Quantum Boltzmann equation for bilayer graphene

Dung X. Nguyen, Glenn Wagner, Steven H. Simon

Published 2019-01-21Version 1

Bilayer graphene has massive electron and hole-like excitations with zero gap in the nearest-neighbor hopping model. At low energies in the semi-classical description, these excitations can be considered as quasiparticles with Fermi-Dirac statistics. In this paper, we present a semi-classical formalism for calculating the DC quantum transport coefficients of bilayer graphene (BLG) near charge neutrality in the non-Fermi liquid regime. We derive the explicit form of conserved current operators in terms of electron and hole fields. Starting from the Kadanoff-Baym equations, we obtain the quantum Boltzmann equation of the electron and hole distribution functions in a perturbed background. The effect of disorder and finite system size are incorporated through the generalized collision integral. The quantum transport coefficients including the electrical and thermal conductivity, the thermopower, as well as the shear viscosity are calculated in the linear response regime. We also extend the formalism to include an external magnetic field in the case of the thermoelectric transport coefficients.