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.
Highlights
In the recent years the nondissipative transport effects attract attention both in the framework of condensed matter physics and in the high energy physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
It has been found that in the chiral limit the axial current is proportional to the external magnetic field strength Fij and the ordinary chemical potential μ counted from the Fermi point: Jk5
We show that under the above conditions the axial current of chiral separation effect (CSE) in the nonhomogeneous system of general type is still proportional to external magnetic field
Summary
In the recent years the nondissipative transport effects attract attention both in the framework of condensed matter physics and in the high energy physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. In the case of condensed matter systems, it is shown that this approximation holds for any physically reasonable fields from the experimental point of view In this approach, Weyl-Wigner phase space formalism is used to calculate Dirac operators and Green’s functions. Weyl-Wigner phase space formalism is used to calculate Dirac operators and Green’s functions These techniques are widely used in recent research [63,64,65,66,67] dealing with linear response to electromagnetic fields which are shown to be topological invariants, as quantum Hall conductance for example. We show that under the above conditions (chiral symmetry of low energy effective theory) the axial current of CSE in the nonhomogeneous system of general type is still proportional to external magnetic field. The consideration of this issue remains out of the scope of the present paper
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