Fine structure of excitons in Cu$_2$O

TL;DR

This paper investigates the complex structure of excitons in Cu$_2$O, revealing deviations from simple models and providing a detailed theoretical analysis that aligns well with experimental data.

Contribution

It introduces a self-consistent variational method incorporating band structure effects to accurately describe exciton properties in Cu$_2$O.

Findings

Exciton energies deviate from the Rydberg formula.

Total exciton mass exceeds electron and hole masses.

Triplet excitons are higher in energy than singlet excitons.

Abstract

Three experimental observations on 1s-excitons in Cu$_2$O are not consistent with the picture of the exciton as a simple hydrogenic bound state: the energies of the 1s-excitons deviate from the Rydberg formula, the total exciton mass exceeds the sum of the electron and hole effective masses, and the triplet-state excitons lie above the singlet. Incorporating the band structure of the material, we calculate the corrections to this simple picture arising from the fact that the exciton Bohr radius is comparable to the lattice constant. By means of a self-consistent variational calculation of the total exciton mass as well as the ground-state energy of the singlet and the triplet-state excitons, we find excellent agreement with experiment.