Calculation of exchange interaction for modified Gaussian coupled quantum dots

Abstract

A system of two laterally coupled quantum dots with modified Gaussian potential has been considered. Each quantum dot has an electron under electric and magnetic field. The quantum dots have been considered as hydrogen-like atoms. The physical picture has translated into the Heisenberg spin Hamiltonian. The Schrodinger equation using finite element method has been numerically solved. The exchange energy factor has been calculated as a functions of electric field, magnetic field, and the separation distance between the centers of the dots (d). According to the results, it is found that there is the transition from anti-ferromagnetic to ferromagnetic for constant electric field. Also, the transition occurs from ferromagnetic to anti-ferromagnetic for constant magnetic field (\(B>1\,\hbox {T}\)). With decreasing the distance between the centers of the dots and increasing magnetic field, the transition occurs from anti-ferromagnetic to ferromagnetic. It is found that a switching of exchange energy factor is presented without canceling the interactions of the electric and magnetic fields on the system.