- Open Access
Impact of the valence band on Rydberg excitons in cuprous oxide quantum wells
Phys. Rev. B 113, 115413 – Published 12 March, 2026
DOI: https://doi.org/10.1103/1yqx-syzy
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.
Physics Subject Headings (PhySH)
Article Text
References (63)
- T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, Giant Rydberg excitons in the copper oxide , Nature (London) 514, 343 (2014).
- F. Schweiner, J. Main, M. Feldmaier, G. Wunner, and C. Uihlein, Impact of the valence band structure of on excitonic spectra, Phys. Rev. B 93, 195203 (2016).
- J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, High-resolution study of the yellow excitons in subject to an electric field, Phys. Rev. B 95, 035210 (2017).
- L. Butov, Excitonic devices, Superlattices Microstruct. 108, 2 (2017).
- D. H. Meyer, Z. A. Castillo, K. C. Cox, and P. D. Kunz, Assessment of Rydberg atoms for wideband electric field sensing, J. Phys. B: At. Mol. Opt. Phys. 53, 034001 (2020).
- M. A. Chukeev, S. Zheng, E. S. Khramtsov, I. V. Ignatiev, S. A. Eliseev, V. A. Lovtcius, Y. P. Efimov, and M. A. Lozhkin, Excitonic sensor of electric field in quantum-well heterostructures, Phys. Rev. B 109, 235305 (2024).
- G. Grosso, J. Graves, A. T. Hammack, A. A. High, L. V. Butov, M. Hanson, and A. C. Gossard, Excitonic switches operating at around 100 K, Nat. Photon. 3, 577 (2009).
- P. Andreakou, S. V. Poltavtsev, J. R. Leonard, E. V. Calman, M. Remeika, Y. Y. Kuznetsova, L. V. Butov, J. Wilkes, M. Hanson, and A. C. Gossard, Optically controlled excitonic transistor, Appl. Phys. Lett. 104, 091101 (2014).
- J. Thewes, J. Heckötter, T. Kazimierczuk, M. Aßmann, D. Fröhlich, M. Bayer, M. A. Semina, and M. M. Glazov, Observation of high angular momentum excitons in cuprous oxide, Phys. Rev. Lett. 115, 027402 (2015).
- F. Schöne, S.-O. Krüger, P. Grünwald, H. Stolz, S. Scheel, M. Aßmann, J. Heckötter, J. Thewes, D. Fröhlich, and M. Bayer, Deviations of the exciton level spectrum in from the hydrogen series, Phys. Rev. B 93, 075203 (2016).
- F. Schweiner, J. Main, and G. Wunner, Linewidths in excitonic absorption spectra of cuprous oxide, Phys. Rev. B 93, 085203 (2016).
- F. Schweiner, J. Main, G. Wunner, M. Freitag, J. Heckötter, C. Uihlein, M. Aßmann, D. Fröhlich, and M. Bayer, Magnetoexcitons in cuprous oxide, Phys. Rev. B 95, 035202 (2017).
- P. Rommel, F. Schweiner, J. Main, J. Heckötter, M. Freitag, D. Fröhlich, K. Lehninger, M. Aßmann, and M. Bayer, Magneto-Stark effect of yellow excitons in cuprous oxide, Phys. Rev. B 98, 085206 (2018).
- J. Heckötter, M. Freitag, D. Fröhlich, M. Aßmann, M. Bayer, M. A. Semina, and M. M. Glazov, Dissociation of excitons in by an electric field, Phys. Rev. B 98, 035150 (2018).
- J. Heckötter, A. Farenbruch, D. Fröhlich, M. Aßmann, D. Yakovlev, M. Bayer, M. Semina, M. Glazov, P. Rommel, J. Ertl, J. Main, and H. Stolz, The energy level spectrum of the yellow excitons in cuprous oxide, Phys. Rep. 1100, 1 (2025).
- E. F. Gross and N. A. Karryev, The light absorption by copper oxide in the infrared and visible spectrum, Sov. Phys. Dokl. USSR Acad. Sci. 84, 261 (1952).
- E. F. Gross and N. A. Karryev, Optical spectrum of an exciton, Sov. Phys. Dokl. USSR Acad. Sci. 84, 471 (1952).
- C. Uihlein, D. Fröhlich, and R. Kenklies, Investigation of exciton fine structure in , Phys. Rev. B 23, 2731 (1981).
- J. H. Davies, The Physics of Low-Dimensional Semiconductors: An Introduction (Cambridge University Press, New York, 1998).
- Z. I. Alferov, The history and future of semiconductor heterostructures, Semiconductors 32, 1 (1998).
- A. L. Efros and M. Rosen, The electronic structure of semiconductor nanocrystals, Annu. Rev. Mater. Res. 30, 475 (2000).
- A. L. Efros and L. E. Brus, Nanocrystal quantum dots: From discovery to modern development, ACS Nano 15, 6192 (2021).
- S. A. Lynch, C. Hodges, S. Mandal, W. Langbein, R. P. Singh, Liam A. P. Gallagher, J. D. Pritchett, D. Pizzey, J. P. Rogers, C. S. Adams, and Matthew P. A. Jones, Rydberg excitons in synthetic cuprous oxide , Phys. Rev. Mater. 5, 084602 (2021).
- J. DeLange, K. Barua, A. S. Paul, H. Ohadi, V. Zwiller, S. Steinhauer, and H. Alaeian, Highly-excited Rydberg excitons in synthetic thin-film cuprous oxide, Sci. Rep. 13, 16881 (2023).
- M. Takahata, K. Tanaka, and N. Naka, Nonlocal optical response of weakly confined excitons in mesoscopic films, Phys. Rev. B 97, 205305 (2018).
- M. Takahata, K. Tanaka, and N. Naka, Superradiance-to-polariton crossover of Wannier excitons with multiple resonances, Phys. Rev. Lett. 121, 173604 (2018).
- G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, Exciton binding energy in quantum wells, Phys. Rev. B 26, 1974 (1982).
- E. Ivchenko, Optical Spectroscopy of Semiconductor Nanostructures (Alpha Science, Harrow, 2005).
- E. S. Khramtsov, P. A. Belov, P. S. Grigoryev, I. V. Ignatiev, S. Y. Verbin, Y. P. Efimov, S. A. Eliseev, V. A. Lovtcius, V. V. Petrov, and S. L. Yakovlev, Radiative decay rate of excitons in square quantum wells: Microscopic modeling and experiment, J. Appl. Phys. 119, 184301 (2016).
- L. C. Andreani, F. Tassone, and F. Bassani, Radiative lifetime of free excitons in quantum wells, Solid State Commun. 77, 641 (1991).
- P. A. Belov, F. Morawetz, S. O. Krüger, N. Scheuler, P. Rommel, J. Main, H. Giessen, and S. Scheel, Energy states of Rydberg excitons in finite crystals: From weak to strong confinement, Phys. Rev. B 109, 235404 (2024).
- L. Kühner, P. Rommel, J. Main, S. Scheel, and P. A. Belov, Wave functions and oscillator strengths of Rydberg excitons in cuprous oxide quantum wells, Phys. Rev. B 112, 075409 (2025).
- D. Ziemkiewicz, G. Czajkowski, K. Karpiński, and S. Zielińska-Raczyńska, Rydberg magnetoexcitons in quantum wells, Phys. Rev. B 103, 035305 (2021).
- D. Ziemkiewicz, G. Czajkowski, K. Karpiński, and S. Zielińska-Raczyńska, Electro-optical properties of excitons in quantum wells. I. Discrete states, Phys. Rev. B 104, 075303 (2021).
- H. Feshbach, Unified theory of nuclear reactions, Ann. Phys. 5, 357 (1958).
- D. A. Broido, E. S. Koteles, C. Jagannath, and J. Y. Chi, Resonance broadening of the light-hole exciton in GaAs/ quantum wells, Phys. Rev. B 37, 2725 (1988).
- A. Pasquarello and L. C. Andreani, Variational calculation of Fano linewidth: Application to excitons in quantum wells, Phys. Rev. B 44, 3162 (1991).
- P. A. Belov, An estimate for the nonradiative linewidths of the quasibound electron-hole pairs in narrow quantum wells, Semiconductors 53, 2049 (2019).
- N. Scheuler, P. Rommel, J. Main, and P. A. Belov, Resonance energies and linewidths of Rydberg excitons in quantum wells, Phys. Rev. B 109, 165440 (2024).
- A. Aslanidis, J. Main, P. Rommel, S. Scheel, and P. A. Belov, Bound states in the continuum in cuprous oxide quantum wells, Phys. Rev. B 111, L121103 (2025).
- C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljčć, Bound states in the continuum, Nat. Rev. Mater. 1, 16048 (2016).
- L. Happ and P. Naidon, Stabilization of three-body resonances to bound states in a continuum, Phys. Rev. A 113, 032203 (2026).
- A Practical Guide to Splines, edited by C. De Boor (Springer, New York, 2001).
- H. Bachau, E. Cormier, P. Decleva, J. E. Hansen, and F. Martín, Applications of B-splines in atomic and molecular physics, Rep. Prog. Phys. 64, 1815 (2001).
- R. Y. Kezerashvili, Few-body systems in condensed matter physics, Few-Body Syst. 60, 52 (2019).
- N. S. Rytova, The screened potential of a point charge in a thin film, Moscow Uni. Phys. Bull. 22, 18 (1967) [Vestnik Moskovskogo Universiteta. Fiz. 22, 30 (1967)].
- L. V. Keldysh, Coulomb interaction in thin semiconductor and semimetal films, JETP Lett. 29, 658 (1979) [Pis'ma Zh. Eksp. Teor. Fiz. 29, 716 (1979)].
- A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, Exciton binding energy and nonhydrogenic Rydberg series in monolayer , Phys. Rev. Lett. 113, 076802 (2014).
- L. S. R. Cavalcante, A. Chaves, B. Van Duppen, F. M. Peeters, and D. R. Reichman, Electrostatics of electron-hole interactions in van der Waals heterostructures, Phys. Rev. B 97, 125427 (2018).
- R. Y. Kezerashvili, Trions in three-, two- and one-dimensional materials, in Recent Progress in Few-Body Physics, edited by N. A. Orr, M. Ploszajczak, F. M. Marqués, and J. Carbonell (Springer International Publishing, Cham, 2020), pp. 827–831.
- M. N. Brunetti, O. L. Berman, and R. Y. Kezerashvili, Optical properties of anisotropic excitons in phosphorene, Phys. Rev. B 100, 155433 (2019).
- N. V. Leppenen, L. E. Golub, and E. L. Ivchenko, Exciton oscillator strength in two-dimensional Dirac materials, Phys. Rev. B 102, 155305 (2020).
- J. M. Luttinger, Quantum theory of cyclotron resonance in semiconductors: General theory, Phys. Rev. 102, 1030 (1956).
- K. Suzuki and J. C. Hensel, Quantum resonances in the valence bands of germanium. I. Theoretical considerations, Phys. Rev. B 9, 4184 (1974).
- J. W. Hodby, T. E. Jenkins, C. Schwab, H. Tamura, and D. Trivich, Cyclotron resonance of electrons and of holes in cuprous oxide, , J. Phys. C 9, 1429 (1976).
- Landolt-Börnstein - Group III Condensed Matter, edited by O. Madelung, U. Rössler and M. Schulz (Springer-Verlag, Berlin Heidelberg, 1998).
- G. Koster, J. Dimmock, R. Wheeler, and H. Statz, Properties of the Thirty-two Point Groups, Massachusetts Institute of Technology Press Research Monograph (M.I.T. Press, Cambridge, 1963).
- F. Schweiner, J. Main, G. Wunner, and C. Uihlein, Even exciton series in , Phys. Rev. B 95, 195201 (2017).
- F. Schweiner, J. Ertl, J. Main, G. Wunner, and C. Uihlein, Exciton-polaritons in cuprous oxide: Theory and comparison with experiment, Phys. Rev. B 96, 245202 (2017).
- R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, 1998).
- C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del Río, M. Wiebe, P. Peterson, P. Gérard-Marchant, et al., Array programming with NumPy, Nature (London) 585, 357 (2020).
- M. French, R. Schwartz, H. Stolz, and R. Redmer, Electronic band structure of by spin density functional theory, J. Phys.: Condens. Matter 21, 015502 (2009).
- A. Chaves, J. G. Azadani, H. Alsalman, D. R. da Costa, R. Frisenda, A. J. Chaves, S. H. Song, Y. D. Kim, D. He, J. Zhou, A. Castellanos-Gomez, F. M. Peeters, Z. Liu, C. L. Hinkle, S.-H. Oh, P. D. Ye, S. J. Koester, Y. H. Lee, P. Avouris, X. Wang, et al., Bandgap engineering of two-dimensional semiconductor materials, npj 2D Mater. Appl. 4, 29 (2020).