石墨烯介绍

Quantum Hall Effect
Y. Zhang et al, Nature 438, 201(2005)
Optical Studies of Graphene
Optical microscopy contrast; Raman spectroscopy; Landau level spectroscopy.
20 m
Monolayer
Bilayer
K. S. Novoselov et al., Science 306, 666 (2004).
Raman Spectroscopy of Graphene
(Allowing ID of monolayer and bilayer)
A.S.Ferrari, et al, PRL 97, 187401 (2006)
-dR/R (RA-RB)/RA versus w
dR/R = -Re[h(w)s(w)]
h(w) from substrate
s(w) from graphene: interband transitons
Re s(w)/w: Absorption spectrum
free carrier absorption
Differential reflection spectroscopy: Difference between bare substrate and graphene on substrate
20 m
A
B
RA: bare substrate reflectivity RB: substrate + graphene reflectivity
Ep 1 4 cos2( 3kxa / 2) 4 cos( 3kxa / 2) cos(3kya / 2)
Ep vF k '
near K points
P.R.Wallace, Phys.Rev.71,622-634(1947)
Band Structure of Monolayer Graphere
Reflection Spectroscopy on Graphene
Experimental Arrangement
Det
OPA
Gold
Graphene
Doped Si
290-nm Silica
Infrared Reflection Spectroscopy to Deduce Absorption Spectrum
Crystalline Structure of Graphite
Graphene
2D Hexagonal lattice
Band Structure of Graphene Monolayer
r H Hat Hint (k )
Tight-binding calculation on bands:
Direct Observation of a Widely Tunable Bandgap in Bilayer Graphene Yuanbo Zhang, Tsung-Ta Tang, Caglar Girit1, Zhao Hao, Michael C. Martin, Alex Zettl1, Michael F. Crommie, Y. Ron Shen and Feng Wang (2009)
r
H
u1 u2
Ep, r
f *(k
),
f (k Ep
)
u1 u2
f
r (k )
[1
er ik
ar1
er ik
ar 2
]
r
r
E (k ) Ep | f (k ) |
rr
rr
rr r
Ep 3 2 cos k a1 2 cos k a2 2 cos k (a2 a1)
Optics on Graphene
Gate-Variable Optical Transitions in Graphene Feng Wang, Yuanbo Zhang, Chuanshan Tian, Caglar Girit, Alex Zettl, Michael Crommie, and Y. Ron Shen, Science 320, 206 (2008).
Mechanically: Large Young’s modulus.
Thermally: High thermal conductance.
Exotic Behaviors
Quantum Hall effect, Barry Phase Ballistic transport, Klein paradox Others
Graphene
(A Monolayer of Graphite)
2D Hexagonal lattice
Properties of Graphene
Electrically: High mobility at room temperature, Large current carrying capability
Other Possibilites
• Spectroscopic probe of electronic structure. • Interlayer coupling effect. • Electrical gating effect on optical transitions. • Others
Monolayer
Bilayer
K
x K
Baidu Nhomakorabea
x
Vertical optical transition
Van Hove Singularity
EF is adjustable
Exfoliated Graphene Monolayers and Bilayers
Reflecting microscope images.
Electron Bands of Graphene Monolayer
Band Structure in Extended BZ
Band Structure near K Points
~10 eV
Relativistic Dirac fermion.
Band Structures of Graphene Monolayer and Bilayer near K