石墨烯_神奇的碳原子_英国曼彻斯特大学 Graphene magic of flat carbon

Graphene: Magic of Flat Carbon
Andre Geim
Nature Hates Low Dimensions
“island growth” clustering of thin films
1D & 2D precursors rapidly morph into various 3D shapes
growth of low-dimensional crystals is strictly forbidden
Peierls; Landau; Mermin-Wagner; …

Can We Cheat Nature?
epitaxial growth
overlooked before
monolayer is a part of the 3D crystal
remove substrate
does NOT contradict to theory:
removal at low temperatures; finite size crystals
Can We Cheat Nature?
ANY LAYERED MATERIAL
SLICE DOWN TO ONE ATOMIC PLANE?

Can We Cheat Nature?
O.1 mm
graphite trace on oxidized Si wafer
⋅ 1 μm
first 2D material demonstrated - Manchester, Science ‘04
Geim&Kim Sci Am 2008
Current State of the Art
zigzag
crystal faces
10 μm
armchair
graphene 2D crystallites

Current State of the Art
100 µm
one-atom-thick single-crystal membranes
direct visualization in SuperSTEM
MOTHER OF ALL GRAPHITES
true low dimensional crystal
all previously known materials were three dimensional

Conceptually New Class of Materials
2D boron nitride in AFM
0Å 9Å 16Å 23Å
2D NbSe2 in AFM
0Å 8Å
23Å
1μm
0.5μm
1μm
also,
2,3,4… layers
1 μm
2D Bi2Sr2CaCu2Ox in SEM
1 μm
2D MoS2 in optics
Manchester, PNAS ’05
WHAT‘S SO SPECIAL ABOUT GRAPHENE?

MAGICAL QUALITY
electronic quality
SiO2
carrier mobility currently: up to 15,000 cm2/V·s at 300K up to 200,000 cm2/V·s at 4K
even when strongly doped
Si
graphene intrinsic (phonon-limited):
>200,000 cm2/V·s at 300K
6
(higher than in any other material)
ρ (kΩ)
4
2
0-100 -50 0
50 100
Vg (V)
ballistic transport on submicron scale under ambient conditions
crystal quality: few defects (~1 per μm2)
Single-Molecule Detection
δR (Ω)
number of steps
NO2 exposure
adsorption
30
1e
20 desorption
1e
10
300K
0
0
200
400
600
t (s)
step-like changes near zero concentration
Manchester, Nature Mat ’07
600
annealed
400
200
0
600 desorption
+1e
400
adsorption -1e
200
0
-4 -2 0
2
4
δR (Ω)
GRAPHENE IS EXTREMELY ELECTRONICALLY QUIET: FEW UNSTABLE DEFECTS

Exceptional Electronic Structure
mass of charge carriers strongly depends on concentration
E=pvF
0.06
0.04
S
ky
mc/m0
0.02
kx
0
-6 -3 0
3
6
n (1012 cm-2)
BF =(ħ/2πe)S and mc =(ħ2/2π)∂S/∂E
experimental dependences BF ~ n and mc ~ n1/2
necessitates S ~ E(k)2 or E ~k
effective mass
E = mcvF2
(ZERO REST MASS) vF = 106 m/s ±5%
Exceptional Electronic Structure
B
A
Dirac-like equation:
Hˆ
=
vF
⎜⎜⎝⎛ pˆx
0 − ipˆy
pˆ x
+ ipˆy 0
⎟⎟⎠⎞
=
v F σr
⋅
pr
McClure 1956; Semenoff 1984