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  • Letter
  • Open Access

Cubic Hall viscosity in three-dimensional topological semimetals

Iñigo Robredo1,2,*, Pranav Rao3,*, Fernando de Juan1,4, Aitor Bergara1,2,5, Juan L. Mañes2, Alberto Cortijo6,7, M. G. Vergniory1,4,†, and Barry Bradlyn3,‡

  • 1Donostia International Physics Center, 20018 Donostia-San Sebastian, Spain
  • 2Department of Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
  • 3Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
  • 4IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
  • 5Centro de Física de Materiales CFM, CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 Donostia, Basque Country, Spain
  • 6Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid E-28049, Spain
  • 7Condensed Matter Physics Center (IFIMAC), Madrid E-28049, Spain

  • *These authors contributed equally to this work.
  • †maiagvergniory@dipc.org
  • ‡bbradlyn@illinois.edu
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Phys. Rev. Research 3, L032068 – Published 16 September, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032068

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] P213 (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.

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Phys. Rev. Research 3, L032068– Published 16 September, 2021
  • Received 16 February 2021
  • Accepted 20 August 2021
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