Exact solutions of the (2+1) Dimensional Dirac equation in a constant magnetic field in the presence of a minimal length

TL;DR

This paper derives exact solutions for the (2+1)D Dirac equation under a magnetic field considering a minimal length scale, revealing modified degeneracy and novel states absent in standard quantum mechanics, with implications for materials like Graphene.

Contribution

It provides explicit solutions to the Dirac equation with GUP in a magnetic field, highlighting how minimal length alters state degeneracy and introduces new states.

Findings

Degeneracy of states is modified by minimal length.

New states emerge that are absent in standard quantum mechanics.

Results applicable to charged fermions in materials like Graphene.

Abstract

We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit representation of the GUP and provide expressions of the wave functions in the momentum representation. We find that in the minimal length case the degeneracy of the states is modified and that there are states that do not exist in the ordinary quantum mechanics limit (\beta -->0). We also discuss the mass-less case which may find application in describing the behavior of charged fermions in new materials like Graphene.