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