Direct Determination of Exciton Wave Function Amplitudes by the Momentum-Resolved Photo-Electron Emission Experiment

TL;DR

This paper demonstrates that momentum-resolved photo-electron emission experiments can directly measure the exciton wave function amplitudes in insulators, providing a new method to analyze excitonic states.

Contribution

It introduces a novel approach to determine exciton wave functions directly from photo-electron emission spectra, clarifying the underlying physical process.

Findings

PEE spectrum reflects the square of the exciton wave function amplitude.

Recoil of the hole in PEE spectra encodes exciton binding information.

Application to GaAs excitons illustrates the method's effectiveness.

Abstract

We study conceptional problems of a photo-electron emission (PEE) process from a free exciton in insulating crystals. In this PEE process, only the electron constituting the exciton is suddenly emitted out of the crystal, while the hole constituting the exciton is still left inside and forced to be recoiled back to its original valence band. This recoil on the hole is surely reflected in the spectrum of the PEE with a statistical distribution along the momentum-energy curve of the valence band. This distribution is nothing but the square of the exciton wave function amplitude, since it shows how the electron and the hole are originally bound together. Thus, the momentum-resolved PEE can directly determine the exciton wave function. These problems are clarified, taking the $\Gamma$ and the saddle point excitons in GaAs, as typical examples. New PEE experiments are also suggested.