Chiral separation effect in nonhomogeneous systems

Abstract

We discuss chiral separation effect in the systems with spatial nonhomogeneity. It may be caused by nonuniform 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 nondissipative 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.

Wigner-Weyl calculus in description of non-dissipative transport phenomena

“…In the present paper we review the recent works by the group working in Ariel University on the topological description of non -dissipative transport in non -homogeneous systems. We summarize here the results reported earlier in a series of papers (see [26,[47][48][49][50][51][52][53] and references therein). We used Wigner -Weyl formalism and start from the extension of Eq.…”

“…4. The CSE is considered for the non -homogeneous systems with chiral fermions [50]. We assume that in these systems the effective low energy theory obeys chiral symmetry.…”

“…Here we consider the chiral separation effect, which is the appearance of axial current in the 4D fermionic systems with finite chemical potential and external magnetic field. Here we follow [50]. We assume that the magnetic field is uniform.…”

Classification of Emergent Weyl Spinors in Multi-Fermion Systems

“…Here Σ is the three -dimensional hypersurface surrounding the given singularity M (i) of expression standing inside the integral. This expression resembles the one of [38]. The general procedure for the construction of such invariants has been proposed in [36].…”

“…Another direction for the extension of the classification of emergent Weyl fermions is related to consideration of the non -homogeneous systems following methodology of [36][37][38]. Namely, the conventional expression for invariant N 3 is defined as an integral in momentum space and is valid for the homogeneous systems only.…”