Quantum Boltzmann equation for bilayer graphene

Abstract

A-B stacked bilayer graphene has massive electron and hole-like excitations with zero gap in the nearest-neighbor hopping approximation. In equilibrium, the quasiparticle occupation approximately follows the usual Fermi-Dirac distribution. In this paper we consider perturbing this equilibrium distribution so as to determine DC transport coefficients near charge neutrality. We consider the regime $\beta |\mu |\lesssim 1$ (with $\beta$ the inverse temperature and $\mu$ the chemical potential) where there is not a well formed Fermi surface. Starting from the Kadanoff-Baym equations, we obtain the quantum Boltzmann equation of the electron and hole distribution functions when the system is weakly perturbed out of equilibrium. The effect of phonons, disorder, and boundary scattering for finite sized systems are incorporated through a generalized collision integral. The transport coefficients, including the electrical and thermal conductivity, thermopower, and shear viscosity, are calculated in the linear response regime. We also extend the formalism to include an external magnetic field. We present results from numerical solutions of the quantum Boltzmann equation. Finally, we derive a simplified two-fluid hydrodynamic model appropriate for this system, which reproduces the salient results of the full numerical calculations.

arXiv comment27 pages, 7 figures, fixed typos, add a section on a two-fluid model

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• Dissipation-enabled hydrodynamic conductivity in a tunable bandgap semiconductor
• Transport in bilayer graphene near charge neutrality: Which scattering mechanisms are important?
• Transport properties of multilayer graphene
• Coulomb drag of viscous electron fluids: drag viscosity and negative drag conductivity
• Thermoelectric properties in semimetals with inelastic electron-hole scattering
• Die Hard Holographic Phenomenology of Cuprates
• Observability of cyclotron resonance in the hydrodynamic regime of bilayer graphene
• Time-reversal odd transport in bilayer graphene: Hall conductivity and Hall viscosity