Fermi Edge Singularities in the Mesoscopic Regime: II. Photo-absorption Spectra

TL;DR

This paper investigates how Fermi edge singularities manifest in the photo-absorption spectra of mesoscopic systems, revealing deviations from bulk behavior due to quantum coherence effects and system size, with implications for experimental observation.

Contribution

It introduces a theoretical model for mesoscopic Fermi edge singularities considering system size and coherence, predicting modified spectral features distinct from macroscopic metals.

Findings

Rounded K-edge in metals becomes peaked in mesoscopic systems

Fluctuations due to coherence significantly affect the spectra

The model accounts for the effect of a bound state created by the core hole

Abstract

We study Fermi edge singularities in photo-absorption spectra of generic mesoscopic systems such as quantum dots or nanoparticles. We predict deviations from macroscopic-metallic behavior and propose experimental setups for the observation of these effects. The theory is based on the model of a localized, or rank one, perturbation caused by the (core) hole left behind after the photo-excitation of an electron into the conduction band. The photo-absorption spectra result from the competition between two many-body responses, Anderson's orthogonality catastrophe and the Mahan-Nozieres-DeDominicis contribution. Both mechanisms depend on the system size through the number of particles and, more importantly, fluctuations produced by the coherence characteristic of mesoscopic samples. The latter lead to a modification of the dipole matrix element and trigger one of our key results: a rounded K-edge typically found in metals will turn into a (slightly) peaked edge on average in the mesoscopic regime. We consider in detail the effect of the "bound state" produced by the core hole.