Semi-Dirac semi-metals quantum dots

Abstract

Novel findings on nanostructures in semi-metal and semi-graphene materials are discussed regarding rectangular quantum dots with zigzag edges, MIT bag models, and Dirichlet boundary conditions. The article theoretically investigates some models of quantum dots for these hybrid materials and the point spectra of the semi-Dirac semi-Laplacians via one-dimensional Laplace and Dirac operators. We also prove the self-adjointness of the semi-Laplacian defined on a rectangle, subject to zigzag and hard-wall boundary conditions, and study its spectral properties.