# Localization of massless Dirac particles via spatial modulations of the Fermi velocity

## TL;DR

This paper explores how spatial variations in Fermi velocity in 2D Dirac materials can induce electron localization, enabling confinement and guiding of electronic waves through exactly solvable models.

## Contribution

It introduces a novel approach to localize Dirac electrons by modulating Fermi velocity, providing exactly solvable models and insights into bound state properties.

## Key findings

- Fermi velocity gradients are crucial for bound state formation.
- Spatial velocity modulations can achieve electron confinement.
- Guiding electronic waves in Fermi velocity-engineered waveguides is feasible.

## Abstract

The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.