Impact of the valence band structure of Cu$_{2}$O on excitonic spectra

TL;DR

This paper introduces a comprehensive method to calculate excitonic spectra in semiconductors with complex valence bands, applied specifically to Cu₂O, revealing the influence of valence band structure on exciton properties and spectral features.

Contribution

The paper develops a new computational approach using Coulomb Sturmian functions to analyze excitonic spectra considering complex valence band structures, specifically applied to Cu₂O.

Findings

Differences from previous exciton spectrum calculations are identified and explained.

The valence band structure significantly influences excitonic spectral features.

Large K-dependent line splitting is attributed to valence band complexity, not exchange interactions.

Abstract

We present a method to calculate the exciton spectra of all direct semiconductors with a complex valence band structure. The Schr\"odinger equation is solved using a complete basis set with Coulomb Sturmian functions. This method also allows for the computation of oscillator strengths. Here we apply this method to investigate the impact of the valence band structure of cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ on the yellow exciton spectrum. Results differ from those in [Phys. Rev. Lett. 115, 027402 (2015)]; the differences are discussed and explained. The difference between the second and third Luttinger parameter can be determined by comparisons with experiments, however, the evaluation of all three Luttinger parameters is not uniquely possible. Our results are consistent with band structure calculations. Considering also a finite momentum $\hbar K$ of the center of mass, we show that the large $K$-dependent line splitting observed for the $1S$ exciton state [Phys. Rev. Lett. 91, 107401 (2003)] is not related to an exchange interaction but rather to the complex valence band structure of $\mathrm{Cu_{2}O}$.