Impurity center in a semiconductor quantum ring in the presence of a radial electric field

TL;DR

This paper investigates how a strong radial electric field affects the binding energy of an impurity electron in a semiconductor quantum ring, providing analytical and numerical insights into the control of impurity states.

Contribution

It develops both analytical and numerical methods to analyze impurity electron binding energies in quantum rings under radial electric fields, revealing controllable energy maxima and electric field effects.

Findings

Binding energy shows a maximum at a specific impurity position.

Maximal binding energy increases with electric field strength.

Electric field inversion effect can be achieved.

Abstract

The problem of an impurity electron in a quantum ring (QR) in the presence of a radially directed strong external electric field is investigated in detail. Both an analytical and a numerical approach to the problem are developed. The analytical investigation focuses on the regime of a strong wire-electric field compared to the electric field due to the impurity. An adiabatic and quasiclassical approximation is employed. The explicit dependencies of the binding energy of the impurity electron on the electric field strength, parameters of the QR and position of the impurity within the QR are obtained. Numerical calculations of the binding energy based on a finite-difference method in two and three dimensions are performed for arbitrary strengths of the electric field. It is shown that the binding energy of the impurity electron exhibits a maximum as a function of the radial position of the impurity that can be shifted arbitrarily by applying a corresponding wire-electric field. The maximal binding energy monotonically increases with increasing electric field strength. The inversion effect of the electric field is found to occur. An increase of the longitudinal displacement of the impurity typically leads to a decrease of the binding energy. Results for both low- and high-quantum rings are derived and discussed. Suggestions for an experimentally accessible set-up associated with the GaAs/GaAlAs QR are provided.