  Klein quantum dot (KQD) refers to a QD with quasi-bound states and a finite
trapping time, which has been observed in experiments focused on graphene
recently. In this paper, we develop a numerical method to calculate local
density of states (LDOS) of KQD and apply it to monolayer graphene. By
investigating the variation of LDOS in a circular quantum dot, we obtain the
dependence of the quasi-bound states on the quantum dot parameters (e.g. the
electron energy, radius, confined potential, etc). Based on these results, not
only can we well explain the experimental phenomena, but also demonstrate how
quasi-bound states turn to real bound states when intervalley scattering is
taken into considered. We further study the evolution of the LDOS for KQD
varying from a circle shape to a semicircle shape, which reveals the mechanism
of whispering gallery mode on the quasi-bound states.
