Berry curvature and Hall viscosities in an anisotropic Dirac semimetal

We investigate parity-odd nondissipative transport in an anisotropic Dirac semimetal in two spatial dimensions. The analysis is relevant for interacting electronic systems with merging Dirac points at charge neutrality. For such systems the dispersion relation is relativistic in one direction and nonrelativistic in the other. We give a proposal of how to calculate the Berry curvature for this system and use it to derive more than one odd viscosities, in contrast to rotationally invariant systems. We observe that in such a model the odd part of viscosity tensor is parametrized by two independent transport coefficients and one that is identically zero.