Soluciones exactas para la interacción de materiales de Dirac anisótropos con campos eléctricos y magnéticos

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.

Master's thesis, in Spanish language