ν =N + ½ and, at the same time, the “odd” phase of SdHO (minima in ρxx correspond to plateaux in ρxy and, hence, occur at half-integer ν; see Figs. 2&3), in agreement with theory [9-12]. Note however that from another perspective the phase shift can be viewed as the direct manifestation of Berry’s phase acquired by Dirac fermions moving in magnetic field [15,16]. Finally, we return to zero-field behaviour and discuss another feature related to graphene’s relativistic-like spectrum. The spectrum implies vanishing concentrations of both carriers near the Dirac point E =0 (Fig. 3e), which suggests that low-T resistivity of the zero-gap semiconductor should diverge at Vg ≈0. However, neither of our devices showed such behaviour. On the contrary, in the transition region between holes and electrons graphene’s conductivity never falls below a well-defined value, practically independent of T between 4 and 100K. Fig. 1c plots values of the maximum resistivity ρmax(B =0) found in 15 different devices, which within an experimental error of ≈15% all exhibit ρmax ≈6.5kΩ, independent of their mobility that varies by a factor of 10. Given the quadruple degeneracy f, it is obvious to associate ρmax with h/fe2 =6.45kΩ where h/e2 is the resistance quantum. We emphasize that it is the resistivity (or conductivity) rather than resistance (or conductance), which is quantized in graphene (i.e., resistance R measured experimentally was not quantized but scaled in the usual manner as R =ρL/w with changing length L and width w of our devices). Thus, the effect is completely different from the conductance quantization observed previously in quantum transport experiments. However surprising, the minimum conductivity is an intrinsic property of electronic systems described by the Dirac equation [17-20]. It is due to the fact that, in the presence of disorder, localization effects in such systems are strongly suppressed and emerge only at exponentially large length scales. Assuming the absence of localization, the observed minimum conductivity can be explained qualitatively by invoking Mott’s argument [21] that mean-free-path l of charge carriers in a metal can never be shorter that their wavelength λF. Then, σ =neµ can be re-written as σ = (e2/h)kFl and, hence, σ cannot be smaller than ≈e2/h per each type of carriers. This argument is known to have failed for 2D systems with a parabolic spectrum where disorder leads to localization and eventually to insulating behaviour [17,18]. For the case of 2D Dirac fermions, no localization is expected [17-20] and, accordingly, Mott’s argument can be used. Although there is a broad theoretical consensus [18-23,10,11] that a 2D gas of Dirac fermions should exhibit a minimum 3conductivity of about e2/h, this quantization was not expected to be accurate and most theories suggest a value of ≈e2/πh, in disagreement with the experiment. In conclusion, graphene exhibits electronic properties distinctive for a 2D gas of particles described by the Dirac rather than Schrödinger equation. This 2D system is not only interesting in itself but also allows one to access – in a condensed matter experiment – the subtle and rich physics of quantum electrodynamics [24-27] and provides a bench-top setting for studies of phenomena relevant to cosmology and astrophysics [27,28].1. Novoselov, K.S. et al. PNAS 102, 10451 (2005). 2. Novoselov, K.S. et al. Science 306, 666 (2004); cond-mat/0505319. 3. Zhang, Y., Small, J.P., Amori, M.E.S. & Kim, P. Phys. Rev. Lett. 94, 176803 (2005). 4. Berger, C. et al. J. Phys. Chem. B, 108, 19912 (2004). 5. Bunch, J.S., Yaish, Y., Brink, M., Bolotin, K. & McEuen, P.L. Nanoletters 5, 287 (2005). 6. Dresselhaus, M.S. & Dresselhaus, G. Adv. Phys. 51, 1 (2002). 7. Brandt, N.B., Chudinov, S.M. & Ponomarev, Y.G. Semimetals 1: Graphite and Its Compounds (North-Holland, Amsterdam, 1988). 8. Vonsovsky, S.V. and Katsnelson, M.I. Quantum Solid State Physics (Springer, New York, 1989). 9. Gusynin, V.P. & Sharapov, S.G. Phys. Rev. B 71, 125124 (2005). 10. Gusynin, V.P. & Sharapov, S.G. cond-mat/0506575. 11. Peres, N.M.R., Guinea, F. & Castro Neto, A.H. cond-mat/0506709. 12. Zheng, Y. & Ando, T. Phys. Rev. B 65, 245420 (2002). 13. Kaku, M. Introduction to Superstrings (Springer, New York, 1988). 14. Nakahara, M. Geometry, Topology and Physics (IOP Publishing, Bristol, 1990). 15. Mikitik, G. P. & Sharlai, Yu.V. Phys. Rev. Lett. 82, 2147 (1999). 16. Luk’yanchuk, I.A. & Kopelevich, Y. Phys. Rev. Lett. 93, 166402 (2004). 17. Abrahams, E., Anderson, P.W., Licciardello, D.C. & Ramakrishnan, T.V. Phys. Rev. Lett. 42, 673 (1979). 18. Fradkin, E. Phys. Rev. B 33, 3263 (1986). 19. Lee, P.A. Phys. Rev. Lett. 71, 1887 (1993). 20. Ziegler, K. Phys. Rev. Lett. 80, 3113 (1998). 21. Mott, N.F. & Davis, E.A. Electron Processes in Non-Crystalline Materials (Clarendon Press, Oxford, 1979). 22. Morita, Y. & Hatsugai, Y. Phys. Rev. Lett. 79, 3728 (1997). 23. Nersesyan, A.A., Tsvelik, A.M. & Wenger, F. Phys. Rev. Lett. 72, 2628 (1997). 24. Rose, M.E. Relativistic Electron Theory (John Wiley, New York, 1961). 25. Berestetskii, V.B., Lifshitz, E.M. & Pitaevskii, L.P. Relativistic Quantum Theory (Pergamon Press, Oxford, 1971). 26. Lai, D. Rev. Mod. Phys. 73, 629 (2001). 27. Fradkin, E. Field Theories of Condensed Matter Systems (Westview Press, Oxford, 1997). 28. Volovik, G.E. The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003).Acknowledgements This research was supported by the EPSRC (UK). We are most grateful to L. Glazman, V. Falko, S. Sharapov and A. Castro Netto for helpful discussions. K.S.N. was supported by Leverhulme Trust. S.V.M., S.V.D. and A.A.F. acknowledge support from the Russian Academy of Science and INTAS.43µ (m2/Vs)0.8c4P0.4 22 σ (1/kΩ)10K0 0 1/RH(T/kΩ) 1 2ρmax (h/4e2)1-5010 Vg (V) 50 -10ab 0 -100-500 Vg (V)50100Figure 1. Electric field effect in graphene. a, Scanning electron microscope image of one of our experimental devices (width of the central wire is 0.2µm). False colours are chosen to match real colours as seen in an optical microscope for larger areas of the same materials. Changes in graphene’s conductivity σ (main panel) and Hall coefficient RH (b) as a function of gate voltage Vg. σ and RH were measured in magnetic fields B =0 and 2T, respectively. The induced carrier concentrations n are described by [2] n/Vg =ε0ε/te where ε0 and ε are permittivities of free space and SiO2, respectively, and t ≈300 nm is the thickness of SiO2 on top of the Si wafer used as a substrate. RH = 1/ne is inverted to emphasize the linear dependence n ∝Vg. 1/RH diverges at small n because the Hall effect changes its sign around Vg =0 indicating a transition between electrons and holes. Note that the transition region (RH ≈ 0) was often shifted from zero Vg due to chemical doping [2] but annealing of our devices in vacuum normally allowed us to eliminate the shift. The extrapolation of the linear slopes σ(Vg) for electrons and holes results in their intersection at a value of σ indistinguishable from zero. c, Maximum values of resistivity ρ =1/σ (circles) exhibited by devices with different mobilites µ (left y-axis). The histogram (orange background) shows the number P of devices exhibiting ρmax within 10% intervals around the average value of ≈h/4e2. Several of the devices shown were made from 2 or 3 layers of graphene indicating that the quantized minimum conductivity is a robust effect and does not require “ideal” graphene.ρxx (kΩ)0.60 aVg = -60V4B (T)810K12∆σxx (1/kΩ)0.4 1ν=4 140K 80K B =12T0 b 0 25 50 Vg (V) 7520K100Figure 2. Quantum oscillations in graphene. SdHO at constant gate voltage Vg as a function of magnetic field B (a) and at constant B as a function of Vg (b). Because µ does not change much with Vg, the constant-B measurements (at a constant ωcτ =µB) were found more informative. Panel b illustrates that SdHO in graphene are more sensitive to T at high carrier concentrations. The ∆σxx-curves were obtained by subtracting a smooth (nearly linear) increase in σ with increasing Vg and are shifted for clarity. SdHO periodicity ∆Vg in a constant B is determined by the density of states at each Landau level (α∆Vg = fB/φ0) which for the observed periodicity of ≈15.8V at B =12T yields a quadruple degeneracy. Arrows in a indicate integer ν (e.g., ν =4 corresponds to 10.9T) as found from SdHO frequency BF ≈43.5T. Note the absence of any significant contribution of universal conductance fluctuations (see also Fig. 1) and weak localization magnetoresistance, which are normally intrinsic for 2D materials with so high resistivity.75 BF (T) 500.2 0.11/B (1/T)b5 10 N 1/2025 a 0 0.061dmc /m00.04∆0.02 0c0 0 T (K) 150n =0e-6-3036Figure 3. Dirac fermions of graphene. a, Dependence of BF on carrier concentration n (positive n correspond to electrons; negative to holes). b, Examples of fan diagrams used in our analysis [2] to find BF. N is the number associated with different minima of oscillations. Lower and upper curves are for graphene (sample of Fig. 2a) and a 5-nm-thick film of graphite with a similar value of BF, respectively. Note that the curves extrapolate to different origins; namely, to N = ½ and 0. In graphene, curves for all n extrapolate to N = ½ (cf. [2]). This indicates a phase shift of π with respect to the conventional Landau quantization in metals. The shift is due to Berry’s phase [9,15]. c, Examples of the behaviour of SdHO amplitude ∆ (symbols) as a function of T for mc ≈0.069 and 0.023m0; solid curves are best fits. d, Cyclotron mass mc of electrons and holes as a function of their concentration. Symbols are experimental data, solid curves the best fit to theory. e, Electronic spectrum of graphene, as inferred experimentally and in agreement with theory. This is the spectrum of a zero-gap 2D semiconductor that describes massless Dirac fermions with c∗ 300 times less than the speed of light.n (1012 cm-2)σxy (4e2/h)4 3 2 -2 1 -1 -2 -3 2 44Kn7/ 5/ 3/ 1/2 2 2 210 ρxx (kΩ)-4σxy (4e2/h)0-1/2 -3/2 -5/2514T0-7/2 -4 -2 0 2 4 n (1012 cm-2)Figure 4. Quantum Hall effect for massless Dirac fermions. Hall conductivity σxy and longitudinal resistivity ρxx of graphene as a function of their concentration at B =14T. σxy =(4e2/h)ν is calculated from the measured dependences of ρxy(Vg) and ρxx(Vg) as σxy = ρxy/(ρxy + ρxx)2. The behaviour of 1/ρxy is similar but exhibits a discontinuity at Vg ≈0, which is avoided by plotting σxy. Inset: σxy in “two-layer graphene” where the quantization sequence is normal and occurs at integer ν. The latter shows that the half-integer QHE is exclusive to “ideal” graphene.。
tpo45三篇托福阅读TOEFL原文译文题目答案译文背景知识
tpo45三篇托福阅读TOEFL原文译文题目答案译文背景知识阅读-1 (2)原文 (2)译文 (5)题目 (7)答案 (15)背景知识 (16)阅读-2 (16)原文 (16)译文 (19)题目 (23)答案 (30)背景知识 (31)阅读-3 (32)原文 (32)译文 (35)题目 (37)答案 (45)背景知识 (45)阅读-1原文The Beringia Landscape①During the peak of the last ice age,northeast Asia(Siberia)and Alaska were connected by a broad land mass called the Bering Land Bridge.This land bridge existed because so much of Earth’s water was frozen in the great ice sheets that sea levels were over100meters lower than they are today.Between25,000and10,000years ago,Siberia,the Bering Land Bridge,and Alaska shared many environmental characteristics.These included a common mammalian fauna of large mammals,a common flora composed of broad grasslands as well as wind-swept dunes and tundra,and a common climate with cold,dry winters and somewhat warmer summers.The recognition that many aspects of the modern flora and fauna were present on both sides of the Bering Sea as remnants of the ice-age landscape led to this region being named Beringia.②It is through Beringia that small groups of large mammal hunters, slowly expanding their hunting territories,eventually colonized North and South America.On this archaeologists generally agree,but that is where the agreement stops.One broad area of disagreement inexplaining the peopling of the Americas is the domain of paleoecologists,but it is critical to understanding human history:what was Beringia like?③The Beringian landscape was very different from what it is today. Broad,windswept valleys;glaciated mountains;sparse vegetation;and less moisture created a rather forbidding land mass.This land mass supported herds of now-extinct species of mammoth,bison,and horse and somewhat modern versions of caribou,musk ox,elk,and saiga antelope.These grazers supported in turn a number of impressive carnivores,including the giant short-faced bear,the saber-tooth cat,and a large species of lion.④The presence of mammal species that require grassland vegetation has led Arctic biologist Dale Guthrie to argue that while cold and dry, there must have been broad areas of dense vegetation to support herds of mammoth,horse,and bison.Further,nearly all of the ice-age fauna had teeth that indicate an adaptation to grasses and sedges;they could not have been supported by a modern flora of mosses and lichens. Guthrie has also demonstrated that the landscape must have been subject to intense and continuous winds,especially in winter.He makes this argument based on the anatomy of horse and bison,which do not have the ability to search for food through deep snow cover.They needlandscapes with strong winds that remove the winter snows,exposing the dry grasses beneath.Guthrie applied the term“mammoth steppe"to characterize this landscape.⑤In contrast,Paul Colinvaux has offered a counterargument based on the analysis of pollen in lake sediments dating to the last ice age.He found that the amount of pollen recovered in these sediments is so low that the Beringian landscape during the peak of the last glaciation was more likely to have been what he termed a"polar desert,"with little or only sparse vegetation,in no way was it possible that this region could have supported large herds of mammals and thus,human hunters. Guthrie has argued against this view by pointing out that radiocarbon analysis of mammoth,horse,and bison bones from Beringian deposits revealed that the bones date to the period of most intense glaciation.⑥The argument seemed to be at a standstill until a number of recent studies resulted in a spectacular suite of new finds.The first was the discovery of a1,000-square-kilometer preserved patch of Beringian vegetation dating to just over17,000years ago—the peak of the last ice age.The plants were preserved under a thick ash fall from a volcanic eruption.Investigations of the plants found grasses,sedges,mosses,and many other varieties in a nearly continuous cover,as was predicted by Guthrie.But this vegetation had a thin root mat with no soil formation,demonstrating that there was little long-term stability in plant cover,a finding supporting some of the arguments of Colinvaux.A mixture of continuous but thin vegetation supporting herds of large mammals is one that seems plausible and realistic with the available data.译文洞察白令地貌①在上一次冰期的高峰，东北亚地区（西伯利亚）和阿拉斯加曾由一片广阔的陆地相连，这片土地被叫做白令陆桥。
选择性必修Unit 4 Fun with science 知识清单
三、重点句型
1. They are the estimated 39 trillion microorganisms living in and on our body, like bacteria and viruses, which compose the human microbiome!（P.44，L.2-3） 译文：据估计，它们是生活在我们体内和身体上的39万亿微生物（如细菌和病 毒）,构成了人类的微生物组！ 分析：这句话使用现在分词短语作定语；which引导非限制性定语从句。
7. nerve n.神经；（pl.）神经质，神经紧张；勇气，气魄→nervous adj.紧张的 8. isolation n.隔离，隔离状态;孤独，孤立状态→isolate v.隔离→isolated adj.孤立 的 9. inject vt.（给……）注射（药物）；（给……）添加，增加→injection n.注射 →injector n. 注射器 10. sequence vt.测定（整套基因或分子成分的）序列；按顺序排列n.一系列，一连 串；顺序，次序→sequent adj. 继续的;连续的;随着……而发生的 11. accumulate vt.积累，积聚 vi.（数量）逐渐增加→accumulation n.累积 12. humidity n.湿度；高温潮湿→humid adj.潮湿的
29. in the hope of doing sth抱着做某事的希望 30. take on呈现 31. be defined as被定义为 32. slide over the surface 滑过表面 33. experiment with用……做实验 34. determining factors决定因素 35. the limited technological knowledge有限的技术知识 36. apply sth to sth将某物应用到某物上 37. draw scientists’ attention吸引科学家的注意 38. draft laws起草法律
群的概念教学中几个有限生成群的例子
群的概念教学中几个有限生成群的例子霍丽君(重庆理工大学理学院重庆400054)摘要：群的概念是抽象代数中的最基本的概念之一，在抽象代数课程的教学环节中融入一些有趣的群例，借助于这些较为具体的群例来解释抽象的群理论，对于激发学生的学习兴趣以及锻炼学生的数学思维能力等方面都会起到一定的积极作用。
该文介绍了一种利用英文字母表在一定的规则下构造的有限生成自由群的例子，即该自由群的同音商，称为英语同音群。
此外，该文结合线性代数中的矩阵相关知识，给出了有限生成群SL2(Z )以及若于有限生成特殊射影线性群的例子。
关键词：有限生成群英语同音群一般线性群特殊射影线性群中图分类号：O151.2文献标识码：A文章编号：1672-3791(2022)03(b)-0165-04Several Examples of Finitely Generated Groups in the ConceptTeaching of GroupsHUO Lijun(School of Science,Chongqing University of Technology,Chongqing,400054China)Abstract:The concept of group is one of the most basic concepts in abstract algebra.Integrating some interesting group examples into the teaching of abstract algebra course and explaining the abstract group theory with the help of these more specific group examples will play a positive role in stimulating students'learning interest and training students'mathematical thinking ability.In this paper,we introduce an example of finitely generated free group by using the English alphabet under some certain rules,which is called homophonic quotients of free groups,or briefly called English homophonic group.In addition,combined with the theory of matrix in linear algebra,we give some examples of about finitely generated group SL_2(Z)and finitely generated special projective linear groups.Key Words:Group;Finitely generated group,English homophonic group;General linear group;Special projective linear group1引言及准备知识群是代数学中一个最基本的代数结构，群的概念已有悠久的历史，最早起源于19世纪初叶人们对代数方程的研究，它是阿贝尔、伽罗瓦等著名数学家对高次代数方程有无公式解问题进行探索的结果，有关群的理论被公认为是19世纪最杰出的数学成就之一[1-2]。
The electronic properties of graphene
155
109
©2009 The American Physical Society
110
Edited by Foxit Reader Castro Neto et al.: The elecCtroonpicyprriogphertt(ieCs )ofbgyrapFhoenxeit Software Company,2005-2008
Graphene was eventually spotted due to the subtle op-
tical effect it creates on top of a chosen SiO2 substrate ͑Novoselov et al., 2004͒ that allows its observation with
For Evaluation Only.
efit of hindsight, no experimental tools existed to search
for one-atom-thick flakes among the pencil debris cov-
ering macroscopic areas ͑Geim and MacDonald, 2007͒.
REVIEWS OF MODERN PHYSICS, VOLUME 81, JANUARY–MARCH 2009
The electronic properties of graphene
A. H. Castro Neto Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
石墨烯的表面性质及其分析测试技术
Journal of Advances in Physical Chemistry 物理化学进展, 2016, 5(2), 48-57Published Online May 2016 in Hans. /journal/japc/10.12677/japc.2016.52006Progress in Surface Propertiesand the Surface Testing of GrapheneJinfeng Dai1*, Guojian Wang1,2, Chengken Wu11School of Materials Science and Engineering, Tongji University, Shanghai2Key Laboratory of Advanced Civil Engineering Materials, Ministry of Education, ShanghaiReceived: Apr. 22nd, 2016; accepted: May 10th, 2016; published: May 13th, 2016Copyright © 2016 by authors and Hans Publishers Inc.This work is licensed under the Creative Commons Attribution International License (CC BY)./licenses/by/4.0/AbstractGraphene has been paid much attention for its special two-dimensional structure and excellent physicochemical properties. Researchers have done a great number of studies on these fields, and have made lots of outstanding results, while less on the surface properties, relatively. However, the surface properties of graphene usually play an important role in the practical application of graphene-based materials, especially, in the nano-composites, nano-coating and electrical nano- devices. In this review, the recent developments of surface properties and surface modification of graphene are summarized, where the relationship between the structure and surface properties of graphene is highlighted. The method of surface testing is also compared and commented on briefly. We believe that the future prospects of research emphasis on preparation of functiona-lized graphene with special surface properties, and a new comprehensive technique for testing the surface properties of graphene. Finally, the current challenges of research on structural surface and surface properties of graphene are commented based on our own opnion.KeywordsSurface Properties, Structural Surface, Surface Energy, Surface Testing, Graphene石墨烯的表面性质及其分析测试技术戴进峰1*，王国建1,2，吴承恳11同济大学材料科学与工程学院，上海*通讯作者。
硫-氟的邻位交叉效应
大 学 化 学Univ. Chem. 2022, 37 (7), 2110088 (1 of 5)收稿：2021-10-28；录用：2021-11-29；网络发表：2021-12-24*通讯作者，Emails:********************.cn(袁耀锋);************.cn(叶克印)基金资助：福州大学一流学科本科教学改革建设项目；中国高等教育学会2021年度理科专项课题(21LKYB07)•知识介绍• doi: 10.3866/PKU.DXHX202110088 硫-氟的邻位交叉效应李懿伦，余意，袁耀锋*，叶克印*福州大学化学学院，福州 350108摘要：乙烷分子中相邻的两个氢原子被氟取代以后，它的最优构象就从全交叉式转变为邻位交叉，这就是邻位交叉效应影响分子构象最具代表性的一个例子。
本文简要回顾了含氟邻位交叉效应的发展历史与重要应用，重点介绍了物理有机科研前沿的硫-氟邻位交叉效应。
结合当前最新的科研成果，验证了通过改变硫原子的电正性可以达到有效调控邻位交叉效应这一重要策略。
通过科研反哺教学，有助于进一步加深对硫-氟邻位交叉效应的理解和认识。
关键词：邻位交叉效应；立体电子效应；构象中图分类号：G64；O6The Sulfur-Fluorine Gauche EffectYilun Li, Yi Yu, Yaofeng Yuan *, Keyin Ye *College of Chemistry, Fuzhou University, Fuzhou 350108, China.Abstract: The most favored anti-conformation of ethane would turn into gauche-conformation when the vicinal hydrogen atoms are replaced by two fluorine atoms. Such a switch shows how the gauche effect impacts the relative conformation of organic molecules. Herein, we briefly survey the history of the gauche effect as well as its broad applications in organic synthesis. Particularly, we highlight the recent investigations on the related sulfur-fluorine gauche effect. With the aid of experiments, we confirmed that the sulfur-fluorine gauche effect could be easily regulated via the subtle change of positive charges on the sulfur atom. Such a positive interplay between scientific research and organic course teaching would profoundly help students to understand the basic concepts and advanced applications of the sulfur-fluorine gauche effect.Key Words: Gauche effect; Stereoelectronic effect; Conformation1 前言立体化学是有机化学十分重要的一个组成部分[1]。
Graphene A Wonder Material 石墨烯：一种神奇材料
Graphene: A Wonder Material 石墨烯：一种神奇材料作者：来源：《时代英语·高三》2022年第02期導读：石墨烯，一种神奇的材料，能够让有语言障碍的人“说话”，从此不再被交流困扰。
如今，中国正大力发展石墨烯在各个领域内的应用……How wonderful it would be if new technology could help the physically challenged. A smart wearable device that enables people with speaking disabilities to communicate normally is giving hope to those without a voice.Tao Luqi， a research fellow at Chongqing University， used a material called graphene to produce an artificial throat with a tiny sensor that allows people with speech impairments to speak normally， according to a paper published in Nature Communications. Tao has continued his work on the device for the last few years.Although it’s a tiny mechanical sensor， it can work wonders. The device can detect weak vibrations and can produce sounds across a wide spectrum， from 100 Hz to 40 kHz， China Daily reported. Humans can detect sounds in a frequency range from 20 Hz to 20 kHz.如果新技术能帮助残障人士该有多好。
详细 介绍石墨烯英文版
Notes Best electrical conductor of any known metal
59.6 × 106
Commonly used in electrical wire applications due to very good conductivity and price compared to silver.
Introduction
Properties of graphene
Mechanical properties
- High Young’s modulus (~1,100 Gpa) High fracture strength (125 Gpa)
- Graphene is as the strongest material
Content
Introduction to graphene. Preparation and characterization graphene Potential application of graphene Conclusions
Introduction to graphene
Graphene is a one-atom-thick planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice The name ‘graphene’ comes from graphite + -ene = graphene
Molecular structure of graphene
High resolution transmission electron microscope images (TEM) of graphene
柱状图英语作文范文
柱状图英语作文范文Title: Exploring the Significance of Bar Graphs in Data Representation。
Introduction:Bar graphs, also known as bar charts, serve as fundamental tools in data representation and analysis across various fields. From depicting sales figures to showcasing population trends, bar graphs offer a visually appealing and accessible means of conveying information. This essay delves into the significance of bar graphs, highlighting their utility and versatility in effectively communicating data.Understanding Bar Graphs:At its core, a bar graph comprises a series of rectangular bars of varying lengths, each representing different categories or variables. The length of each barcorresponds to the magnitude of the data it represents, making it easy to compare values visually. Typically, the horizontal axis denotes categories or time intervals, while the vertical axis signifies the corresponding numerical values.Importance of Bar Graphs:1. Visual Clarity:One of the primary advantages of bar graphs lies in their ability to present data in a visually clear and concise manner. The distinct bars allow viewers to quickly grasp relative differences between categories or variables without the need for complex numerical analysis.2. Comparison of Data:Bar graphs facilitate straightforward comparisons between multiple sets of data. Whether contrasting sales figures between different quarters or comparing demographic statistics across regions, the visual layout of bar graphsenables easy identification of trends and patterns.3. Trend Analysis:By plotting data over time intervals, bar graphs enable analysts to identify trends and patterns effectively. Whether tracking fluctuations in stock prices or monitoring changes in temperature over seasons, bar graphs offer valuable insights into the underlying dynamics of a phenomenon.4. Audience Accessibility:Bar graphs are inherently accessible to a wide range of audiences, including those with limited statistical literacy. Their intuitive design allows viewers tointerpret data effortlessly, making them valuable tools for presentations, reports, and educational materials.5. Flexibility:Bar graphs can accommodate various types of data,including categorical, ordinal, and interval data. Additionally, they can be customized with different colors, patterns, and labels to enhance clarity and highlight key insights.Example Applications:1. Sales Analysis:In a retail setting, bar graphs can be used to analyze sales performance across different product categories or store locations. By visualizing revenue data over time, managers can identify trends, prioritize inventory, and make informed decisions to optimize profitability.2. Academic Performance:Educators often use bar graphs to track students' academic progress over time. By plotting grades or test scores across subjects or semesters, teachers can identify areas for improvement, tailor instructional strategies, and provide targeted support to individual students.3. Market Research:Market researchers utilize bar graphs to present findings from consumer surveys, product evaluations, and demographic analyses. By visualizing preferences, purchasing behaviors, and market trends, businesses can develop targeted marketing strategies and launch successful products.Conclusion:In conclusion, bar graphs play a crucial role in data representation, offering a visually compelling and accessible means of conveying information. Fromfacilitating comparisons and trend analysis to enhancing audience accessibility, bar graphs are indispensable tools across various fields. By harnessing the power of bar graphs, researchers, analysts, and decision-makers can gain valuable insights and make informed choices in an increasingly data-driven world.。
无机化学碳族元素
第12页/共64页
碳 硅 锗锡铅
相似性
锗分族
课本p726
第13页/共64页
1. 基本性质
C Si Ge Sn Pb
价电子构型：
ns2np2
主要氧化态稳定性： +2 小
大
+4 大
小
原子半径：
小
大
I1 EA1 / kJ·mol-1 X (Pauling)
问题：设计一个实验证明CO中有CO2 ?
气体通入澄清的石灰水，若出现白色沉淀，后又澄清，即证实有CO2 CO2 + Ca(OH)2 = CaCO3 + H2O CaCO3+ H2O+CO2＝ Ca(HCO3)2
第23页/共64页
③CO与其它非金属的作用：
CO＋2HC2r=2O=3·=Zn=O=，=6=23=－=67=3=K======= CH3OH
干燥剂、催化剂载体，色谱柱填料
第8页/共64页
Asbestos(石棉) Consist of long chains based on SiO4 tetrahedra.
镁硅酸盐，纤维素矿物质形式，不燃、抗化 学变化，用作防火，电绝缘，建筑材料。
The aluminosilicate mica (云母)
SiH4＝Si (纯) ＋2H2（△）
第34页/共64页
二、硅烷
1、性质：
SiH4＋2O2
燃烧 =======
SiO2＋2H2O
SiH4＋2KMnO4 ==== 2MnO2↓＋K2SiO3＋H2 ↑＋H2O
此反应可以检测硅烷的存在
第35页/共64页
2024北京怀柔高二(上)期末英语(教师版)
2024北京怀柔高二（上）期末英语注意事项：1.考生要认真填写姓名和考号。
2.本试卷共11页，分为三部分。
考试时间90分钟，满分100分。
3.试题所有答案必须填涂或书写在答题卡的对应位置．．．．．．．．。
选择题必须用2B ．．．．．．．．．．．．．．．．．．．．．．，在试卷上作答无效铅笔作答；书面表达部分必须用黑色字迹的签字笔作答。
4.考试结束后，考生应将试卷和答题卡放在桌面上，待监考员收回。
第一部分：知识运用（共两节，30分）第一节完形填空（共10小题；每小题1.5分，共15分）阅读下面短文，掌握其大意，然后从各题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
The story of Jennifer Bricker is one of the most amazing story, which is full of both great surprises and life lessons.Jennifer was born in Romania without any legs. She was later ____1____ by a loving American family, the Brickers, and raised in the small town of Hardinville, Illinois.The Brickers never let this ____2____ stop her from achieving her dreams. Her new parents gave her a simple rule, “Never say can’t”! They did whatever they could to make her life a success.The girl was ____3____ just like the Brickers’ own children. She was encouraged to play with the other normal boys and girls and became good at many ____4____, including volleyball, softball and basketball.But it was tumbling (翻腾运动) that was her true love. When she was a little girl, she was a big ____5____ of the Olympic gold medalist--- Dominque Moceanu. She would copy her on TV whenever Dominque Moceanu ____6____in the tumbling programs and continue practicing afterwards.As she grew older Jennifer began ____7____ against professional tumbling athletes around Illinois. Not only did she compete, but she even went on to become a State Champion! Jennifer and her family always believed she could do whatever she wanted to and that her positive attitude and hard work would make it another ____8____.If her story was not amazing enough already, when Jennifer turned 16, she got the most ____9____ news in her life. She learned that her beloved Dominque Moceanu was actually her biological sister! Now Jennifer is touring the country as a(n)_____10_____ speaker to encourage more disabled youngsters.1. A. adopted B. injured C. sold D. seen2. A. disability B. gift C. excuse D. failure3. A. signed up B. brought up C. put up D. kept up4. A. roles B. instruments C. sports D. tricks5. A. audience B. athlete C. member D. fan6. A. performed B. appeared C. hosted D. challenged7. A. competing B. fighting C. acting D. going8. A. pity B. topic C. challenge D. success9. A. disturbing B. popular C. unbelievable D. reliable10. A. fluent B. loud C. silent D. inspiring第二节（共10小题；每小题1.5分，共15分）阅读下列短文，根据短文内容填空。
雅思英语作文典型范文graphs
雅思英语作文典型范文The graphs comprehensively display the full recycling procedure of plastic bottles.Initially, plastic bottles are thrown into recycle bins, and the garbage truck will collect and transport the bins to a solid waste treatment center on a regular basis. Inside the recycle center, workers are responsible for separating the bottles from other wastes.After sorting, the bottles will be squeezed into cube-shaped blocks, then the powerful crusher machines will crush the cubes, turning them into tiny pieces. Once the bottles are broken into small parts, there will be a cleansing process to wash the dust off them. Subsequently, those cleaned parts will undergo another aggressive breaking process and will be torn into even smaller pieces by a more effective machine.Finally, the last step involves heating, which transform the plastic pellets to qualified raw materials available for industrial production. For example, commodities such as bottles, containers, clothes and luggage can be manufactured fromthose raw materials. When those products are thrown into the trash bin by consumers, a new recycling process begins.In short, plastic bottles are collected, sorted, broken down and made into new products.In the future, nobody will buy printed newspapers or books because they will be able to read everything they want online without buying. To what extent do you agree or disagree with this statement?As the popularity of electronic devices such as smart phones and iPad grows, more and more people switch their reading habits from reading printed books to reading online. Some believe that paper books will eventually vanish from the market because reading online is free and more convenient, while others state that legislation on copyright will be better enforced to prevent such situation. I believe that the advance of technology is inevitable, and more people will adopt online reading.First of all, the average book price ranges from 15 - 50 dollars before tax, which means that a considerable amount of money will be spent on purchasing books by readers. This will be anunfavourable financial burden on reading lovers, especially among young people who are at their golden age of learning. Given the realistic financial situation, more people prefer to search online, where ample and diverse reading materials are available. Most reading applications on iPad are not only free, but also very user friendly. Indeed, some applications demand a charge, but more and more companies are removing the charges to drive more traffic to their websites, which has been proved to be an effective business strategy.Additionally, internet provides a much wider range of choices than brick-and-mortar stores, for the reason that almost every book with a paper version are digitized and commercialized in modern society. What is more, searching for a electronic book is much more convenient as well as efficient than going to a physical bookstore or placing an online order for a printed book from online platforms such as Amazon.However, concerns on copyrights are claimed by many. The opposing voices state that authors’income are jeopardized due to reduced sales volume and that many online resources lack proper legal copyright. While statement is true, the issue can be resolved by the corresponding government authority who canenforce the copyright law on the firms running the online reading platforms. For example, firms must buy copyrights from the authors beforehand, otherwise they will be penalized with a fine. Argument involving readers’eyesight also remains popular, nevertheless, I believe that technology innovation oneye-friendly monitors like LCD (liquid crystal display) will gradually cease such debate.To sum up, the fact that online reading material being endorsed by a growing number of readers is an inevitable social trend. Although some concerns on copyright as well as public eyesight exist, they will be resolved by improved government regulation and advanced technology. Besides, the companies can use advertising as their primary income stream just like how Google profit, so they do not necessarily charge their clients directly. Eventually, reader will have free access to every book online, whereas paper books will vanish.The chart illustrates the number of tourists travelling to a particular island in Caribbean from 2010 to 2017. It also compares the number of visitors staying on cruise ships and thaton island, which are the two groups constituting the total number of tourists.To start with, there was a clear upward trend throughout the 7 years. In 2010, only a quarter of a million visitors stayed on cruise ships and 0.75 million visitors stayed on island, adding up to 1 million, whereas in 2017, those figures rose to 2 million and 1.5 million respectively, which total up to 3.5 million.During the year from 2010 to 2011, unlike the number of visitors staying on island which remained constant, the number of visitors staying on ships doubled and total number increased to 1.25 million. Following that, the amount of visitors staying on island experienced a dramatic increase and grew from 0.75 to 1.25 million by 2012. During the same period, the figure of visitors staying on cruise ships falls by 50% (0.25 million).The next year, which is 2013, the numbers of both groups moved up by 0.25 million and aggregated to 2 million in total. After that, the number of visitors staying on island remained unchanged for 3 consecutive years in a row, then dropped to 1.25 million in 2016, and rose back to the previous level in the final year. On the contrary, the figure of the other group increased consistently, which totaled 1, 1.25, 1.5 and 2 in the following 4 years.Overall, the graph shows more visitors went to the island during the given period. Additionally, more visitors stayed on island until mid-2015, where number of visitors staying on cruise ships surpassed the number of the other party for the first time.。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Simulation of Graphene Electronic Devices
by
Yudong Wu
A thesis submitted to the University of Birmingham for the degree of Doctor of Philosophy School of Electronic, Electrical and Computer Engineering The University of Birmingham
3
Table of Contents
Chapter 1 1.1 1.2 1.3 1.4 1.5 1.6 Chapter 2 2.1 2.2
Introduction .............................................................................................................................. 7 Significance of Graphene .............................................................................................................. 7 Energy Bandstructure of Graphene .............................................................................................. 9 Graphene Nanoribbons................................................................................................................. 9 Graphene Based Electronics Devices .......................................................................................... 10 Levels of Device Simulation ........................................................................................................ 11 Thesis outline .............................................................................................................................. 12 Bandstructure of Graphene and Graphene Nanoribbons ...................................................... 13 The Secular Equation .................................................................................................................. 13 Analytical solution of the Secular Equation for Graphene ......................................................... 15 Nearest neighbour approximation...................................................................................... 16 Third nearest neighbour approximation ............................................................................. 18 Results ................................................................................................................................. 20
Supervisor Dr. P.A Childs
University of Birmingham Research Archive
e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
2.2.1 2.2.2 2.2.3 2.3
Numerical solution for the bandstructure of Graphene nanoribbons....................................... 21 Armchair nanoribbons ........................................................................................................ 21 Energy band gap of armchair graphene nanoribbons ........................................................ 24 Zigzag nanoribbons ............................................................................................................. 26 Quasi one-dimensional model ............................................................................................ 29