Dirac electron in graphene under supersymmetry generated magnetic fields
B Midya, DJ Fernández - Journal of Physics A: Mathematical and …, 2014 - iopscience.iop.org
Journal of Physics A: Mathematical and Theoretical, 2014•iopscience.iop.org
We use supersymmetry transformations to obtain new one parameter families of
inhomogeneous magnetic fields $\boldsymbol {B}=\widetilde {\mathcal {B}}(x,\lambda)\hat
{e} _z $ for which the massless Dirac electron possesses exact solutions. The
inhomogeneity appearing in $\widetilde {\mathcal {B}}(x,\lambda) $ 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, that of a constant …
inhomogeneous magnetic fields $\boldsymbol {B}=\widetilde {\mathcal {B}}(x,\lambda)\hat
{e} _z $ for which the massless Dirac electron possesses exact solutions. The
inhomogeneity appearing in $\widetilde {\mathcal {B}}(x,\lambda) $ 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, that of a constant …
Abstract
We use supersymmetry transformations to obtain new one parameter families of inhomogeneous magnetic fields for which the massless Dirac electron possesses exact solutions. The inhomogeneity appearing in 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, that of a constant magnetic field being 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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