Topological waves in fluids with odd viscosity

TL;DR

This paper explores how odd viscosity in fluids that break time-reversal and parity symmetries influences topological sound waves, leading to phase transitions and edge modes without closing the bulk gap.

Contribution

It introduces a novel topological invariant for continuum fluids with odd viscosity, revealing a unique phase transition mechanism without gap closing.

Findings

Odd viscosity affects the number and profile of topological edge modes.

A bulk topological invariant can be defined using odd viscosity as a short-distance cutoff.

A topological phase transition occurs without gap closing, due to ill-defined invariant at the transition point.

Abstract

Fluids in which both time-reversal and parity are broken can display a dissipationless viscosity that is odd under each of these symmetries. Here, we show how this odd viscosity has a dramatic effect on topological sound waves in fluids, including the number and spatial profile of topological edge modes. Odd viscosity provides a short-distance cutoff that allows us to define a bulk topological invariant on a compact momentum space. As the sign of odd viscosity changes, a topological phase transition occurs without closing the bulk gap. Instead, at the transition point, the topological invariant becomes ill-defined because momentum space cannot be compactified. This mechanism is unique to continuum models and can describe fluids ranging from electronic to chiral active systems.