Hall and dissipative viscosity and conductivity in a disordered 2D electron gas

Hydrodynamic charge transport is at the center of recent research efforts. Of particular interest is the nondissipative Hall viscosity, which conveys topological information in clean gapped systems. The prevalence of disorder in the real world calls for a study of its effect on viscosity, as well as on its relation with the nonlocal conductivity, the main venue to its experimental measurement. Here we address this question for disordered noninteracting 2D electrons. Analytically, we employ the self-consistent Born approximation, accounting for the modification of the single-particle density of states and the elastic transport time by the Landau quantization. Our results interpolate smoothly between the limiting cases of weak (strong) magnetic field and strong (weak) disorder. In the regime of weak magnetic field we describe the quantum (Shubnikov-de Haas type) oscillations of the viscosity, nonlocal conductivity, and Wen-Zee response. For strong magnetic fields we characterize the effects of the disorder-induced broadening of the Landau levels on the transport coefficients. This is supplemented by numerical calculations for a few filled Landau levels. Our results show that the Hall viscosity and its relation with conductivity are surprisingly robust to disorder.