# Trapping charge carriers in low-dimensional Dirac materials

## TL;DR

This paper investigates how to confine Dirac-like quasiparticles in low-dimensional materials by analyzing a solvable model with a position-dependent mass, revealing conditions for bound states and novel energy structures.

## Contribution

It introduces an exactly-solvable model demonstrating the emergence of bound states in Dirac materials with a spatially varying mass, highlighting a critical confinement condition and exotic energy features.

## Key findings

- Bound states appear after a critical mass size
- Exotic chevron energy structure observed
- Confinement conditions depend on mass parameters

## Abstract

We consider the problem of confining the famously elusive Dirac-like quasiparticles, as found in some recently discovered low-dimensional systems. After briefly surveying the existing theoretical proposals for creating bound states in Dirac materials, we study relativistic excitations with a position-dependent mass term. With the aid of an exactly-solvable model, we show how bound states begin to emerge after a critical condition on the size of the mass term is met. We also reveal some exotic properties of the unusual confinement discovered, including an elegant chevron structure of the bound state energies as a function of the size of the mass.