Konstantin Efetov started by drawing parallels between high-T_cs (which

dominated earlier discussion) and graphene. He emphasized that both are 2D

systems which have been lauded as materials of the future for energy and

nanoelecronics respectively. Konstantin reminded the audience that grapehene

has 2D honeycomb crystal lattice, and therefore contains two sublattices. The

Brillouin Zone has two valleys with linear, Dirac-like, energy dispersion, so

that the effective hamiltonian for pure graphene is a 4x4 block-diagonal

matrix. Gating the substrate with graphene film on top allows changing the

filling fraction easily.

Konstantin then described the effects of impurity scattering on transport in a

system with such an energy spectrum following his recent work with Igor

Aleiner [PRL 97, 236801 (2006)]. The work was motivated by experimental claims

of delocalized low energy states and universal metallic resistivity in

graphene (which, it seems, is no longer universal), and theoretical analyses

of weak localization corrections.

Efetov and Aleiner considered general purely potential impurity scattering

(spin-orbit interaction is graphene is weak), which replaces zeros in the

block-diagonal Hamiltonian with finite values. Symmetries of the problem

(time-reversal, translation, etc.) dictate that there are 5 independent

parameters that characterize disorder. Konstantin pointed out that the

self-consistent Born approximation does not work for Dirac spectrum as there

are many logarithmic corrections that need to be resummed using the RG

methods. The main conclusion is that all 5 impurity constants grow under RG flow.

The work considers a finite filling fraction and proceeds by looking at the

free energy functional using the

supersymmetry approach. The main conclusions are that, if one neglects the

scattering between bands, the system maps onto a symplectic ensemble,

resulting in antilocalization: increase in conductivity upon lowering the

temperature. However, upon lowering the temperature, intervalley scattering

becomes important, and one finds an orthogonal ensemble for which all states

are known to be localized.

The prediction is for a non-monotonous behavior of the conductivity with

temperature. As T is decreased, first the conductivity is reduced in accord

with the log corrections. At lower T antilocalization kicks in and the

conductivity increases when the temperature is lowered. At yet lower T, the

intervalley scattering takes over, and the conductivity drops to zero as the

states become localized. Konstantin concluded by saying that there is no

chance for minimal metallic conductivity due to generic disorder.

Assa Auerbach asked whether this behavior had been found numerically since

this is a non-interacting theory that lends itself easily to modeling.

Konstantin replied that exploring the phase space of 5 parameters is hard, and

that the localization length is expected to be large.

Claudio Castellani and Andrey Chubukov both asked what happens when graphene

is tuned very close to the Dirac point, i.e. filling fraction is small. The

system is right away in the strong disorder limit, but Konstantin believes the

conductivity still goes to zero at T=0 since the states are almost localized

already.

John Mydosh asked what are the potential impurities, and apparently these are

mostly charged impurities on the substrate.

Victor Galitskii asked what determines the crossover scale between

antilocalization and localization. There is no unique answer, this is related

to how different components of the impurity scattering vary with T.

Catherine Pepin asked whether interaction correction have been considered and

what they do. There seems to be some work done on that, but lunch truck was

about to arrive, and we stopped.

## Wednesday, August 22, 2007

### Konstantin Efetov: Transport in Graphene

Posted by Ilya Vekhter at 6:28 PM

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## 6 comments:

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