$K$ dependent exchange interaction of the $1S$ ortho exciton in Cu${}_2$O

Abstract

When treating the exchange interaction of Wannier excitons, usually only the leading terms of the analytic and the nonanalytic exchange interaction are considered. However, higher order terms can lead to a splitting of exciton states, for which reason a splitting of the $1S$~exciton in cuprous oxide $\left(\mathrm{C}{\mathrm{u}}_2\mathrm{O}\right)$ depending on its total momentum $\hslash K$ has been attributed to a $K$ dependent analytic exchange interaction by Dasbach et al [Phys. Rev. Lett. 91, 107401 (2003)]. Going beyond the common treatment of the exchange interaction, we derive the correct expressions for these $K$ dependent higher order terms using $\mathbf{k}\cdot \mathbf{p}$ perturbation theory. We prove that the appearance of a $K$ dependent exchange interaction is inseparably connected with a $K$ independent exchange interaction of $P$ and $D$ excitons. We estimate the magnitude of these terms for $\mathrm{C}{\mathrm{u}}_2\mathrm{O}$ from microscopic calculations and show that they are far too small to explain the observed $K$ dependent splitting. Instead, this splitting has to be treated in terms of the dispersion of the excitons. Furthermore, we prove the occurence of a coupling between longitudinal and transverse excitons in $\mathrm{C}{\mathrm{u}}_2\mathrm{O}$ due to the $K$ dependent nonanalytic exchange interaction.

arXiv commentAccepted for publication in Phys. Rev. B

References in corpus (9)

• Giant Rydberg Excitons in Cuprous Oxide
• Observation of high angular momentum excitons in cuprous oxide
• Fine structure of excitons in Cu${}_2$O
• Deviations of the exciton level spectrum in cuprous oxide from the hydrogen series
• Impact of the valence band structure of Cu${}_2$O on excitonic spectra
• Electrooptical Properties of Rydberg Excitons
• Optical Properties of Rydberg Excitons and Polaritons
• Linewidths in excitonic absorption spectra of cuprous oxide
• Rydberg systems in parallel electric and magnetic fields: an improved method for finding exceptional points

Cited by in corpus (9)

• High resolution study of the yellow excitons in Cu${}_2$O subject to an electric field
• The even exciton series in Cu${}_2$O
• Magnetoexcitons in cuprous oxide
• Magnetooptical Properties of Rydberg Excitons - Center-of-Mass Quantization Approach
• Magnetoexcitons break antiunitary symmetries
• GOE-GUE-Poisson transitions in the nearest neighbor spacing distribution of magnetoexcitons
• Exciton-polaritons in cuprous oxide: Theory and comparison with experiment
• Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics
• Exciton-phonon interaction breaking all antiunitary symmetries in external magnetic fields