Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

Abstract

The behaviour of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, where two one-dimensional Schrödinger Hamiltonians $H^{\pm }$ are intertwined by a first order differential operator. Special magnetic field are initially chosen, in order that $V^{\pm }$ will be shape invariant exactly solvable potentials. When looking for more general first order operators, intertwining $H^{-}$ with a non-necessarily shape invariant Hamiltonian, new magnetic fields associated also to analytic solutions will be generated. The iteration of this procedure is as well discussed.

arXiv commentSeveral misprints corrected

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Cited by in corpus (18)

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• Supersymmetric Dirac-Hamiltonians in $(1+1)$ dimensions revisited
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• Coherent states for graphene under the interaction of crossed electric and magnetic fields
• Schrödinger-type 2D coherent states of magnetized uniaxially strained graphene
• Complex Supersymmetry in Graphene
• Pseudo-Hermitian Dirac operator on the torus for massless fermions under the action of external fields
• Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations
• Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well
• Optical ladder operators in the Glauber-Fock oscillator array
• Bilayer graphene in periodic and quasiperiodic magnetic superlattices
• Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
• Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
• Non-hermitian Dirac Hamiltonian in the presence of local Fermi velocity
• Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators
• Landau levels of a Dirac electron in graphene from non-uniform magnetic fields