Massive and massless two-dimensional Dirac particles in electric quantum dots

TL;DR

This paper explores how mass and angular momentum influence the confinement of Dirac particles in electric quantum dots, revealing phenomena like atomic collapse and resonance behavior in both massive and massless cases.

Contribution

It provides a comprehensive analysis of confinement, resonances, and atomic collapse phenomena in Dirac particles considering mass and angular momentum effects.

Findings

Atomic collapse limits the number of bound states in massive particles.

Massless particles exhibit bound states only at discrete potential depths.

Resonance intensities are sensitive to angular momentum in massless particles.

Abstract

In this work we investigate the confining properties of charged particles of a Dirac material in the plane subject to an electrostatic potential well, that is, in an electric quantum dot. Our study focuses on the effect of mass and angular momenta on such confining properties. To have a global picture of confinement, both bound and resonance states are considered. The resonances will be examined by means of the Wigner time delay of the scattering states, as well as through the complex eigenvalues of outgoing states in order to show that they are physically meaningful. By tuning the potential intensity of the well, electron captures and atomic collapses are observed for critical values. In these processes, the bound states of the discrete spectrum become resonances of the continuous spectrum or vice versa. For massive charges, the atomic collapse phenomenon keeps the number of bound levels in the quantum dot below a maximum value. In the massless case, the bound states have zero energy and occur only for some discrete values of the potential depth, as is known. We also show that although the intensity of the resonances for massive particles is not significantly influenced by angular momenta, on the contrary, for massless particles they are quite sensitive to angular momenta, as it is the case of graphene.