The even exciton series in Cu${}_2$O

Abstract

In $\mathrm{C}{\mathrm{u}}_2\mathrm{O}$ parity is a good quantum number and thus the exciton spectrum falls into two parts: The dipole-active exciton states of negative parity and odd angular momentum, which can be observed in one-photon absorption (${\Gamma }_4^{-}$ symmetry) and the exciton states of positive parity and even angular momentum, which can be observed in two-photon absorption (${\Gamma }_5^{+}$ symmetry). The unexpected observation of $D$ excitons in two-photon absorption and of $F$ excitons in one-photon absorption has given evidence that the dispersion properties of the ${\Gamma }_5^{+}$ orbital valence band is giving rise to a coupling of the yellow and green exciton series. In this paper we show that the even and odd parity exciton system can be consistently described within the same theoretical approach. However, the Hamiltonian of the even parity system needs, in comparison to the odd exciton case, modifications to account for the very small radius of the $1S$ exciton. In the presented treatment we take special care of the central-cell corrections, which comprise a reduced screening of the Coulomb potential at distances comparable to the polaron radius, the exchange interaction being responsible for the exciton splitting into ortho and para states, and the inclusion of terms in the fourth power of $p$ in the kinetic energy. Since the yellow $1S$ exciton state is coupled to all other states of positive parity, we show how the central-cell corrections affect the whole even exciton series. The close resonance of the $1S$ green exciton with states of the yellow exciton series has a strong impact on the energies and oscillator strengths of all implied states. The consistency between theory and experiment with respect to energies and oscillator strengths for the even and odd exciton system in $\mathrm{C}{\mathrm{u}}_2\mathrm{O}$ is a convincing proof for the validity of the applied theory.

References in corpus (10)

• Giant Rydberg Excitons in Cuprous Oxide
• Observation of high angular momentum excitons in cuprous oxide
• Coulomb-Sturmian basis for the nuclear many-body problem
• Impact of the valence band structure of Cu${}_2$O on excitonic spectra
• High resolution study of the yellow excitons in Cu${}_2$O subject to an electric field
• Magnetoexcitons in cuprous oxide
• Electrooptical Properties of Rydberg Excitons
• Magnetooptical Properties of Rydberg Excitons - Center-of-Mass Quantization Approach
• Magnetoexcitons break antiunitary symmetries
• $K$ dependent exchange interaction of the $1S$ ortho exciton in Cu${}_2$O

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• Giant Rydberg excitons in Cu${}_2$O probed by photoluminescence excitation spectroscopy
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• The phonon assisted absorption of excitons in Cu${}_2$O
• GOE-GUE-Poisson transitions in the nearest neighbor spacing distribution of magnetoexcitons
• Green exciton series in cuprous oxide
• Exciton-polaritons in cuprous oxide: Theory and comparison with experiment
• Dynamics of incoherent exciton formation in Cu${}_2$O: Time- and angle-resolved photoemission spectroscopy
• Electro-optical properties of Cu${}_2$O in the regime of Franz-Keldysh oscillations
• High resolution nanosecond spectroscopy of even-parity Rydberg excitons in Cu${}_2$O
• Interseries transitions between Rydberg excitons in Cu${}_2$O
• Magneto-Stark-effect of yellow excitons in cuprous oxide
• Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics
• Exchange interaction in the yellow exciton series of cuprous oxide
• Temperature Study of Rydberg Exciton Optical Properties in Cu2O
• Second Harmonic Generation of cuprous oxide in magnetic fields
• Exciton mass and exciton spectrum in the cuprous oxide
• Energy states of Rydberg excitons in finite crystals: From weak to strong confinement
• Rydberg excitons in electric and magnetic fields obtained with the complex-coordinate-rotation method
• Exciton-phonon interaction breaking all antiunitary symmetries in external magnetic fields
• Coherent transfer matrix analysis of the transmission spectra of Rydberg excitons in Cuprous Oxide
• Signatures of exciton orbits in quantum mechanical recurrence spectra of Cu${}_2$O
• Interseries dipole transitions from yellow to green excitons in cuprous oxide
• Classical and semiclassical description of Rydberg excitons in cuprous oxide
• Classical dynamics and semiclassical analysis of excitons in cuprous oxide
• Gaussian-process-regression-based method for the localization of exceptional points in complex resonance spectra
• Bound states in the continuum in cuprous oxide quantum wells
• Wavefunctions and oscillator strengths of Rydberg excitons in cuprous oxide quantum wells
• Quantum defects of Rydberg excitons in cuprous oxide: A semiclassical spherical model