Soluciones exactas para la interacci\'on de materiales de Dirac anis\'otropos con campos el\'ectricos y magn\'eticos

TL;DR

This paper provides exact solutions and perturbative analysis of anisotropic Dirac materials under inhomogeneous electric and magnetic fields, revealing effects on energy spectra, Landau levels, and localization relevant for nanoelectronic device design.

Contribution

It introduces exact solutions for anisotropic Dirac materials in complex fields and extends analysis with the Asymptotic Iteration Method, highlighting finite-range effects and Landau level collapse.

Findings

Exact solutions for energy spectra under singular and decaying fields.

Finite range modifies localization and transport properties.

Critical electric field causes Landau level collapse.

Abstract

This work analyzes anisotropic Dirac materials, such as graphene and borophene, under inhomogeneous electric and magnetic fields with position-dependent profiles. Exact solutions of the Dirac--Weyl equation are obtained for singular and exponentially decaying interactions, showing how anisotropy and field shape influence the energy spectrum, Landau levels, and state localization. The analysis is further extended using the Asymptotic Iteration Method (AIM) in its perturbative form, applied to systems with bounded domains $( -\infty, x_0 ]$ or $( 0, x_0 ]$. In particular, we consider the case $( -\infty, x_0 ]$, where the field vanishes asymptotically. The first-order corrections reveal how the finite range $x_0$ modifies localization and transport, and how a critical electric field emerges at which Landau levels collapse, providing insight into the design of field-defined regions in two-dimensional nanoelectronic and quantum devices.