# Lorentz Violation and Topologically Trapped Charge Carriers in 2D Materials

## TL;DR

This paper explores how Lorentz symmetry breaking affects the spectrum and trapping of charge carriers in 2D materials with domain walls, revealing new insights into edge states and band structures.

## Contribution

It extends analytical methods to study Lorentz violation effects on charge carrier trapping in 2D materials, connecting field theory with material properties.

## Key findings

- Lorentz violation influences the width and depth of trapping potentials.
- Band structures and trapped states are analytically characterized.
- Results expand understanding of edge states in strained graphene and similar materials.

## Abstract

The full spectrum of two-dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of the novel 2D materials, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in 2D materials. We extend the analytical methods developed in the context of 1+1 field theories to explore the effect of the Lorentz symmetry breaking in the charge carrier density of 2D materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. Our findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.