The Ground State Energy Of Excitons And Charged Exctions In Elliptical Quantum Ring Under Magnetic Fields

In the framework of effective-mass envelope function, the properties of Aharonov-Bohm(A-B)oscillations of the excitons and charged excitons(X-1) system in elliptical quantum ring under magnetic fields are studied theoretically. In zhe numerical calculation, In the numerical calculation, the elliptical adiabatic model of quantum ring are adopted. The Hamiltonian matrix elements will be simplified in polar coordinates, at last the ground state energy can be got by using exact matrix diagonalization techniques. We analyze and discuss the calculation results in detail, which show that:(1)the ground state of the excitons and charged excitons on the ring changes with the magnetic field, showing a clear A-B oscillations. The oscillation forms are similar and the oscillation periods are the same. As the ring radius increases, in order to achieve the same magnetic flux, magnetic field strength is reduced and system oscillation period decreases. Since the kinetic energy term's weakening effect on the energy, the amplitude decreases. Coulomb interaction potential is also reduced, but gradually in the whole energy of the dominant, so that the system's ground state energy increases, A-B effects gradually disappear.(2)The excitons on elliptical ring increases with the eccentricity. The elliptical ring gets more and more flat and the size of ring decreases. In order to achieve a certain degree of flux, we need to increase the magnetic field strength and then the oscillation period gets larger. Because elliptical ring's space constraint increased, the average ring radius is smaller, Coulomb interaction potential enhanced and the ground state can be increased.Wave function gathers at both ends of the elliptical ring, which destroys the system's coherence. So A-B oscillations are not obvious.(3) The charged excitons on elliptical ring make the ground state energy of the whole system lower. Because compared with exaction, the charged excitons in the system have one more excitons kinetic energy term and two electron interaction potential.With eccentricity increasing, quantum ring gets more and more flat. In order to achieve the same magnetic flux ring size, we need to enhance the magnetic field's strength. So the oscillation period increases.With the average radius of the ring decreasing, the Coulomb interaction potential increases and the ground state energy increases.The elliptical ring's shape gets flatter and flatter, which destroys the periodic boundary conditions of wave function. And the wave function appears uneven probability on the elliptical quantum rings.All these influence the system's coherence and A-B oscillations disappear.