The influence of electric field and geometry on relativistic Landau levels in spheroidal fullerene molecules

In this paper, we study relativistic Landau levels on a spheroidal fullerene molecule in the presence of a crossed electric and magnetic field. A specific profile of external fields is considered as an illustration to examine the dependence of Landau levels on electric field strength and two geometric parameters, namely the Gaussian curvature and ellipticity of the spheroidal molecule. Similar to results in other allotropes of carbon such as spherical fullerene or carbon pseudosphere, the electric field induces a collapse of the Landau levels while the Gaussian curvature tends to prevent them from collapse. However, the ellipticity does not play any role in preventing the collapse of the Landau levels. Furthermore, in certain limiting cases are results agree with those obtained for flat graphene and carbon nanotubes. •Dirac-Weyl equation on a problate spheroid.•Orthogonal electric and magnetic fields.•Bound state solutions.•Landau level collapse.•Effect of Gaussian curvature and ellipticity.