Energy Levels of Quantum Dots in Monolayer of Molybdenum Disulfide MoS2

We are conducting a study on the energy levels of a magnetic circular quantum dot made of metal dichalcogenide MoS 2 , which is exposed to a perpendicular magnetic field. To obtain the eigenspinors analytically, we solve the Dirac equation for the K and K ′ valleys. By utilizing the Hamiltonian for low energies, we derive analytical expressions for the energy levels and apply boundary conditions at the interface. We explore four different configurations of the system and numerically analyze our findings. Specifically, we show the relationship between the energy levels, quantum dot radius, and magnetic field for both the K and K ′ valleys. We demonstrate that the energy levels depends on the spin-orbit interaction and on the quantum number m . In addition, for m ≠ 0 , due to the influence of the spin-orbit interaction of the quantum dot of MoS 2 , there is a degeneration of the valleys and spins, and this degeneracy is lifted if m = 0 . The resulting eigenenergies E nm exhibit a symmetric behavior between the valence and conduction bands. In addition, for m < 0 , the eigenenergies are independent of m but for m > 0 , they increase as long as m increases. Finally, we show that the radial probability exhibits a damped oscillatory behavior as the dot radius increases. Furthermore, the behavior of the radial probability is strongly dependent on both the quantum numbers n and m .