Transport properties of multilayer graphene
Abstract:
We apply the semi-classical Boltzmann formalism for the computation of transport properties to multilayer graphene. We compute the electrical conductivity as well as the thermal conductivity and thermopower for Bernal-stacked multilayers with an even number of layers. We show that the window for hydrodynamic transport in multilayer graphene is similar to the case of bilayer graphene. We introduce a simple hydrodynamic model which we dub the multi-fluid model and which can be used to reproduce the results for the electrical conductivity and thermopower from the semi-classical Boltzmann equation.Partial equilibration of the anti-Pfaffian edge due to Majorana Disorder
Abstract:
We consider electrical and thermal equilibration of the edge modes of the Anti-Pfaffian quantum Hall state at ν = 5/2 due to tunneling of the Majorana edge mode to trapped Majorana zero modes in the bulk. Such tunneling breaks translational invariance and allows scattering between Majorana and other edge modes in such a way that there is a parametric difference between the length scales for equilibration of charge and heat transport between integer and Bose mode on the one hand, and for thermal equilibration of the Majorana edge mode on the other hand. We discuss a parameter regime in which this mechanism could explain the recent observation of quantized heat transport [Banerjee et all, Nature 559, 7713 (2018)].Energetics of Pfaffian–anti-Pfaffian domains
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.Quantum Boltzmann equation for bilayer graphene
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.