Exact solution of Dirac electron in graphene under SUSY generated magnetic fields

We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields B = B(x, λ)ez for which the massless Dirac electron possesses exact solution. The inhomogeneity appearing in 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. The 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.