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arXiv:2511.20441

Impact of the valence band on Rydberg excitons in cuprous oxide quantum wells

Niklas Scheuler, Jörg Main, Patric Rommel, Frieder Pfeiffer, Stefan Scheel, Pavel A. Belov

cond-mat.mes-hallquant-phSubmitted Nov 25, 2025• Announced Nov 26, 2025

v1 · Nov 25, 2025 v2 · Feb 17, 2026

Abstract

The complex valence band structure of bulk cuprous oxide necessitates going beyond the parabolic approximation to precisely estimate exciton binding energies. The same is true for excitons in cuprous oxide quantum wells, for which many effects have been obtained so far only qualitatively within a hydrogenlike two-band model. Here, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells based on the Luttinger-Kohn model, taking into account the full complex valence band structure. Symmetry properties of the system are discussed. Numerical results based on the diagonalization of the Hamiltonian using B-spline functions reveal the energy shifts and the lifting of degeneracies due to the nondiagonal coupling terms of the complex valence band. The relative oscillator strengths of the excitonic transitions induced by circularly polarized light are also calculated.

Journal reference: Phys. Rev. B 113, 115413 (2026)
DOI: 10.1103/1yqx-syzy
Comments: 13 pages, 5 figures

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The complex valence band structure of bulk cuprous oxide necessitates going beyond the parabolic approximation to precisely estimate exciton binding energies. The same is true for excitons in cuprous oxide quantum wells, for which many effects have been obtained so far only qualitatively within a hydrogenlike two-band model. Here, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells based on the Luttinger-Kohn model, taking into account the full complex valence band structure. Symmetry properties of the system are discussed. Numerical results based on the diagonalization of the Hamiltonian using B-spline functions reveal the energy shifts and the lifting of degeneracies due to the nondiagonal coupling terms of the complex valence band. The relative oscillator strengths of the excitonic transitions induced by circularly polarized light are also calculated.

The recent observation of excitons in highly excited states has allowed the study of Rydberg physics in cuprous oxide crystals. This opens the unique possibility to elaborate on similarities and differences between Rydberg atoms and Rydberg excitons, as done here experimentally and theoretically for quantities related to the splitting of multiplets with particular principal quantum number

n

in zero and finite electric or magnetic fields. The authors find characteristic scaling laws with

n

with some discrepancies between excitons and atoms, but surprisingly, they find mostly similarities, even though the underlying physics, such as the complex valence band structure, are quite different.

We report experimental and theoretical investigations of interacting excitons of the yellow series in cuprous oxide (Cu

_2

O) with principal quantum numbers up to by means of second harmonic generation (SHG). Using picosecond pulsed laser excitation up to 10 GW/cm

^2

peak intensity we observe a pronounced change of the spectra with increasing pump laser intensity: an energetic shift to lower absolute energies and a spectral broadening. The absolute intensities of the spectral lines scale for low powers with the square of the pump power, but saturates at higher powers. At still higher powers the SHG intensity is actually reduced. To explain these results quantitively, we developed a semi-classical theory of resonant SHG where the process of SHG is fully coherent. The excitons are assumed to be bosons interacting by a distance dependent potential giving rise to both the changes in spectral line shape and the saturation by a

\it{Rydberg}

blockade. The concomitant measurement of two-photon absorption allows to derive quantitative values for the exciton-exciton interaction. While the results agree in order of magnitude with those calculated by state-of-the art atomic-like van der Waals interaction theory, the scaling with principle quantum number is quite different. As a possible screening by an electron-hole plasma created by three-photon absorption into blue and violet band states could be ruled out, our results point toward fundamental differences between excitons and atoms.

The coherent optical response of semiconductor quantum wells is studied theoretically using the multiband semiconductor Bloch equations which include coupling of the heavy- and light-hole bands as well as many-body Coulomb effects. For the case of a two-pulse excitation scheme it is shown how the different rotational symmetries of heavy- and light-hole bands induce a strong polarization dependence of the signal in the photon echo direction. The selection rules are based on the Kane-Luttinger theory while the transition amplitudes are obtained by numerically solving the multiband semiconductor Bloch equations. In addition, the influence of valence-band mixing effects on the optical Stark effect is demonstrated.

Abstract The recent observation of high-lying Rydberg states of excitons in semiconductors with relatively high binding energy motivates exploring their applications in quantum nonlinear optics and quantum information processing. Here, we study Rydberg excitation dynamics of a mesoscopic array of excitons to demonstrate its application in simulation of quantum many-body dynamics. We show that the Z 2 -ordered phase can be reached using physical parameters available for cuprous oxide (Cu 2 O) by optimizing driving laser parameters such as duration, intensity, and frequency. In an example, we study the application of our proposed system to solving the maximum independent set problem based on the Rydberg blockade effect.

The quantum confinement of Rydberg excitons (REs) in quantum structures opens the way towards considering nonlinear interactions in such systems. We present a theoretical calculation of optical functions in the case of a nonlinear coupling between REs in a quantum well with an electromagnetic wave. Using the real density matrix approach (RDMA), the analytical expressions for a linear and nonlinear absorption are derived and numerical calculations for

{\mathrm{Cu}}_{2}\mathrm{O}

quantum wells are performed. The results indicate the conditions in which quantum well confinement states can be observed in linear and nonlinear optical spectra. The Kerr nonlinearity and self-phase modulation in such a system are studied. The effect of the Rydberg blockade and the associated optical bleaching are also discussed and confronted with available experimental data.