- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Shubnikov–de Haas oscillations in two-dimensional hole gases with competing cyclotron and Zeeman energy

Davide Costa, Lucas E. A. Stehouwer, Davide Degli Esposti, and Giordano Scappucci*

  • *Contact author: g.scappucci@tudelft.nl
PDF

Phys. Rev. B 113, 115418 – Published 19 March, 2026

DOI: https://doi.org/10.1103/pc57-schm

Abstract

Evaluation of the quantum lifetime in two-dimensional hole systems, together with band-structure parameters such as the effective mass and g factor, becomes challenging when competing energy scales shape Shubnnikov–de Haas oscillations in a magnetic field. Here, we overcome this challenge for holes with pseudospin Jz=±32, confined in low-disorder strained germanium quantum wells. We extract self-consistently the effective mass, g factor, and quantum lifetime, and estimate a maximum quantum mobility of 133(3)×103cm2/Vs, setting a benchmark for holes in group IV semiconductors. The high quality of the hole gas if further highlighted by observing clean fractional quantum Hall states at low magnetic field and density.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (29)

  1. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023).
  2. E. Prada, P. San-Jose, M. W. A. De Moor, A. Geresdi, E. J. H. Lee, J. Klinovaja, D. Loss, J. Nygård, R. Aguado, and L. P. Kouwenhoven, From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires, Nat. Rev. Phys. 2, 575 (2020).
  3. P. T. Coleridge, Small-angle scattering in two-dimensional electron gases, Phys. Rev. B 44, 3793 (1991).
  4. S. Das Sarma and F. Stern, Single-particle relaxation time versus scattering time in an impure electron gas, Phys. Rev. B 32, 8442 (1985).
  5. G. Scappucci, C. Kloeffel, F. A. Zwanenburg, D. Loss, M. Myronov, J.-J. Zhang, S. De Franceschi, G. Katsaros, and M. Veldhorst, The germanium quantum information route, Nat. Rev. Mater. 6, 926 (2021).
  6. R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems, Springer Tracts in Modern Physics Vol. 191 (Springer, Berlin, 2003).
  7. M. Lodari, A. Tosato, D. Sabbagh, M. A. Schubert, G. Capellini, A. Sammak, M. Veldhorst, and G. Scappucci, Light effective hole mass in undoped Ge/SiGe quantum wells, Phys. Rev. B 100, 041304(R) (2019).
  8. L. A. Terrazos, E. Marcellina, Z. Wang, S. N. Coppersmith, M. Friesen, A. R. Hamilton, X. Hu, B. Koiller, A. L. Saraiva, D. Culcer, and R. B. Capaz, Theory of hole-spin qubits in strained germanium quantum dots, Phys. Rev. B 103, 125201 (2021).
  9. P. Lawaetz, Valence-band parameters in cubic semiconductors, Phys. Rev. B 4, 3460 (1971).
  10. T. M. Lu, C. T. Harris, S. H. Huang, Y. Chuang, J. Y. Li, and C. W. Liu, Effective g factor of low-density two-dimensional holes in a Ge quantum well, Appl. Phys. Lett. 111102108 (2017).
  11. T. M. Lu, L. A. Tracy, D. Laroche, S.-H. Huang, Y. Chuang, Y.-H. Su, J.-Y. Li, and C. W. Liu, Density-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system, Sci. Rep. 7, 2468 (2017).
  12. M. Lodari, O. Kong, M. Rendell, A. Tosato, A. Sammak, M. Veldhorst, A. R. Hamilton, and G. Scappucci, Lightly strained germanium quantum wells with hole mobility exceeding one million, Appl. Phys. Lett. 120, 122104 (2022).
  13. L. E. Stehouwer, A. Tosato, D. Degli Esposti, D. Costa, M. Veldhorst, A. Sammak, and G. Scappucci, Germanium wafers for strained quantum wells with low disorder, Appl. Phys. Lett. 123, 092101 (2023).
  14. M. Myronov, J. Kycia, P. Waldron, W. Jiang, P. Barrios, A. Bogan, P. Coleridge, and S. Studenikin, Holes outperform electrons in group IV semiconductor materials, Small Sci. 3, 2200094 (2023).
  15. M. Myronov, P. Waldron, P. Barrios, A. Bogan, and S. Studenikin, Electric field-tuneable crossing of hole Zeeman splitting and orbital gaps in compressively strained germanium semiconductor on silicon, Commun. Mater. 4, 104 (2023).
  16. S. Das Sarma and E. H. Hwang, Mobility versus quality in two-dimensional semiconductor structures, Phys. Rev. B 90, 035425 (2014).
  17. F. F. Fang and P. J. Stiles, Effects of a tilted magnetic field on a two-dimensional electron gas, Phys. Rev. 174, 823 (1968).
  18. G. M. Minkov, V. Y. Aleshkin, O. E. Rut, A. A. Sherstobitov, S. A. Dvoretski, N. N. Mikhailov, and A. V. Germanenko, Anisotropy of the in-plane g-factor of electrons in HgTe quantum wells, Phys. Rev. B 101, 085305 (2020).
  19. Z. Lei, C. A. Lehner, K. Rubi, E. Cheah, M. Karalic, C. Mittag, L. Alt, J. Scharnetzky, P. Märki, U. Zeitler, W. Wegscheider, T. Ihn, and K. Ensslin, Electronic g factor and magnetotransport in InSb quantum wells, Phys. Rev. Res. 2, 033213 (2020).
  20. D. Costa, L. E. A. Stehouwer, Y. Huang, S. Martí-Sánchez, D. Degli Esposti, J. Arbiol, and G. Scappucci, Reducing disorder in Ge quantum wells by using thick SiGe barriers, Appl. Phys. Lett. 125, 222104 (2024).
  21. A. Sammak, D. Sabbagh, N. W. Hendrickx, M. Lodari, B. Paquelet Wuetz, A. Tosato, L. Yeoh, M. Bollani, M. Virgilio, M. A. Schubert, et al., Shallow and undoped germanium quantum wells: A playground for spin and hybrid quantum technology, Adv. Funct. Mater. 29, 1807613 (2019).
  22. In our measurements, Δρxx(B) is obtained by subtracting a second-degree polynomial background from the normalized longitudinal magnetoresistivity given by Δρxx0(B)=ρxx(B)−ρxx(0)ρxx(0).
  23. T. Irisawa, M. Myronov, O. A. Mironov, E. H. C. Parker, K. Nakagawa, M. Murata, S. Koh, and Y. Shiraki, Hole density dependence of effective mass, mobility and transport time in strained Ge channel modulation-doped heterostructures, Appl. Phys. Lett. 82, 1425 (2003).
  24. D. R. Candido, S. I. Erlingsson, H. Gramizadeh, J. V. I. Costa, P. J. Weigele, D. M. Zumbühl, and J. C. Egues, Beating-free quantum oscillations in two-dimensional electron gases with strong spin-orbit and Zeeman interactions, Phys. Rev. Res. 5, 043297 (2023).
  25. B. Rössner, H. von Känel, D. Chrastina, G. Isella, and B. Batlogg, Effective mass measurement: The influence of hole band nonparabolicity in SiGe/Ge quantum wells, Semicond. Sci. Technol. 22, S191 (2007).
  26. I. L. Drichko, A. A. Dmitriev, V. Malysh, I. Y. Smirnov, H. von Känel, M. Kummer, D. Chrastina, and G. Isella, Effective g factor of 2D holes in strained Ge quantum wells, J. Appl. Phys. 123, 165703 (2018).
  27. T. Wimbauer, K. Oettinger, A. L. Efros, B. K. Meyer, and H. Brugger, Zeeman splitting of the excitonic recombination in InxGa1−xAs/GaAs single quantum wells, Phys. Rev. B 50, 8889 (1994).
  28. M. Lodari, N. W. Hendrickx, W. I. Lawrie, T.-K. Hsiao, L. M. Vandersypen, A. Sammak, M. Veldhorst, and G. Scappucci, Low percolation density and charge noise with holes in germanium, Mater. Quantum Technol. 1, 011002 (2021).
  29. D. Costa and G. Scappucci, Data Repository for “Quantum oscillations in two-dimensional hole gases with competing cyclotron and Zeeman energy” [Dataset], Zenodo (2025), https://doi.org/10.5281/zenodo.17099877.

Outline

Information

Phys. Rev. B 113, 115418– Published 19 March, 2026
  • Received 22 September 2025
  • Revised 20 February 2026
  • Accepted 2 March 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation