Multipole-based modal analysis of gate-defined quantum dots in graphene

A new numerical method based on the multipoles of the Dirac equation is presented for rigorous and fast analysis of electron scattering from gate-defined structures in graphene. The new method is used to study the strongly bound states and the weakly bound states of a circular quantum dot. The accuracy of the obtained results is then verified by the T-matrix method. Furthermore, we characterize the resonances of elliptical gate-defined quantum dots and compare these resonances with the strongly bound states of circular dots. The effects of coupling between two quantum dots are also investigated.