Pontos quânticos induzidos por geometria em superfícies com deformações gaussianas.

Abstract

A quantum particle, over a two-dimensional orientable surface, suffers the action of a geometric potential induced attractive, characterized by mean and Gaussian curvatures. In this work we investigate the behavior of electrons on surfaces showing Gaussian bumps. For surfaces showing single bumps, we a nd that the geometrical potential gives rise to a geometry-induced quantum ring. For surfaces with multiples bumps, quantum particles could be trapped around the center of those surfaces, which gives rise to a geometry-induced quantum dot. Information about mean and Gaussian curvatures are of great importance for the understanding of the behavior of a given particle when it on a surface to be. Joining this information with some concepts of quantum mechanics, as the Schr odinger equation, analysis of potential and other resources, we obtain equations that relate the potential energy with the mean and Gaussian curvatures. Our results can nd applications in the context of usual semiconductors as well as in the context of bilayer graphene sheets.