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

2025/08/30 by Daniel O-Campa, Omar Pedraza, O-Campa, Daniel +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2509.00401

openalex publication_date 2025/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials
• Supersymmetric quantum electronic states in graphene under uniaxial strain

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