Impact of the valence band structure of Cu${}_2$O on excitonic spectra

Abstract

We present a method to calculate the exciton spectra of all direct semiconductors with a complex valence band structure. The Schrödinger equation is solved using a complete basis set with Coulomb Sturmian functions. This method also allows for the computation of oscillator strengths. Here we apply this method to investigate the impact of the valence band structure of cuprous oxide $\left(\mathrm{C}{\mathrm{u}}_2\mathrm{O}\right)$ on the yellow exciton spectrum. Results differ from those in [Phys. Rev. Lett. 115, 027402 (2015)]; the differences are discussed and explained. The difference between the second and third Luttinger parameter can be determined by comparisons with experiments, however, the evaluation of all three Luttinger parameters is not uniquely possible. Our results are consistent with band structure calculations. Considering also a finite momentum $\hslash K$ of the center of mass, we show that the large $K$-dependent line splitting observed for the $1S$ exciton state [Phys. Rev. Lett. 91, 107401 (2003)] is not related to an exchange interaction but rather to the complex valence band structure of $\mathrm{C}{\mathrm{u}}_2\mathrm{O}$.

Some corrections and improvements. Accepted for publication in Phys. Rev. B

References in corpus (7)

• 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
• Coulomb-Sturmian basis for the nuclear many-body problem
• Optical Properties of Rydberg Excitons and Polaritons
• Linewidths in excitonic absorption spectra of cuprous oxide

Cited by in corpus (36)

• Scaling laws of Rydberg excitons
• High resolution study of the yellow excitons in Cu${}_2$O subject to an electric field
• The even exciton series in Cu${}_2$O
• Interaction of Rydberg Excitons in Cuprous Oxide with Phonons and Photons: Optical Linewidth and Polariton Effect
• Magnetoexcitons in cuprous oxide
• Electrooptical Properties of Rydberg Excitons
• Interaction of charged impurities and Rydberg excitons in cuprous oxide
• Magnetoexcitons break antiunitary symmetries
• GOE-GUE-Poisson transitions in the nearest neighbor spacing distribution of magnetoexcitons
• Rydberg systems in parallel electric and magnetic fields: an improved method for finding exceptional points
• Green exciton series in cuprous oxide
• Exciton-polaritons in cuprous oxide: Theory and comparison with experiment
• Topological spin phases of trapped Rydberg excitons in Cu${}_2$O
• Excitonic giant-dipole potentials in cuprous oxide
• Interseries transitions between Rydberg excitons in Cu${}_2$O
• Magneto-Stark-effect of yellow excitons in cuprous oxide
• $K$ dependent exchange interaction of the $1S$ ortho exciton in Cu${}_2$O
• Exchange interaction in the yellow exciton series of cuprous oxide
• Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics
• Second Harmonic Generation of cuprous oxide in magnetic fields
• Exciton mass and exciton spectrum in the cuprous oxide
• Rydberg excitons in electric and magnetic fields obtained with the complex-coordinate-rotation method
• Energy states of Rydberg excitons in finite crystals: From weak to strong confinement
• Exciton-phonon interaction breaking all antiunitary symmetries in external magnetic fields
• 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
• Resonance energies and linewidths of Rydberg excitons in Cu${}_2$O quantum wells
• Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields
• 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
• Rydberg excitons in cuprous oxide: A two-particle system with classical chaos
• Quantum defects of Rydberg excitons in cuprous oxide: A semiclassical spherical model
• Eigenenergies of excitonic giant-dipole states in cuprous oxide