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arXiv · 1905.12045

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

Miguel Castillo-Celeita·David J. Fernández C
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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 Schr\"{o}dinger 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.

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Miguel Castillo-Celeita, David J. Fernández C. 2019-05-28. Dirac electron in graphene with magnetic fields arising from first-order intertwining operators. https://doi.org/10.1088/1751-8121%2Fab3f40

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