Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions

TL;DR

This paper uses conformal field theory techniques to analyze the Landauer conductance of Dirac fermions in two dimensions, with applications to graphene and disordered systems, revealing new insights into transmission eigenvalues and conductivity behavior.

Contribution

It introduces a novel approach linking generating functions to conformal field theory for analyzing Dirac fermions' conductance and explores disorder effects on conductivity.

Findings

Relation of transmission eigenvalue density to conformal field theory partition functions

Scaling behavior of ac Kubo conductivity and its dc limits

Disorder-averaged Einstein conductivity is analytic with zero first-order correction

Abstract

We apply the generating function technique developed by Nazarov to the computation of the density of transmission eigenvalues for a two-dimensional free massless Dirac fermion, which, e.g., underlies theoretical descriptions of graphene. By modeling ideal leads attached to the sample as a conformal invariant boundary condition, we relate the generating function for the density of transmission eigenvalues to the twisted chiral partition functions of fermionic ($c=1$) and bosonic ($c=-1$) conformal field theories. We also discuss the scaling behavior of the ac Kubo conductivity and compare its \textit{different} $dc$ limits with results obtained from the Landauer conductance. Finally, we show that the disorder averaged Einstein conductivity is an analytic function of the disorder strength, with vanishing first-order correction, for a tight-binding model on the honeycomb lattice with weak real-valued and nearest-neighbor random hopping.