The role of the effective mass in two-dimensional Dirac electric quantum dots

Abstract

We investigate the influence that different effective masses, inside and outside, of an electric quantum dot have on its discrete energy spectrum. The method to arrive at the solutions is standard: The Hamiltonian is simplified by the rotational symmetry, then the reduced equation is solved in the domains of the dot, and finally the solutions are obtained by means of the boundary conditions. Employing this procedure we have obtained quite different spectra depending on the value of mass. Specifically, when the mass is positive but smaller inside the dot than outside it, the spectrum increases and splits into two types of eigenvalues separated by a gap. Conversely, if the mass inside the quantum dot is greater than outside, the spectrum has fewer points and it is necessary stronger fields in order to confine states. All these spectral points correspond to bulk eigenfunctions. However, in the case of inverted mass (negative mass inside the quantum dot and positive outside it) there are new eigenvalues corresponding to edge states. The edge states are limited to a well defined region determined by the electrostatic potential and the mass. All these cases have been analyzed in full detail along this paper.