# Dissipative and Hall viscosity of a disordered 2D electron gas

## TL;DR

This paper investigates how disorder affects the dissipative and Hall viscosities in a 2D electron gas under magnetic fields, revealing robustness of Hall viscosity against disorder through analytical and numerical methods.

## Contribution

It provides a combined analytical and numerical analysis of viscosity in disordered 2D electron gases, highlighting the robustness of Hall viscosity to disorder effects.

## Key findings

- Hall viscosity remains robust despite disorder broadening.
- Quantum oscillations of viscosities are described in weak magnetic fields.
- Disorder effects are weak on Hall viscosity in strong magnetic fields.

## Abstract

We study the dissipative and Hall viscosity of a disordered noninteracting 2D electrons, both analytically and numerically. Analytically, we employ the self-consistent Born approximation, explicitly taking into account the modification of the single-particle density of states and the elastic transport time due to the Landau quantization. The reported results interpolate smoothly between the limiting cases of weak (strong) magnetic field and strong (weak) disorder. In the regime of weak magnetic field, our results describes the quantum (de Haas-van Alphen type) oscillations of the dissipative and Hall viscosity. For strong magnetic field, we computed the dependence of the dissipative and Hall viscosity on disorder broadening of a Landau level. In particular, for the Hall viscosity the effect of the disorder broadening is weak. This theoretical conclusion is in agreement with our numerical results for a few lowest Landau levels, which show that Hall viscosity is robust to disorder.