# Fermion bound states in geometrically deformed backgrounds

## TL;DR

This paper investigates how fermions behave in two-dimensional spacetime backgrounds with kinklike structures, revealing conditions for bound states and effects of parity symmetry breaking.

## Contribution

It analyzes fermion bound states in different scalar field models, including parity-preserving and parity-breaking backgrounds, highlighting how these structures influence fermionic spectra.

## Key findings

- Parity symmetry affects fermion bound state existence.
- Some models exclude fermion bound states, others include them.
- Parity-breaking models produce asymmetric fermion bound states.

## Abstract

This work deals with the behavior of fermions in the background of kinklike structures in the two-dimensional spacetime. The kinklike structures appear from bosonic scalar field models that engender distinct profiles and interact with the fermion fields via the standard Yukawa coupling. We first consider two models that engender parity symmetry, one leading to the exclusion of fermion bound states, and the other to the inclusion of bound states, when the parameter that controls the bosonic structure varies from zero to unity. We then go on and investigate another model where the kinklike solution explicitly breaks parity symmetry, leading to fermion bound states that are spatially asymmetric.