Dirac electron in graphene under supersymmetry generated magnetic fields

Abstract

We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields $\mathbf{B}=\tilde{\mathcal{B}}(x,\lambda ){\hat{e}}_z$ for which the massless Dirac electron possesses exact solution. The inhomogeneity appearing in $\tilde{\mathcal{B}}(x,\lambda )$ can be controlled by the parameter $\lambda$. The obtained magnetic fields are interpreted as deformed variants of some physically attainable well known magnetic fields. A particular example, when a constant magnetic field is deformed, is considered to show that equidistant Landau levels exist even in the presence of an infinite number of specially designed inhomogeneous magnetic fields.

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• Two-dimensional Dirac fermion in presence of an asymmetric vector potential
• Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
• Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials
• Modular Operators and Entanglement in Supersymmetric Quantum Mechanics
• Bound states for massive Dirac fermions in graphene in a magnetic step field
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• Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators