Emergent spacetime and gravitational Nieh-Yan anomaly in chiral $p+ip$ Weyl superfluids and superconductors

TL;DR

This paper demonstrates how chiral p+ip superfluids and superconductors exhibit emergent curved spacetime with torsion and curvature, leading to a gravitational Nieh-Yan anomaly affecting momentum transport and conservation laws.

Contribution

It reveals the emergence of a Riemann-Cartan spacetime structure and links the Nieh-Yan anomaly to the superfluid's normal state properties and symmetry.

Findings

Emergent curved spacetime with torsion and curvature for quasiparticles.

The Nieh-Yan anomaly explains anomalous momentum conservation.

The anomaly coefficient depends on a non-universal ultraviolet cutoff.

Abstract

Momentum transport is anomalous in chiral $p+ip$ superfluids and superconductors in the presence of textures and superflow. Using the gradient expansion of the semi-classical approximation, we show how gauge and Galilean symmetries induce an emergent curved spacetime with torsion and curvature for the quasirelativistic low-energy Majorana-Weyl quasiparticles. We explicitly show the emergence of the spin-connection and curvature, in addition to torsion, using the superfluid hydrodynamics. The background constitutes an emergent quasirelativistic Riemann-Cartan spacetime for the Weyl quasiparticles and they satisfy the conservation laws associated with local Lorentz symmetry, restricted to the plane of uniaxial anisotropy of the superfluid (or -conductor). Moreover, we show that the anomalous Galilean momentum conservation is a consequence of the gravitational Nieh-Yan (NY) chiral anomaly the Weyl fermions experience on the background geometry. Notably, the NY anomaly coefficient features a non-universal ultraviolet cut-off scale $\Lambda$, with canonical dimensions of momentum. Comparison of the anomaly equation and the hydrodynamic equations suggests that the value of the cut-off parameter $\Lambda$ is determined by the normal state Fermi liquid and non-relativistic uniaxial symmetry of the $p$-wave superfluid or superconductor.