Geometry Dynamics in Chiral Superfluids

TL;DR

This paper explores how geometric fluctuations influence chiral superfluids, revealing unique chirality-dependent effects such as chiral drag, mode localization, and anisotropic wave propagation, which serve as signatures of chiral condensate formation.

Contribution

It derives the coupled dynamics of superfluid and geometric modes, uncovering novel chirality-dependent phenomena and providing a framework to manipulate chiral superfluid properties via background geometry.

Findings

Background supercurrent induces chiral drag effect.

Curvature causes anisotropic phase and velocity corrections.

Flexural and phase modes form tilted Dirac cones along curvature directions.

Abstract

We investigate the geometric response of chiral superfluids when coupled to a dynamic background geometry. We find that geometry fluctuations, represented by the flexural mode, interact with the superfluid phase fluctuations (the Goldstone mode). Starting from a minimally coupled theory, we derive the equilibrium conditions for a static background defined by supercurrent, curvature, and tension, and then obtain linearized equations for the propagation of the Goldstone and flexural modes. The equations reveal distinctive chirality-dependent effects in the propagation of the flexural mode. Specifically, a background supercurrent induces a chiral drag effect, localizing flexural waves at the superfluid boundary, while background curvature introduces anisotropic corrections to the superfluid phase and group velocities, as well as a tension in the flexural mode dispersion. Furthermore, curvature couples flexural and phase modes into dressed excitations, with tilted Dirac cones along the principal curvature directions. These effects provide dynamical signatures of the formation of a chiral condensate, and can be tuned by manipulating the background geometry.