Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations

Abstract

This work focuses on the non-dissipative, parity-odd spin transport of $(2+1)$-dimensional relativistic electrons, generated by torsion, and the torsional Hall viscosity ${\zeta }_{\mathrm{H}}$. We first determine ${\zeta }_{\mathrm{H}}$ for massive Dirac fermions in the presence of a constant electromagnetic field. We predict that the magnetic field induces a contribution to ${\zeta }_{\mathrm{H}}$ competing with the one originating from the Dirac mass. Moreover, we quantify the impact on ${\zeta }_{\mathrm{H}}$ originating from the band structure deformation quadratic in momentum terms that was proposed by Bernevig-Hughes-Zhang (BHZ). We find that the BHZ deformation substantially enhances ${\zeta }_{\mathrm{H}}$ in magnitude as measured in a domain wall configuration, when compared to the free Dirac fermion result. Nevertheless, the torsional Hall viscosity still discriminates between topologically trivial and non-trivial regimes. Our results, hence, pave the way for a deeper understanding of hydrodynamic spin transport and its possible verification in experiments.

15+7pages, 5 figures; v3: typos fixed; corrected a normalization error in Eq. (70); the corresponding numerical value in the main result updated

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