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

TL;DR

This paper develops a comprehensive theoretical framework for exciton-polaritons in cuprous oxide, incorporating complex band structures and interactions, and compares the predictions with experimental data on polariton spectra and properties.

Contribution

It extends the Hamiltonian to include full valence band structure, exchange, and central-cell effects for finite momentum, and models anisotropic polariton dispersion in cuprous oxide.

Findings

Complex polariton spectra for different orientations of K.

Strong mixing of exciton states observed.

Good agreement with experimental measurements of splitting and dispersion.

Abstract

The observation of giant Rydberg excitons in cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ up to a principal quantum number of $n=25$ by T.~Kazimierczuk \emph{et al.} [Nature \textbf{514}, 343, (2014)] inevitably raises the question whether these quasi-particles must be described within a multi-polariton framework since excitons and photons are always coupled in the solid. In this paper we present the theory of exciton-polaritons in $\mathrm{Cu_{2}O}$. 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 \emph{et al.} [Phys.~Rev.~B \textbf{95}, 195201, (2017)], for finite values of the exciton momentum $\hbar K$. We derive formulas to calculate not only dipole but also quadrupole oscillator strengths when using the complete basis of F.~Schweiner \emph{et al.}. Very complex polariton spectra for the three orientations of $\boldsymbol{K}$ 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 $5\times 5$ 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 $\boldsymbol{K}$. We especially discuss the dispersions for $\boldsymbol{K}$ being oriented in the planes perpendicular to $[1\bar{1}0]$ 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.