Commutation technique for an exciton photocreated close to a metal

TL;DR

This paper proves that the exciton diagram technique for analyzing exciton absorption near a metal is valid at all interaction orders using a commutation method, extending previous second-order approximations.

Contribution

It introduces a commutation technique to rigorously validate the exciton diagram approach for all interaction orders.

Findings

Exciton diagram method is valid at any order of interaction.

The commutation technique confirms previous second-order approximations.

Enhanced understanding of exciton-metal interactions in absorption spectra.

Abstract

Recently, we have derived the changes in the absorption spectrum of an exciton when this exciton is photocreated close to a metal. The resolution of this problem -- which has similarities with Fermi edge singularities -- has been made possible by the introduction of ``exciton diagrams''. The validity of this procedure relied on a dreadful calculation based on standard free electron and free hole diagrams, with the semiconductor-metal interaction included at second order only, and its intuitive extention to higher orders. Using the commutation technique we recently introduced to deal with interacting excitons, we are now able to \emph{prove} that this exciton diagram procedure is indeed valid at any order in the interaction. =