Dirac Fermions and Domain Wall Defects in 2+1 Dimensions

TL;DR

This paper studies Dirac fermions in 2+1 dimensions with spatially varying mass defects, analyzing localized zero modes, higher mode effects, and induced currents near domain walls.

Contribution

It provides a method to analyze fermion dynamics with domain wall defects and explores the effects of mass profile and external fields on induced currents.

Findings

Existence of localized fermionic zero modes on domain walls.

Quantitative analysis of higher mode contributions.

Calculation of induced fermionic current in external electric fields.

Abstract

We investigate some properties of a system of Dirac fermions in 2+1 dimensions, with a space dependent mass having domain wall like defects.These defects are defined by the loci of the points where the mass changes sign. In general, they will be curves lying on the spatial plane. We show how to treat the dynamics of the fermions in such a way that the existence of localized fermionic zero modes on the defects is transparent. Moreover, effects due to the higher, non zero modes, can be quantitatively studied. We also consider the relevance of the profile of the mass near the region where it changes sign. Finally, we apply our general results to the calculation of the induced fermionic current, in the linear response approximation, in the presence of an external electric field and defects.