Shear viscosity as a probe of nodal topology

TL;DR

This paper demonstrates that shear viscosity's frequency dependence in collisionless regimes reveals the topological nature of nodal band structures in electronic materials, offering a new probe beyond traditional methods.

Contribution

It introduces shear viscosity as a novel physical quantity that encodes information about the topological invariants of nodal band touchings in electronic materials.

Findings

Shear viscosity exhibits distinct power-law scaling depending on band topology.

Different topological phases show unique shear viscosity signatures at low temperatures.

Shear viscosity can distinguish between topological nodal structures and trivial phases.

Abstract

Electronic materials can sustain a variety of unusual, but symmetry protected touchings of valence and conduction bands, each of which is identified by a distinct topological invariant. Well-known examples include linearly dispersing pseudo-relativistic fermions in monolayer graphene, Weyl and nodal-loop semimetals, biquadratic (bicubic) band touching in bilayer (trilayer) graphene, as well as mixed dispersions in multi-Weyl systems. Here we show that depending on the underlying band curvature, the shear viscosity in the collisionless regime displays a unique power-law scaling with frequency at low temperatures, bearing the signatures of the band topology, which are distinct from the ones when the system resides at the brink of a topological phase transition into a band insulator. Therefore, besides the density of states (governing specific heat, compressibility) and dynamic conductivity, shear viscosity can be instrumental to pin nodal topology in electronic materials.