Spectral properties of a short-range impurity in a quantum dot

TL;DR

This paper investigates how a short-range impurity affects the spectral properties of a quantum dot, providing explicit Green function expressions and analyzing the impact of impurity position and strength on the spectrum.

Contribution

It derives an explicit Green function for a quantum dot with a short-range impurity and analyzes spectral dependence on impurity parameters, revealing how to recover confinement potential from spectroscopy.

Findings

Explicit Green function obtained for the impurity system

Spectrum depends on impurity position and strength

Confinement potential can be reconstructed from spectral data

Abstract

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.