Curved non-interacting two-dimensional electron gas with anisotropic mass

TL;DR

This paper investigates how anisotropic effective mass influences the behavior of a non-interacting two-dimensional electron gas confined on curved surfaces, revealing potential for improved electronic system design without altering geometry.

Contribution

It introduces the effects of anisotropic mass on curved surface electron gases, a novel exploration in the context of geometric confinement and potential applications.

Findings

Mass anisotropy affects geometric potential and electron behavior.

Examples include particles on helicoidal, cylindrical, catenoid, and conical surfaces.

Potential applications in electronic system design.

Abstract

In the da Costa's thin-layer approach, a quantum particle moving in a 3D sample is confined on a curved thin interface. At the end, the interface effects are ignored and such quantum particle is localized on a curved surface. A geometric potential arises and, since it manifests due to this confinement procedure, it depends on the transverse to the surface mass component. This inspired us to consider, in this paper, the effects due to an anisotropic effective mass on a non-interacting two dimensional electron gas confined on a curved surface, a fact not explored before in this context. By tailoring the mass, many investigations carried out in the literature can be improved which in turns can be useful to better designing electronic systems without modifying the geometry of a given system. Some examples are examined here, as a particle on helicoidal surface, on a cylinder, on a catenoid and on a cone, with some possible applications briefly discussed.