Numerical study of Klein quantum dots in graphene systems

The Klein quantum dot (KQD) refers to a quantum dot (QD) having quasi-bound states with a finite trapping time, which has been observed in experiments focusing on graphene recently. In this paper, we develop a numerical method to study the quasi- bound states of the KQD in graphene systems. By investigating the variation of the local density of states (LDOS) in a circular QD, we obtain the dependence of the quasi-bound states on the QD parameters, such as the electron energy, the radius and the confined potential. Based on these results, not only the experimental phenomena can be well explained, but also the crossover between quasi-bound states and real bound states is demonstrated when the intervalley scattering is included. We further study the evolution of the LDOS as the shape of the KQD varies from a circle to a semicircle. The ways of forming closed interference paths of carriers are suppressed during the deformation, and thus the corresponding quasi-bound states are eliminated. Our study reveals the mechanism of the whispering gallery mode on the quasi-bound states in graphene systems.