On resonant scattering states in graphene circular quantum dots


Due to the effect of Klein tunneling, two-dimensional graphene quantum dots do not possess genuine bound states but quasi-bound (resonant tunneling) states only. We discuss in detail the attempt to describe these states within the framework of the Dirac pseudo-fermion model for circular dots. We demonstrate explicitly that introduced earlier the so-called "resonance condition" corresponds to the inconsistent system of linear equations obtained from matching conditions on the boundary of the quantum dot when one tries to use it for complex energy values and in the case of total reflection for the energies coincided with the potential well top.