Steve Simon

Abstract:

In several recent works it has been proposed that, due to disorder, the experimentally observed ν = 5/2 quantum Hall state could be microscopically composed of domains of Pfaffian order along with domains of anti-Pfaffian order. We numerically examine the energetics required for forming such domains and conclude that for the parameters appropriate for recent experiments, such domains would not occur.

Abstract:

AB-stacked bilayer graphene has massive electron and holelike excitations with zero gap in the nearestneighbor 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 β|μ| 1 (with β the inverse temperature and μ 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 effects 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.