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Graphene as a new page in Solid State Physics
L.A. FalkovskyLandau Institute for Theoretical Physics Institute of High Pressure Physics
Graphene sample in the Hall conductivity experiment
Novoselov et al (2005)
GraphiteWallace, PR 71, 622 (1947)McClure, PR 108, 612 (1957)Slonczewski, Weiss, PR 109 (1958)
NanotubesSaito, Fujita, Dresselhaus, Dresselhaus, PRB 46, 1804 (1992)
2221 v yx pp ,
two-dimensional massless Dirac fermions
scm /810v
K
K’
graphene doped
Novoselov et al (2005)Field-effect
2) universal minimal conductivity
22emin
1) conductivity proportional to the carrier density
3) universal optical conductivity
4)(
2eopt
2
k=p±p±
Time and space dispersion of conductivity Falkovsky and Varlamov (2006)
g 2 2
T,kv,ω<<τ
10
optical conductivity
T
0T
interband
intraband
T
Falkovsky and Pershoguba (2007)
Gusynin and Sharapov (2007)
optical transmittance of graphene
z
x
r
t
Novoselov et al. (2008)
graphene conductance
D. Basov et al (2008)
x
y
X<0
U=0X<0
X>0
X>0
Klein’s paradox
U
x
(2009)
Bilayer graphene
field effect
bilayerMcCann, Fal’ko (2006-2007)
Novoselov et alOhta et alLi et alKuzmenko et alMak et al
2U
E=2U/d
d2
d2
electron dispersion
Mounet PRB (2005)
Graphite phonon modes