Effect of the electric field orientation on stark shift, dipole moment and electronic properties in a circular toroidal quantum ring: Presence of shallow donor impurity

This research investigates the influence of electric field orientation on the physical properties of a Gallium Arsenide (GaAs) Circular Toroidal Quantum Ring (CTQR) in the presence of shallow donor impurity. Using the effective mass approximation and an infinite potential well, we delve into how electric field directions specifically 0, 45, and 90 degrees on the xy-plane affect physical behaviors such as binding energy, electronic energy, the Stark effect, dipole moment and donor impurity position. Utilizing the finite difference method for our numerical analysis, we discovered interesting size-dependent behaviors. Our findings reveal intriguing insights. Initially, we observed that the electronic energy exhibits minimal sensitivity to the direction of the electric field in smaller CTQR. Notably, the ground state energy increases when the electric field's direction shifts from q) F = 0 to q) F = 90 degrees . The electric field's influence on the binding energy varies depending on its orientation. In larger structures, we observe a lower binding energy. Thus, our study unveils the influence of the electric field's direction on Stark shifts and dipole moment which opens pathways for a deeper understanding of potential applications in this domain.