Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2006-10-23
Phys. Rev. B 75, 205344 (2007)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
13 pages, 2 figures
Scientific paper
10.1103/PhysRevB.75.205344
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.
Furusaki Akira
Ludwig Andreas W. W.
Mudry Christopher
Ryu Seungoh
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