Renormalization of the 3D exciton spectrum by the disorder

TL;DR

This paper investigates how short-range disorder affects the excited states of 3D excitons, revealing a disorder-induced energy shift, level splitting, and an analogy to the Lamb shift, with implications for exciton spectrum renormalization.

Contribution

It demonstrates that short-scale disorder causes a significant down-shift and splitting of exciton levels, providing a microscopic understanding of disorder effects on exciton spectra.

Findings

Short-range disorder causes a parametric down-shift of exciton levels.

Disorder lifts degeneracy, leading to splitting of S and P exciton levels.

The disorder-induced splitting is analogous to the Lamb shift in QED.

Abstract

Effect of short-range disorder on the excited states of the exciton is studied. Disorder causes an obvious effect of broadening. Microscopically, an exciton, as an entity, is scattered by the large-scale disorder fluctuations. Much less trivial is that short-scale fluctuations, with a period of the order of the Bohr radius, cause a well-defined down-shift of the exciton levels. We demonstrate that this shift exceeds the broadening parametrically and study the dependence of this shift on the orbital number. Difference of the shifts for neighboring levels leads to effective renormalization of the Bohr energy. Most remarkable effect is the disorder-induced splitting of S and P exciton levels. The splitting originates from the fact that disorder lifts the accidental degeneracy of the hydrogen-like levels. The draw an analogy between this splitting and the Lamb shift in quantum electrodynamics.