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We consider magnetic graphene quantum dots (MGQDs) and study the impact of the Aharonov-Bohm (AB) flux and gap on the scattering process of electrons. Our emphasis is on the finite lifetimes of quasi-bound states arising from the interaction between electrons and the magnetic field within the dot. Initially, we calculate the scattering coefficients, scattering efficiency, and probability density by ensuring the continuity of eigenspinors at the boundary of MGQD. The results indicate that as the gap increases, the quasi-bound states reach higher maxima. We show that an increase in AB-flux leads to a generation of quasi-bound states requiring less magnetic field, and the scattering efficiency starts to take non-zero values at smaller MGQD sizes. The analysis of probability density shows that the quasi-bound states, corresponding to non-resonantly excited scattering modes, exhibit a significant improvement in the concentrated density at MGQD. The improvement is a result of reducing the diffraction phenomenon and suppressing the Klein effect through an increase in AB-flux and gap. This increases the probability of retaining the electron for a longer period of time., Comment: 11 pages, 7 figures

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., Comment: 10 pages, 7 figures. Clarifications and references added

We investigate the energy levels of fermions within a circular graphene quantum dot (GQD) subjected to external magnetic and Aharonov-Bohm fields. Solving the eigenvalue equation for two distinct regions allows us to determine the eigenspinors for the valleys $K$ and $K^\prime$. By establishing the continuity of eigenspinors at the GQD interface, we derive an equation that reveals the reliance of energy levels on external physical parameters. Our observations suggest that the symmetry of energy levels hinges on the selected physical parameters. We observe that at low magnetic fields, the energy levels display degeneracy, which diminishes as the field strength increases, coinciding with the convergence of energy levels toward the Landau levels. We illustrate that the introduction of a magnetic flux into the GQD leads to the creation of an energy gap, extending the trapping time of electrons without perturbing the system. Conversely, the addition of gap energy widens the band gap, disrupting the system's symmetry by introducing new energy levels., Comment: 9 pages, 7 figures

It is known that the appearance of Klein tunneling in graphene makes it hard to keep or localize electrons in a graphene-based quantum dot (GQD). However, a magnetic field can be used to temporarily confine an electron that is traveling into a GQD. The electronic states investigated here are resonances with a finite trapping time, also referred to as quasi-bound states. By subjecting the GDQ to a magnetic flux, we study the scattering phenomenon and the Aharonov-Bohm effect on the lifetime of quasi-bound states existing in a GQD. We demonstrate that the trapping time increases with the magnetic flux sustaining the trapped states for a long time even after the flux is turned off. Furthermore, we discover that the probability density within the GQD is also clearly improved. We demonstrate that the trapping time of an electron inside a GQD can be successfully extended by adjusting the magnetic flux parameters., Comment: 10 pages, 7 figures

Owing to the Klein tunneling phenomenon, the permanent confinement or localization of electrons within a graphene quantum dot is unattainable. Nonetheless, a constant magnetic field can transiently ensnare an electron within the quantum dot, giving rise to what are known as quasi-bound states characterized by finite lifetimes. To prolong the retention of electrons within the quantum dot, we introduce a mass term into the Hamiltonian, thereby inducing an energy gap. We resolve the Dirac equation to ascertain the eigenspinors, and by ensuring their continuity at the boundaries, we investigate the scattering behavior. Our findings indicate that the presence of an energy gap can extend the lifetimes of these quasi-bound states within the quantum dot. In particular, we demonstrate that even in the absence of a magnetic field, the scattering efficiency attains significant levels when the energy gap gets closed to the incident energy of an electron traversing the quantum dot. It is found that an augmentation in the electron density within the quantum dot results in an enhancement of the electron-trapping time., Comment: 12 pages, 8 figures. Clarification and references added