Exciton-polaritons in cuprous oxide: Theory and comparison with experiment

• Published in: Physical review. B 2017-12, Vol.96 (24), Article 245202
• Main Authors: Schweiner, Frank, Ertl, Jan, Main, Jörg, Wunner, Günter, Uihlein, Christoph
• Format: Article
• Language: English
• Subjects: Copper oxides; Excitation spectra; Excitons; Group velocity; Mathematical models; Oscillator strengths; Photons; Polaritons; Quadrupoles; Splitting
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.96.245202

The observation of giant Rydberg excitons in cuprous oxide Cu2O up to a principal quantum number of n=25 by T. Kazimierczuk et al. [Nature (London) 514, 343 (2014)] inevitably raises the question whether these quasiparticles must be described within a multipolariton framework since excitons and photons are always coupled in the solid. In this paper we present the theory of exciton-polaritons in Cu2O. To this end we extend the Hamiltonian which includes the complete valence-band structure, the exchange interaction, and the central-cell corrections effects, and which has been recently deduced by F. Schweiner et al. [Phys. Rev. B 95, 195201 (2017)], for finite values of the exciton momentum ℏK. We derive formulas to calculate not only dipole but also quadrupole oscillator strengths when using the complete basis of F. Schweiner et al., which has recently been proven as a powerful tool to calculate exciton spectra. Very complex polariton spectra for the three orientations of K along the axes [001], [110], and [111] of high symmetry are obtained and a strong mixing of exciton states is reported. The main focus is on the 1S ortho-exciton-polariton, for which pronounced polariton effects have been measured in experiments. We set up a 5×5 matrix model, which accounts for both the polariton effect and the K-dependent splitting, and which allows treating the anisotropic polariton dispersion for any direction of K. We especially discuss the dispersions for K being oriented in the planes perpendicular to [11¯0] and [111], for which experimental transmission spectra have been measured. Furthermore, we compare our results with experimental values of the K-dependent splitting, the group velocity, and the oscillator strengths of this exciton-polariton. The results are in good agreement. This proves the validity of the 5×5 matrix model as a useful theoretical model for further investigations on the 1S ortho-exciton-polariton.