Electronic structure of a quantum ring in a lateral electric field

Abstract

The electronic states of novel semiconductor quantum rings (QR's) under applied lateral electric fields are theoretically investigated for different values of the ratio ${r}_{2}{/r}_{1},$ where ${r}_{2}$ ${(r}_{1})$ is the outer (inner) radius of the ring. The eigenstates and eigenvalues of the Hamiltonian are obtained from a direct matrix diagonalization scheme. Numerical calculations are performed for a hard-wall confinement potential and the electronic states are obtained as a function of the electric field and the ratio ${r}_{2}{/r}_{1}.$ An anomalous behavior in the energy vs. electric-field fan plot due to the break of symmetry is predicted. Analytical expressions for the energy levels, valid in the weak-field limit, are presented and compared with the exact numerical solutions. The effects of decreasing symmetry and mixing on the energy levels and wave functions of the QR due to the applied electric field are also studied. The oscillator strengths of optical transitions between valence and conduction levels are reported as a function of the electric field.