Cubic Hall viscosity in three-dimensional topological semimetals

Abstract

The nondissipative (Hall) viscosity is known to play an interesting role in two-dimensional (2D) topological states of matter, in the hydrodynamic regime of correlated materials, and in classical active fluids with broken time-reversal symmetry (TRS). However, generalizations of these effects to 3D have remained elusive. In this work, we address this question by studying the Hall viscoelastic response of 3D crystals. We show that for systems with tetrahedral symmetries, there exist new, intrinsically 3D Hall viscosity coefficients that cannot be obtained via a reduction to a quasi-2D system. To study these coefficients, we specialize to a theoretically and experimentally motivated tight-binding model for a chiral magnetic metal in (magnetic) space group [(M)SG] P2${}_1$3 (No. 198.9), a nonpolar group of recent experimental interest that hosts both chiral magnets and topological semimetals (TSMs). Using the Kubo formula for viscosity, we compute two forms of the Hall viscosity, phonon and ``momentum'' (conventional) and show that for the tight-binding model we consider, both forms realize the novel cubic Hall viscosity. We conclude by discussing the implication of our results for transport in 2D magnetic metals and discuss some candidate materials in which these effects may be observed.

v2: Published version. v1: 7+7+epsilon pages, 2 figures

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• Nonreciprocal electron hydrodynamics under magnetic fields: applications to nonreciprocal surface magnetoplasmons
• Resolving Hall and dissipative viscosity ambiguities via boundary effects
• Plasmonic quantum nonlinear Hall effect in noncentrosymmetric 2D materials
• Hele-Shaw flow for parity odd three-dimensional fluids
• Nonlinear shallow-water waves with vertical odd viscosity
• Viscoelastic tensor and hydrodynamics of altermagnets
• Viscoelastic response and anisotropic hydrodynamics in Weyl semimetals
• Light-induced pseudo-magnetic fields in three-dimensional topological semimetals
• Fermi surface and topology of multiband superconductor BeAu