Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

Abstract

We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum dot (or ring) is of a slowly decaying nature. It is found that a modulation of the depth of the magnetic quantum dot leads to successive confinement-deconfinement transitions of vortexlike states with a certain angular momentum, until a regime is reached where only states with one sign of angular momentum are supported. We illustrate these characteristics with both exact solutions and a hitherto unknown quasi-exactly solvable model utilizing confluent Heun functions.

7 pages, 3 figures

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• Trapping charge carriers in low-dimensional Dirac materials
• Energy spectrum of massive Dirac particles in gapped graphene with Morse potential
• On an atom with a magnetic quadrupole moment in a rotating frame
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Quantum vibrational mode in a cavity confining a massless spinor field
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field