Impurity center in a semiconductor quantum ring in the presence of crossed magnetic and electric fields

An analytical approach to the problem of an impurity electron positioned in a quantum ring (QR) in the presence of crossed axially directed homogeneous magnetic and radially directed electric fields is developed. The quantum well wire and quantum disk regimes of the QR and weak and strong magnetic fields as well as low and high QR’s are considered. The analytical dependences of the total and binding energies of the impurity electron on the strengths of the external fields, the radii, and height of the QR and the position of the impurity center within the QR are obtained. It is shown that if the QR confinement and/or magnetic field increase, the binding energy also increases. The binding energy reaches a maximum for the impurity center positioned at the midplane perpendicular to the symmetry axis of the QR. For the quantum disk regime the binding energy decreases while shifting the impurity from the internal surface towards the external one. The effects due to the confinement and magnetic field can be balanced by those produced by a radially directed electric field. For a relatively narrow QR the impurity influences the oscillations of the ground electron energy as a function of the magnetic field only marginally (magnetostatic Aharonov-Bohm effect). Estimates of the linear electron densities needed to bring in balance the blue energy shifts caused by the ring confinement and magnetic fields and the changes of the binding energy induced by the displacement of the impurity are made for parameters of a GaAs QR.