Boosting energy levels in graphene magnetic quantum dots through magnetic flux and inhomogeneous gap

We study the effects of a magnetic flux and an inhomogeneous gap on the energy spectrum of graphene magnetic quantum dots (GMQDs). By considering the Dirac equation in the infinite mass framework, we can analytically obtain eigenspinor expressions. By applying boundary conditions, we obtain an energy spectrum equation in terms of system parameters such as radius, magnetic field, energy, flux, and gap. In the infinite limit, we recover Landau levels for graphene in a magnetic field. We show that the energy spectrum increases significantly in the presence of flux and a gap inside the GMQDs, which prolongs the lifetime of the trapped electron states. We show that higher flux also produces new Landau levels of negative angular momentum. Meanwhile, we find that the gap increases the separation between the electron and hole energy bands. As shown in the radial probability analysis, flux and gap emerge as influential factors in controlling electron mobility, affecting confinement, and prolonging the presence of quasi -bound states.