Renormalised perturbative series for the impurity levels in a quantum well

TL;DR

This paper develops renormalised perturbative series to analytically study impurity energy levels in deep quantum wells, revealing maximal binding energies and wave function deformation at specific well widths.

Contribution

It introduces a novel analytical approach using renormalised perturbative series for impurity levels in quantum wells, applicable to various nanostructures.

Findings

Maximal binding energy occurs at a specific well width L_c.

Wave function deformation to a quasi-two-dimensional form is observed.

Results are extendable to quantum wires, dots, and multiwell structures.

Abstract

The energy levels of an impurity center in a deep quantum well of width L and depth g are studied analytically . Renormalised perturbative series are constructed in the regions g L^ << 1 and g L^2 >> 1. Maximal binding energy and wave function deformation to a quasi-twodimensional function are found to occur at a certain L_c satisfying sqrt{g} L_c ~ 1. Similar results may be obtained for the impurity in a quantum wire, in a dot or in a multiwell structure.