Dirac electron in graphene under supersymmetry generated magnetic fields

We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields $\mathbf{B} = \widetilde{\mathcal{B}}(x,λ) \hat{e}_z$ for which the massless Dirac electron possesses exact solution. The inhomogeneity appearing in $\widetilde{\mathcal{B}}(x,λ)$ can be controlled by the parameter $λ$. 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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