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. Here we address this question, both analytically and numerically, in the context of a disordered noninteracting 2D electrons. 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 (Shubnikov-de Haas type) oscillations of the dissipative and Hall viscosity. For strong magnetic fields we characterize the effects of the disorder-induced broadening of the Landau levels on the viscosity coefficients. This is supplemented by numerical calculations for a few filled Landau levels. Our results show that the Hall viscosity is surprisingly robust to disorder.Introduction. -Ordinary fluid motion is described by the theory of hydrodynamics, one of whose cornerstones is viscosity, which serves as the source of dissipation. Under certain conditions, charge transport in an electronic system can also be dominated by hydrodynamic viscous flow [1,2]. The discovery of graphene stimulated renewed theoretical [3][4][5][6][7][8][9][10][11] and experimental [12][13][14][15][16][17][18] interest in the hydrodynamic description of charge conduction.In the absence of time-reversal symmetry the viscosity tensor has non-dissipative antisymmetric components. In the presence of a magnetic field B, this nondissipative Hall viscosity (η H ) was studied theoretically in the classical limit of high temperature plasmas [19][20][21][22][23], and for low temperature electron gas [24]. Later, interest in the Hall viscosity was rekindled in quantum systems with a gapped spectrum, due to the connection between η H and geometric response [25][26][27][28][29][30][31], and its expected quantization in the presence of translational and rotational symmetries [29]. It was understood that beyond the Hall conductivity and viscosity there are additional non-dissipative electro-magnetic and geometrical response functions in gapped quantum systems [32][33][34][35][36][37][38][39][40][41][42][43][44]. Within the hydrodynamic description of electron transport, non-zero η H influences significantly the structure of the electron flow [45][46][47][48][49][50], which allows one to access η H experimentally [51]. Also, it was argued that the dissipative and Hall viscosity affect the spectrum of edge magnetoplasmons [52][53][54].For noninteracting electrons in the absence of disorder each filled Landau level (LL) gives a contribution to the Hall viscosity equal (2n + 1)/(8πl 2 B ) [25], where n denotes the LL index and l B = c/(eB) ...
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