Sobre os efeitos da massa efetiva anisotrópica no gás de elétrons não interagentes bidimensional curvo

Abstract

The theory proposed by R.C.T. of the Coast, where the dynamics of a quantum particle on a curved surface is described, results in a geometric potential that depends on the transverse component of the mass on the surface. This treatment can be modeled from a curved two-dimensional electron gas system (2DEG). On the other hand, an electron moving in a crystalline lattice is under the effect of the potential of the lattice and its mass is a tensorial property, called textit effective mass, and can assume negative values. The present work proposes to use the approach proposed by da Costa and to analyze the dynamics in the curved surface in an approach where the effective mass is anisotropic, as well as in the case where it is negative. Comparing with the cases where the mass is isotropic, we observe considerable changes in the dynamics of the system. Some surface examples are examined, such as a particle on a helical, cylindrical, catenoid and cone surfaces, with possible applications briefly discussed.