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 exciton in cuprous oxide depending on its total momentum has been attributed to a -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 -dependent higher-order terms using perturbation theory. We prove that the appearance of a -dependent exchange interaction is inseparably connected with a -independent exchange interaction of and excitons. We estimate the magnitude of these terms for from microscopic calculations and show that they are far too small to explain the observed -dependent splitting. Instead, this splitting has to be treated in terms of the dispersion of the excitons. Furthermore, we prove the occurrence of a coupling between longitudinal and transverse excitons in due to the -dependent nonanalytic exchange interaction.
- Received 1 July 2016
- Revised 9 August 2016
DOI:https://doi.org/10.1103/PhysRevB.94.115201
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