# Tuning the Fermi velocity in Dirac materials with an electric field

## TL;DR

This paper presents a universal method to tune the Fermi velocity in Dirac materials using an electric field, demonstrated analytically and through simulations on various systems like graphene and topological insulators.

## Contribution

It introduces a general, experimentally accessible mechanism to control the Fermi velocity in Dirac materials via electric fields, validated across multiple systems.

## Key findings

- Fermi velocity can be significantly modified by a uniform electric field.
- Analytical proof for topological insulator surface states.
- Validation in graphene nanoribbons and nanotubes through simulations.

## Abstract

Dirac materials are characterized by energy-momentum relations that resemble those of relativistic massless particles. Commonly denominated Dirac cones, these dispersion relations are considered to be their essential feature. These materials comprise quite diverse examples, such as graphene and topological insulators. Band-engineering techniques should aim to a full control of the parameter that characterizes the Dirac cones: the Fermi velocity. We propose a general mechanism that enables the fine-tuning of the Fermi velocity in Dirac materials in a readily accessible way for experiments. By embedding the sample in a uniform electric field, the Fermi velocity is substantially modified. We first prove this result analytically, for the surface states of a topological insulator/semiconductor interface, and postulate its universality to other Dirac materials. Then we check its correctness in carbon-based Dirac materials, namely graphene nanoribbons and nanotubes, thus showing the validity of our hypothesis in both continuum and tight-binding calculations and in different Dirac systems.