Fractional Fermion Number and Hall Conductivity of Domain Walls

TL;DR

This paper calculates the fractional fermion number and Hall conductivity of thick domain walls using heat kernel expansion, revealing a direct link between fermion number and Hall response, with special cases for thin walls.

Contribution

It introduces a novel method to compute fractional fermion number and Hall conductivity of domain walls using spectral eta function analysis.

Findings

Fractional fermion number is always accompanied by Hall conductivity.

Derived a formula linking fermion number to Hall conductivity.

Computed Hall conductivity for thin, impenetrable walls with chiral bag boundary conditions.

Abstract

In this letter the fractional fermion number of thick domain walls is computed. The analysis is achieved by developing the heat kernel expansion of the spectral eta functon of the Dirac Hamiltonian governing the fermionic fluctuations around the domain wall. A formula is derived showing that a non null fermion number is always accompanied by a Hall conductivity induced on the wall. In the limit of thin and impenetrable walls the chiral bag boundary conditions arise, and the Hall conductivity is computed for this case as well.