# Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions

## TL;DR

This paper investigates the spectral properties of Dirac materials under position-dependent electromagnetic fields, utilizing Heun functions to solve the resulting differential equations and determine bound state solutions.

## Contribution

It introduces a method to analyze Dirac materials with variable fields using Heun functions, providing new analytical solutions for the spectral problem.

## Key findings

- Decoupled differential equations for Dirac Hamiltonian components.
- Derived quantization relations for bound states.
- Analytical solutions obtained using Heun functions.

## Abstract

This work focuses on the study of the spectral problem for Dirac materials immersed in position-dependent magnetic and electric fields. To achieve this, the system of differential equations satisfied by the eigenfunction components of the Hamiltonian has been decoupled, and the solutions for some specific cases have been analyzed using Heun functions, which provide us with a quantization relation and allow us to determine the solutions for the bound states.