# Quantum Boltzmann equation for bilayer graphene

## TL;DR

This paper derives a quantum Boltzmann equation for bilayer graphene near charge neutrality, incorporating various scattering effects, and computes transport coefficients, providing a comprehensive framework for understanding its non-equilibrium transport properties.

## Contribution

It develops a quantum Boltzmann formalism for bilayer graphene including phonons, disorder, and magnetic fields, and introduces a simplified hydrodynamic model for this system.

## Key findings

- Calculated electrical and thermal conductivities near charge neutrality.
- Extended formalism to include magnetic field effects.
- Derived a hydrodynamic model matching numerical solutions.

## 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.