Chiral Separation effect in non-homogeneous systems

TL;DR

This paper investigates the chiral separation effect in non-homogeneous systems, showing that a universal axial current arises under magnetic fields, extending topological invariants to inhomogeneous conditions.

Contribution

It introduces a universal expression for the chiral separation effect in non-homogeneous systems, extending topological invariants to inhomogeneous low-energy effective theories.

Findings

The axial current response is universal and robust.

The CSE conductivity is expressed as a surface integral in momentum space.

The expression extends topological invariants to inhomogeneous systems.

Abstract

We discuss chiral separation effect in the systems with spatial non - homogeneity. It may be caused by non - uniform electric potential or by another reasons, which do not, however, break chiral symmetry of an effective low energy theory. Such low energy effective theory describes quasiparticles close to the Fermi surfaces. In the presence of constant external magnetic field the non - dissipative axial current appears. It appears that its response to chemical potential and magnetic field (the CSE conductivity) is universal. It is robust to smooth modifications of the system and is expressed through an integral over a surface in momentum space that surrounds all singularities of the Green function. In itself this expression represents an extension of the topological invariant protecting Fermi points to the case of inhomogeneous systems.