The phonon assisted absorption of excitons in Cu${}_2$O

Abstract

The basic theoretical foundation for the modelling of phonon assisted absorption spectra in direct bandgap semiconductors, introduced by Elliott 60 years ago using second order perturbation theory, results in a square root shaped dependency close to the absorption edge. A careful analysis of the experiments reveals that for the yellow S excitons in Cu${}_2$O the lineshape does not follow that square root dependence. The reexamination of the theory shows that the basic assumptions of constant matrix elements and constant energy denominators is invalid for semiconductors with dominant exciton effects like Cu${}_2$O, where the phonon assisted absorption proceeds via intermediate exciton states. The overlap between these and the final exciton states strongly determines the dependence of the absorption on the photon energy. To describe the experimental observed line shape of the indirect absorption of the yellow S exciton states we find it necessary to assume a momentum dependent deformation potential for the optical phonons.

References in corpus (11)

• Giant Rydberg Excitons in Cuprous Oxide
• Observation of high angular momentum excitons in cuprous oxide
• Deviations of the exciton level spectrum in cuprous oxide from the hydrogen series
• Auger decay of degenerate and Bose-condensed excitons in Cu${}_2$O
• High resolution study of the yellow excitons in Cu${}_2$O subject to an electric field
• The even exciton series in Cu${}_2$O
• Signatures of Quantum Coherence in Rydberg Excitons
• Electrooptical Properties of Rydberg Excitons
• Linewidths in excitonic absorption spectra of cuprous oxide
• Magnetoexcitons break antiunitary symmetries
• Solution of the momentum-space Schrödinger equation for bound states of the N-dimensional Coulomb problem (revisited)

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• Electromagnetically induced transparency with Cu${}_2$O excitons in the presence of phonon coupling
• Exciton-polaritons in cuprous oxide: Theory and comparison with experiment
• Plasma-enhanced interaction and optical nonlinearities of Cu${}_2$O Rydberg excitons
• Dynamics of incoherent exciton formation in Cu${}_2$O: Time- and angle-resolved photoemission spectroscopy
• Temperature Study of Rydberg Exciton Optical Properties in Cu2O
• Scrutinizing the Debye plasma model: Rydberg excitons unravel the properties of low-density plasmas in semiconductors
• Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics
• Coherent transfer matrix analysis of the transmission spectra of Rydberg excitons in Cuprous Oxide
• Quantum light from lossy semiconductor Rydberg excitons
• Asymmetric Rydberg blockade of giant excitons in Cuprous Oxide