Chiral vortical effect in relativistic and nonrelativistic systems

TL;DR

This paper formulates the chiral vortical effect using semiclassical wave packet dynamics, revealing its absence in relativistic fermions but potential observability in certain nonrelativistic materials.

Contribution

It introduces a generalized vortical effect framework considering spin-vorticity coupling and distinguishes the CVE behavior in relativistic versus nonrelativistic systems.

Findings

CVE current vanishes in relativistic chiral fermions.

Anisotropic CVE can be observed in specific nonrelativistic materials.

Theoretical formulation using semiclassical wave packet dynamics.

Abstract

We formulate the chiral vortical effect (CVE) and its generalization called generalized vortical effect using the semiclassical theory of wave packet dynamics. We take the spin-vorticity coupling into account and calculate the transport charge current by subtracting the magnetization one from the Noether local one. We find that the transport charge current in the CVE always vanishes in relativistic chiral fermions. This result implies that it cannot be observed in transport experiments in condensed matter systems such as Dirac/Weyl semimetals with the pseudo-Lorentz symmetry. We also demonstrate that the anisotropic CVE can be observed in nonrelativistic systems that belong to the point groups $D_n, C_n (n = 2, 3, 4, 6)$, and $C_1$, such as $n$-type tellurium.