Spatial quasi-bound states of Dirac electrons in graphene monolayer

Our study investigated the emergence of spatial quasi-bound states (QBSs) in graphene monolayers induced by rectangular potential barriers. By solving the time-independent Dirac equation and using the transfer matrix formalism, we calculated the resonance energies and identify the QBSs based on probability density functions (PDF). We analyzed two types of structures: single and double barriers, and we find that the QBSs are located within the barrier region, at energies higher than the single barrier. Additionally, we observe QBSs in the double barrier and their position depends on the distance and width of the well between the two barriers. The width and height of the barrier significantly impact the QBSs while the well width influences the resonance energy levels of the QBSs in the double barrier. Interestingly, the QBSs can be manipulated in the graphene system, offering potential for optoelectronic devices. Finally, our results demonstrated that the spatial localization of these states is counter-intuitive and holds great promise for future research in optolectronic devices.