Density of states analysis of electrostatic confinement in gapped graphene

We investigate the electrostatic confinement of charge carriers in a gapped graphene quantum dot in the presence of a magnetic flux. The circular quantum dot is defined by an electrostatic gate potential demarcated in a large intrinsic graphene circular ribbon which is then connected to a circular lead. Considering different regions composing our system, we explicitly determine the energy spectrum solutions in terms of Hankel functions using the scattering matrix approach. The asymptotic behavior of the Hankel functions for large arguments allowed us to calculate the density of states (DOS) and show that it has an oscillatory behavior with the appearance of some resonant peaks associated with the quantum dot bound states with definite angular momenta. It was also found that the energy gap can control the amplitude and width of these resonances and affect even their location as reflected in the density of states profile.