Dirac field in the background of a planar defect

TL;DR

This paper investigates how massless Dirac fermions behave in a three-dimensional topologically nontrivial background, revealing bound states and scattering characteristics without zero modes.

Contribution

It provides new insights into fermion interactions with planar topological defects, highlighting the absence of zero modes despite nontrivial topology.

Findings

Presence of massive bound states

Calculation of phase shifts and differential cross section

No fermionic zero mode found

Abstract

We study massless Dirac fermions in the background of a specific planar topologically nontrivial configuration in the three-dimensional spacetime. The results show the presence of massive bound states, phase shifts and the consequent differential cross section for the scattering of fermions in the weak coupling regime. Despite the nontrivial topology of the background field, no fermionic zero mode is found.