A curved noninteracting 2D electron gas with anisotropic mass

Abstract

In da Costa's thin‐layer approach, a quantum particle moving in a 3D sample is confined to a curved thin interface. At the end, the interface effects are ignored and the quantum particle is localized on a curved surface. A geometric potential arises and, since it is due to this confinement procedure, it depends on the transverse to the surface mass component. The effects due to an anisotropic effective mass on a noninteracting two‐dimensional electron gas confined to a curved surface are reported. By tailoring the mass, many investigations carried out in the literature can be improved, which in turn can be useful to better designing electronic systems without modifying the geometry of the given system. Some examples are examined, such as a particle on a helicoidal surface, on a cylinder, on a catenoid and on a cone, with some possible applications briefly discussed.