Energy levels of graphene magnetic quantum dot in inhomogeneous gap

We investigate the energy levels of charge carriers confined in a magnetic quantum dot in graphene with an inhomogeneous gap through an electrical potential. We solve the eigenvalue equation for two regions. We explicitly determine the eigenspinors for both valleys $ K $, $ K' $ and use the boundary condition at the quantum dot interface to obtain the energy levels. We show that the energy levels exhibit symmetric and asymmetric behavior under appropriate conditions of the physical parameters. It has been found that changing the energy levels by introducing an energy gap outside the quantum dot changes the electrical properties.