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

S. Ryu·C. Mudry·A. Furusaki·A. W. W. Ludwig
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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.

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S. Ryu, C. Mudry, A. Furusaki, A. W. W. Ludwig. 2007-05-31. Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions. https://doi.org/10.1103/physrevb.75.205344

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