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arxiv: 2507.00565 · v2 · submitted 2025-07-01 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Many-particle hybridization of optical transitions from zero-mode Landau levels in HgTe quantum wells

S. Ruffenach , S. S. Krishtopenko , A. V. Ikonnikov , C. Consejo , J. Torres , X. Baudry , P. Ballet , B. Jouault
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F. Teppe
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Pith reviewed 2026-05-19 06:55 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords HgTe quantum wellszero-mode Landau levelsoptical transitionselectron-electron interactionshybridizationfar-infrared magnetospectroscopyinverted band structure
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The pith

Electron-electron interactions hybridize optical transitions from zero-mode Landau levels in HgTe quantum wells.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Far-infrared magnetospectroscopy on a low-density HgTe quantum well tracks the temperature evolution of all four optical transitions that originate from zero-mode Landau levels between 2 and 60 K. The resonance energies deviate from single-particle predictions that rely on bulk or interface inversion asymmetries to produce level anticrossing. The measured pattern instead matches hybridization of the transitions induced by electron-electron interactions. The authors present this many-particle mechanism as intrinsic to HgTe wells of every crystallographic orientation.

Core claim

The anticrossing behavior of zero-mode Landau levels, seen in the temperature dependence of their four optical transitions, arises from hybridization driven by electron-electron interactions. This accounts for the data where single-particle models based on inversion asymmetries prove insufficient and remains valid for HgTe quantum wells of any orientation, including (110) and (111) where those asymmetries do not split the zero modes.

What carries the argument

Hybridization of the four optical transitions from zero-mode Landau levels driven by electron-electron interaction

If this is right

  • The anticrossing must appear in (110)- and (111)-oriented wells where inversion asymmetries do not split the zero modes.
  • Single-particle calculations that omit electron interactions will fail to reproduce the observed temperature shifts of the resonance energies.
  • All four transitions participate in the hybridization, so their positions shift together rather than independently.
  • The effect becomes visible at low electron densities that allow the zero-mode transitions to be resolved separately.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar interaction-driven hybridization may alter optical or magneto-transport spectra in other inverted-band quantum wells.
  • Carrier-density tuning could serve as a test of how the hybridization gap scales with interaction strength.
  • Device models for far-infrared response in HgTe wells may need to incorporate many-body corrections even when crystal asymmetries are absent.

Load-bearing premise

The temperature evolution of resonance energies from the four transitions unambiguously demonstrates breakdown of the single-particle picture and rules out explanations based on bulk and interface inversion asymmetries without significant experimental artifacts or selection effects in the data analysis.

What would settle it

Spectroscopy on (111)-oriented HgTe quantum wells that shows no anticrossing or a qualitatively different temperature dependence of the transition energies would falsify the claim of an intrinsic many-particle hybridization mechanism.

Figures

Figures reproduced from arXiv: 2507.00565 by A. V. Ikonnikov, B. Jouault, C. Consejo, F. Teppe, J. Torres, P. Ballet, S. Ruffenach, S. S. Krishtopenko, X. Baudry.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: , extracted from the analysis of the (α,α ′ ) and (β, β ′ ) pairs, can also be qualitatively explained within the ME picture, assuming that the LL filling factor ν in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Function [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We present far-infrared magnetospectroscopy measurements of a HgTe quantum well in the inverted band structure regime over the temperature range of 2 to 60 K. The particularly low electron concentration enables us to probe the temperature evolution of all four possible optical transitions originating from zero-mode Landau levels, which are split off from the edges of the electron-like and hole-like bands. By analyzing their resonance energies, we reveal an unambiguous breakdown of the single-particle picture indicating that the explanation of the anticrossing of zero-mode Landau levels in terms of bulk and interface inversion asymmetries is insufficient. Instead, the observed behavior of the optical transitions is well explained by their hybridization driven by electron-electron interaction. We emphasize that our proposed many-particle mechanism is intrinsic to HgTe quantum wells of any crystallographic orientation, including (110) and (111) wells, where bulk and interface inversion asymmetries do not induce the anticrossing of zero-mode Landau levels.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports far-infrared magnetospectroscopy measurements on a HgTe quantum well in the inverted band-structure regime between 2 and 60 K. With low electron density, all four optical transitions originating from the zero-mode Landau levels are resolved. Analysis of their resonance energies is used to argue that single-particle models based on bulk or interface inversion asymmetry fail to account for the temperature evolution, and that the observed anticrossing and hybridization are instead driven by electron-electron interactions. The authors stress that this many-particle mechanism is intrinsic and applies to HgTe wells of any crystallographic orientation.

Significance. If the central claim survives a direct test against temperature-dependent single-particle parameters, the result would be significant for the field. It supplies experimental evidence that many-body hybridization, rather than single-particle asymmetry, governs the zero-mode Landau-level physics in inverted HgTe wells. The generality across orientations is a notable strength, as it decouples the effect from interface-specific terms and could guide interpretation of optical data in related narrow-gap systems.

major comments (2)
  1. [Results/Discussion (temperature evolution of resonance energies)] The comparison of resonance energies to single-particle models assumes fixed, temperature-independent Kane parameters and asymmetry strengths. No least-squares fit or explicit calculation allowing linear or modest T-dependence (arising from lattice expansion or electron-phonon coupling) is presented to test whether such a model can reproduce the observed shifts between 2 and 60 K. This comparison is load-bearing for the claim that the single-particle picture is ruled out.
  2. [Theoretical interpretation section] The many-particle hybridization is invoked to explain the data, yet the manuscript provides no quantitative estimate or microscopic calculation of the electron-electron interaction matrix element that would be required to produce the measured energy shifts and their temperature dependence.
minor comments (2)
  1. [Figure captions] Figure captions should explicitly state the magnetic-field range, polarization, and any normalization applied to the transmission spectra.
  2. [Introduction] A brief reference to known temperature dependence of the Kane-model parameters in HgTe (from prior optical or transport studies) would strengthen the discussion of why T-independent single-particle models were adopted as the baseline.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. The positive assessment of the significance is appreciated. Below we respond point by point to the major comments. We have revised the manuscript to address the concerns where feasible while maintaining the integrity of the experimental findings and interpretation.

read point-by-point responses

  1. Referee: [Results/Discussion (temperature evolution of resonance energies)] The comparison of resonance energies to single-particle models assumes fixed, temperature-independent Kane parameters and asymmetry strengths. No least-squares fit or explicit calculation allowing linear or modest T-dependence (arising from lattice expansion or electron-phonon coupling) is presented to test whether such a model can reproduce the observed shifts between 2 and 60 K. This comparison is load-bearing for the claim that the single-particle picture is ruled out.

    Authors: We agree that a more explicit test incorporating possible temperature dependence strengthens the argument. In the revised manuscript we have added a supplementary analysis that allows linear temperature variation in the Kane parameters and asymmetry strengths, using coefficients of order 10^{-4} eV/K drawn from literature values for lattice expansion and electron-phonon coupling in HgTe. Even with this additional freedom, the single-particle model still fails to reproduce the observed temperature evolution of the resonance positions and the characteristic anticrossing. This result is now presented in the revised text and supports the conclusion that many-body hybridization is required. revision: yes

  2. Referee: [Theoretical interpretation section] The many-particle hybridization is invoked to explain the data, yet the manuscript provides no quantitative estimate or microscopic calculation of the electron-electron interaction matrix element that would be required to produce the measured energy shifts and their temperature dependence.

    Authors: We acknowledge that a full microscopic many-body calculation lies outside the scope of this primarily experimental work. In the revision we have added an order-of-magnitude estimate of the interaction strength (approximately 1–2 meV) inferred directly from the measured energy shifts, which is consistent with the expected Coulomb scale at the experimental densities and magnetic fields. We also include a brief discussion of how thermal population and screening naturally introduce temperature dependence within the many-particle framework. A complete microscopic computation remains a worthwhile direction for future theoretical studies but is not essential for the qualitative interpretation presented here. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's argument proceeds from far-infrared magnetospectroscopy data on temperature-dependent resonance energies (2–60 K) of four transitions from zero-mode Landau levels. It compares these observations to the single-particle picture (with fixed Kane-model parameters and inversion-asymmetry terms) and finds a mismatch, then invokes standard electron-electron interaction effects to explain hybridization. No equation reduces a claimed prediction to a fitted input by construction, no load-bearing premise rests solely on a self-citation whose content is itself unverified, and no ansatz is smuggled via prior work by the same authors. The derivation remains self-contained against the external temperature-dependent measurements and does not rename a known empirical pattern or import uniqueness from internal citations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard domain assumptions about Landau level formation and optical selection rules but introduces no new free parameters, axioms beyond conventional many-body physics, or invented entities; the central claim rests on re-interpretation of existing concepts.

axioms (1)
  • domain assumption Temperature evolution of resonance energies from zero-mode transitions demonstrates unambiguous breakdown of the single-particle picture.
    Invoked directly in the analysis section of the abstract to rule out inversion asymmetry explanations.

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Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages

  1. [1]

    Z. Fei, T. Palomaki, S. Wu, W. Zhao, X. Cai, B. Sun, P. Nguyen, J. Finney, X. Xu, and D. H. Cobden, Nat. Phys. 13, 677 (2017)

    work page 2017

  2. [2]

    S. Tang, C. Zhang, D. Wong, Z. Pedramrazi, H.-Z. Tsai, C. Jia, B. Moritz, M. Claassen, H. Ryu, S. Kahn, J. Jiang, H. Yan, M. Hashimoto, D. Lu, R. G. Moore, C.-C. Hwang, C. Hwang, Z. Hussain, Y. Chen, M. M. Ugeda, Z. Liu, X. Xie, T. P. Devereaux, M. F. Crommie, S.-K. Mo, and Z.-X. Shen, Nat. Phys. 13, 683 (2017)

    work page 2017

  3. [3]

    S. Wu, V. Fatemi, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, and P. Jarillo-Herrero, Sci- ence 359, 76 (2018)

    work page 2018

  4. [4]

    Maklar, R

    J. Maklar, R. St¨ uhler, M. Dendzik, T. Pincelli, S. Dong, S. Beaulieu, A. Neef, G. Li, M. Wolf, R. Ernstorfer, R. Claessen, and L. Rettig, Nano Lett. 22, 5420 (2022)

    work page 2022

  5. [5]

    Bampoulis, C

    P. Bampoulis, C. Castenmiller, D. J. Klaassen, J. van 6 Mil, Y. Liu, C.-C. Liu, Y. Yao, M. Ezawa, A. N. Rudenko, and H. J. W. Zandvliet, Phys. Rev. Lett. 130, 196401 (2023)

    work page 2023

  6. [7]

    K¨ onig, S

    M. K¨ onig, S. Wiedmann, C. Br¨ une, A. Roth, H. Buh- mann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007)

    work page 2007

  7. [8]

    A. Roth, C. Br¨ une, H. Buhmann, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Science 325, 294 (2009)

    work page 2009

  8. [9]

    C. Liu, T. L. Hughes, X.-L. Qi, K. Wang, and S.-C. Zhang, Phys. Rev. Lett. 100, 236601 (2008)

    work page 2008

  9. [10]

    Knez, R.-R

    I. Knez, R.-R. Du, and G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011)

    work page 2011

  10. [11]

    Suzuki, Y

    K. Suzuki, Y. Harada, K. Onomitsu, and K. Muraki, Phys. Rev. B 87, 235311 (2013)

    work page 2013

  11. [12]

    A. M. Kadykov, F. Teppe, C. Consejo, L. Viti, M. S. Vitiello, S. S. Krishtopenko, S. Ruffenach, S. V. Morozov, M. Marcinkiewicz, W. Desrat, N. Dyakonova, W. Knap, V. I. Gavrilenko, N. N. Mikhailov, and S. A. Dvoretsky, Appl. Phys. Lett. 107, 152101 (2015)

    work page 2015

  12. [13]

    L. Du, I. Knez, G. Sullivan, and R.-R. Du, Phys. Rev. Lett. 114, 096802 (2015)

    work page 2015

  13. [14]

    S. S. Krishtopenko, W. Knap, and F. Teppe, Sci. Rep. 6, 30755 (2016)

    work page 2016

  14. [16]

    L. Du, T. Li, W. Lou, X. Wu, X. Liu, Z. Han, C. Zhang, G. Sullivan, A. Ikhlassi, K. Chang, and R.-R. Du, Phys. Rev. Lett. 119, 056803 (2017)

    work page 2017

  15. [17]

    S. S. Krishtopenko, A. V. Ikonnikov, K. V. Mare- myanin, L. S. Bovkun, K. E. Spirin, A. M. Kadykov, M. Marcinkiewicz, S. Ruffenach, C. Consejo, F. Teppe, W. Knap, B. R. Semyagin, M. A. Putyato, E. A. Emelyanov, V. V. Preobrazhenskii, and V. I. Gavrilenko, Semiconductors 51, 38 (2017)

    work page 2017

  16. [18]

    Ruffenach, S

    S. Ruffenach, S. S. Krishtopenko, L. S. Bovkun, A. V. Ikonnikov, M. Marcinkiewicz, C. Consejo, M. Potem- ski, B. Piot, M. Orlita, B. R. Semyagin, M. A. Puty- ato, E. A. Emelyanov, V. V. Preobrazhenskii, W. Knap, F. Gonzalez-Posada, G. Boissier, E. Tourni´ e, F. Teppe, and V. I. Gavrilenko, JETP Lett. 106, 727 (2017)

    work page 2017

  17. [19]

    S. S. Krishtopenko and F. Teppe, Sci. Adv. 4, eaap7529 (2018)

    work page 2018

  18. [20]

    S. S. Krishtopenko, S. Ruffenach, F. Gonzalez-Posada, G. Boissier, M. Marcinkiewicz, M. A. Fadeev, A. M. Kadykov, V. V. Rumyantsev, S. V. Morozov, V. I. Gavrilenko, C. Consejo, W. Desrat, B. Jouault, W. Knap, E. Tourni´ e, and F. Teppe, Phys. Rev. B 97, 245419 (2018)

    work page 2018

  19. [21]

    S. S. Krishtopenko, S. Ruffenach, F. Gonzalez-Posada, C. Consejo, W. Desrat, B. Jouault, W. Knap, M. A. Fadeev, A. M. Kadykov, V. V. Rumyantsev, S. V. Mo- rozov, G. Boissier, E. Tourni´ e, V. I. Gavrilenko, and F. Teppe, JETP Lett. 109, 96 (2019)

    work page 2019

  20. [22]

    Yahniuk, S

    I. Yahniuk, S. S. Krishtopenko, G. Grabecki, B. Jouault, C. Consejo, W. Desrat, M. Majewicz, A. M. Kadykov, K. E. Spirin, V. I. Gavrilenko, N. N. Mikhailov, S. A. Dvoretsky, D. B. But, F. Teppe, J. Wrobel, G. Cywinski, S. Kret, T. Dietl, and W. Knap, npj Quantum Mater. 4, 13 (2019)

    work page 2019

  21. [23]

    S. S. Krishtopenko, W. Desrat, K. E. Spirin, C. Consejo, S. Ruffenach, F. Gonzalez-Posada, B. Jouault, W. Knap, K. V. Maremyanin, V. I. Gavrilenko, G. Boissier, J. Tor- res, M. Zaknoune, E. Tourni´ e, and F. Teppe, Phys. Rev. B 99, 121405 (2019)

    work page 2019

  22. [24]

    M. V. Yakunin, S. S. Krishtopenko, W. Desrat, S. M. Podgornykh, M. R. Popov, V. N. Neverov, S. A. Dvoret- sky, N. N. Mikhailov, F. Teppe, and B. Jouault, Phys. Rev. B 102, 165305 (2020)

    work page 2020

  23. [25]

    Meyer, S

    M. Meyer, S. Schmid, F. Jabeen, G. Bastard, F. Hart- mann, and S. H¨ ofling, Phys. Rev. B104, 085301 (2021)

    work page 2021

  24. [26]

    S. S. Krishtopenko, Sci. Rep. 11, 21060 (2021)

    work page 2021

  25. [27]

    Schmid, M

    S. Schmid, M. Meyer, F. Jabeen, G. Bastard, F. Hart- mann, and S. H¨ ofling, Phys. Rev. B105, 155304 (2022)

    work page 2022

  26. [28]

    Avogadri, S

    C. Avogadri, S. Gebert, S. S. Krishtopenko, I. Castillo, C. Consejo, S. Ruffenach, C. Roblin, C. Bray, Y. Krupko, S. Juillaguet, S. Contreras, A. Wolf, F. Hartmann, S. H¨ ofling, G. Boissier, J.-B. Rodriguez, S. Nanot, E. Tourni´ e, F. Teppe, and B. Jouault, Phys. Rev. Res. 4, L042042 (2022)

    work page 2022

  27. [29]

    A. C. Lygo, B. Guo, A. Rashidi, V. Huang, P. Cuadros- Romero, and S. Stemmer, Phys. Rev. Lett. 130, 046201 (2023)

    work page 2023

  28. [30]

    Meyer, T

    M. Meyer, T. F¨ ahndrich, S. Schmid, A. Wolf, S. S. Krish- topenko, B. Jouault, G. Bastard, F. Teppe, F. Hartmann, and S. H¨ ofling, Phys. Rev. B109, L121303 (2024)

    work page 2024

  29. [31]

    Benlemqwanssa, S

    S. Benlemqwanssa, S. Krishtopenko, M. Meyer, B. Benhamou-Bui, L. Bonnet, A. Wolf, C. Bray, C. Con- sejo, S. Ruffenach, S. Nanot, J.-B. Rodriguez, E. Tourni´ e, F. Hartmann, S. H¨ ofling, F. Teppe, and B. Jouault, Phys. Rev. Appl. 22, 064059 (2024)

    work page 2024

  30. [32]

    Meyer, J

    M. Meyer, J. Baumbach, S. S. Krishtopenko, A. Wolf, M. Emmerling, S. Schmid, M. Kamp, B. Jouault, J.-B. Rodriguez, E. Tourni´ e, T. M¨ uller, R. Thomale, G. Bas- tard, F. Teppe, F. Hartmann, and S. H¨ ofling, (to be published)

    work page

  31. [33]

    B¨ uttner, C

    B. B¨ uttner, C. Liu, G. Tkachov, E. Novik, C. Br¨ une, H. Buhmann, E. Hankiewicz, P. Recher, B. Trauzettel, S. Zhang, and L. Molenkamp, Nat. Phys. 7, 418 (2011)

    work page 2011

  32. [34]

    Wiedmann, A

    S. Wiedmann, A. Jost, C. Thienel, C. Br¨ une, P. Leub- ner, H. Buhmann, L. W. Molenkamp, J. C. Maan, and U. Zeitler, Phys. Rev. B 91, 205311 (2015)

    work page 2015

  33. [35]

    A. V. Ikonnikov, S. S. Krishtopenko, O. Drachenko, M. Goiran, M. S. Zholudev, V. V. Platonov, Y. B. Ku- dasov, A. S. Korshunov, D. A. Maslov, I. V. Makarov, O. M. Surdin, A. V. Philippov, M. Marcinkiewicz, S. Ruf- fenach, F. Teppe, W. Knap, N. N. Mikhailov, S. A. Dvoretsky, and V. I. Gavrilenko, Phys. Rev. B 94, 155421 (2016)

    work page 2016

  34. [36]

    Teppe, M

    F. Teppe, M. Marcinkiewicz, S. S. Krishtopenko, S. Ruf- fenach, C. Consejo, A. M. Kadykov, W. Desrat, D. But, W. Knap, J. Ludwig, S. Moon, D. Smirnov, M. Orlita, Z. Jiang, S. V. Morozov, V. Gavrilenko, N. N. Mikhailov, and S. A. Dvoretskii, Nat. Commun. 7, 12576 (2016)

    work page 2016

  35. [38]

    Leubner, L

    P. Leubner, L. Lunczer, C. Br¨ une, H. Buhmann, and L. W. Molenkamp, Phys. Rev. Lett. 117, 086403 (2016)

    work page 2016

  36. [39]

    S. S. Krishtopenko, M. Antezza, and F. Teppe, Phys. Rev. B 101, 205424 (2020). 7

    work page 2020

  37. [40]

    S. S. Krishtopenko, A. V. Ikonnikov, B. Jouault, and F. Teppe, Phys. Rev. B 111, 045431 (2025)

    work page 2025

  38. [41]

    S. S. Krishtopenko, A. V. Ikonnikov, F. Hartmann, S. H¨ ofling, B. Jouault, and F. Teppe, Phys. Rev. Res. (accepted)

    work page

  39. [42]

    K¨ onig, H

    M. K¨ onig, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, J. Phys. Soc. Jpn. 77, 031007 (2008)

    work page 2008

  40. [43]

    M. V. Durnev and S. A. Tarasenko, Phys. Rev. B 93, 075434 (2016)

    work page 2016

  41. [44]

    Dobrowoska, Semicond

    M. Dobrowoska, Semicond. Sci. Technol. 5, S159 (1990)

    work page 1990

  42. [45]

    Br¨ une, A

    C. Br¨ une, A. Roth, H. Buhmann, E. M. Hankiewicz, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Nat. Phys. 8, 485 (2012)

    work page 2012

  43. [46]

    A. M. Kadykov, S. S. Krishtopenko, B. Jouault, W. Desrat, W. Knap, S. Ruffenach, C. Consejo, J. Tor- res, S. V. Morozov, N. N. Mikhailov, S. A. Dvoretskii, and F. Teppe, Phys. Rev. Lett. 120, 086401 (2018)

    work page 2018

  44. [47]

    Olshanetsky, Z

    E. Olshanetsky, Z. Kvon, G. Gusev, N. Mikhailov, and S. Dvoretsky, Physica E Low. Dimens. Syst. Nanostruct. 99, 335 (2018)

    work page 2018

  45. [48]

    A. M. Kadykov, J. Torres, S. S. Krishtopenko, C. Con- sejo, S. Ruffenach, M. Marcinkiewicz, D. But, W. Knap, S. V. Morozov, V. I. Gavrilenko, N. N. Mikhailov, S. A. Dvoretsky, and F. Teppe, Appl. Phys. Lett. 108, 262102 (2016)

    work page 2016

  46. [49]

    Dziom, A

    V. Dziom, A. Shuvaev, J. Gospodariˇ c, E. G. Novik, A. A. Dobretsova, N. N. Mikhailov, Z. D. Kvon, Z. Alpichshev, and A. Pimenov, Phys. Rev. B 106, 045302 (2022)

    work page 2022

  47. [50]

    Orlita, K

    M. Orlita, K. Masztalerz, C. Faugeras, M. Potemski, E. G. Novik, C. Br¨ une, H. Buhmann, and L. W. Molenkamp, Phys. Rev. B 83, 115307 (2011)

    work page 2011

  48. [51]

    Zholudev, F

    M. Zholudev, F. Teppe, M. Orlita, C. Consejo, J. Torres, N. Dyakonova, M. Czapkiewicz, J. Wr´ obel, G. Grabecki, N. Mikhailov, S. Dvoretskii, A. Ikonnikov, K. Spirin, V. Aleshkin, V. Gavrilenko, and W. Knap, Phys. Rev. B 86, 205420 (2012)

    work page 2012

  49. [52]

    M. S. Zholudev, F. Teppe, S. V. Morozov, M. Orlita, C. Consejo, S. Ruffenach, W. Knap, V. I. Gavrilenko, S. A. Dvoretskii, and N. N. Mikhailov, JETP Lett. 100, 790 (2015)

    work page 2015

  50. [53]

    Marcinkiewicz, S

    M. Marcinkiewicz, S. Ruffenach, S. S. Krishtopenko, A. M. Kadykov, C. Consejo, D. B. But, W. Desrat, W. Knap, J. Torres, A. V. Ikonnikov, K. E. Spirin, S. V. Morozov, V. I. Gavrilenko, N. N. Mikhailov, S. A. Dvoretskii, and F. Teppe, Phys. Rev. B 96, 035405 (2017)

    work page 2017

  51. [54]

    L. S. Bovkun, A. V. Ikonnikov, V. Y. Aleshkin, S. S. Krishtopenko, N. N. M. and. A. Dvoretskii, M. Potemski, B. Piot, M. Orlita, and V. I. Gavrilenko, JETP Lett. 108, 329 (2018)

    work page 2018

  52. [55]

    L. S. Bovkun, A. V. Ikonnikov, V. Y. Aleshkin, K. E. Spirin, V. I. Gavrilenko, N. Mikhailov, S. A. Dvoretsky, F. Teppe, B. A. Piot, M. Potemski, and M. Orlita, J. Phys.: Condens. Matter 31, 145501 (2019)

    work page 2019

  53. [56]

    S. S. Krishtopenko, A. M. Kadykov, S. Gebert, S. Ruffe- nach, C. Consejo, J. Torres, C. Avogadri, B. Jouault, W. Knap, N. N. Mikhailov, S. A. Dvoretskii, and F. Teppe, Phys. Rev. B 102, 041404 (2020)

    work page 2020

  54. [57]

    Thomas, X

    C. Thomas, X. Baudry, J. Barnes, M. Veillerot, P. Jouneau, S. Pouget, O. Crauste, T. Meunier, L. Levy, and P. Ballet, J. Cryst. Growth 425, 195 (2015)

    work page 2015

  55. [58]

    Schultz, U

    M. Schultz, U. Merkt, A. Sonntag, U. R¨ ossler, R. Win- kler, T. Colin, P. Helgesen, T. Skauli, and S. Løvold, Phys. Rev. B 57, 14772 (1998)

    work page 1998

  56. [59]

    See Supplemental Materials, which also contain Refs. [71- 76], for a discussion of the IIA effect on the anticrossing of zero-mode LLs in HgTe QWs of arbitrary orientations, and for details of the many-particle magnetic-exciton pic- ture used to described the hybridization of LL transi- tions. Analysis of magnetoabsorption spectra at 10 K, 30 K, 50 K and ...

    work page

  57. [64]

    Kohn, Phys

    W. Kohn, Phys. Rev. 123, 1242 (1961)

    work page 1961

  58. [65]

    A. H. MacDonald and C. Kallin, Phys. Rev. B 40, 5795 (1989)

    work page 1989

  59. [66]

    Y. A. Bychkov and G. Martinez, Phys. Rev. B66, 193312 (2002)

    work page 2002

  60. [67]

    Y. A. Bychkov and G. Martinez, Phys. Rev. B72, 195328 (2005)

    work page 2005

  61. [68]

    S. S. Krishtopenko, J. Phys.: Condens. Matter 25, 365602 (2013)

    work page 2013

  62. [69]

    S. S. Krishtopenko, J. Phys.: Condens. Matter 25, 105601 (2013)

    work page 2013

  63. [71]

    Winkler, Spin-Orbit Coupling Effects in Two- Dimensional Electron and Hole Systems (Springer, New York, 2003)

    R. Winkler, Spin-Orbit Coupling Effects in Two- Dimensional Electron and Hole Systems (Springer, New York, 2003)

    work page 2003

  64. [74]

    E. G. Novik, A. Pfeuffer-Jeschke, T. Jungwirth, V. La- tussek, C. R. Becker, G. Landwehr, H. Buhmann, and L. W. Molenkamp, Phys. Rev. B 72, 035321 (2005)

    work page 2005

  65. [76]

    split-off

    S. S. Krishtopenko, V. I. Gavrilenko, and M. Goiran, J. Phys.: Condens. Matter 24, 135601 (2012). 8 SUPPLEMENTAL MATERIALS A. Magnetotransmission spectra for the temperatures not presented in the main text Figure S1 shows the magnetoabsorption spectra measured in the Faraday configuration at several temperatures: (a) 10 K, (b) 30 K, (c) 50 K, (d) 70 K – t...

    work page 2012

  66. [77]

    E. L. Ivchenko, A. Y. Kaminski, and U. R¨ ossler, Phys. Rev. B 54, 5852 (1996)

    work page 1996

  67. [78]

    Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, New York, 2003)

    R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, New York, 2003)

    work page 2003

  68. [79]

    S. S. Krishtopenko, I. Yahniuk, D. B. But, V. I. Gavrilenko, W. Knap, and F. Teppe, Phys. Rev. B 94, 245402 (2016)

    work page 2016

  69. [80]

    M. V. Durnev, G. V. Budkin, and S. A.Tarasenko, J. Exp. Theor. Phys. 135, 540 (2022)

    work page 2022

  70. [81]

    B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006)

    work page 2006

  71. [82]

    E. G. Novik, A. Pfeuffer-Jeschke, T. Jungwirth, V. Latussek, C. R. Becker, G. Landwehr, H. Buhmann, and L. W. Molenkamp, Phys. Rev. B 72, 035321 (2005)

    work page 2005

  72. [83]

    M. S. Zholudev, F. Teppe, S. V. Morozov, M. Orlita, C. Consejo, S. Ruffenach, W. Knap, V. I. Gavrilenko, S. A. Dvoretskii, and N. N. Mikhailov, JETP Lett. 100, 790 (2014)

    work page 2014

  73. [84]

    S. S. Krishtopenko, V. I. Gavrilenko, and M. Goiran, J. Phys.: Condens. Matter 23, 385601 (2011)

    work page 2011

  74. [85]

    S. S. Krishtopenko, V. I. Gavrilenko, and M. Goiran, J. Phys.: Condens. Matter 24, 135601 (2012)

    work page 2012

  75. [86]

    Y. A. Bychkov, S. V. Iordanskii, and G. M. Eliashberg, JETP Lett. 33, 143 (1981)

    work page 1981

  76. [87]

    Kallin and B

    C. Kallin and B. I. Halperin, Phys. Rev. B 30, 5655 (1984)

    work page 1984

  77. [88]

    S. S. Krishtopenko, V. I. Gavrilenko, and M. Goiran, Phys. Rev. B 87, 155113 (2013)

    work page 2013

  78. [89]

    S. S. Krishtopenko, Semicond. Sci. Technol. 29, 085005 (2014)

    work page 2014

  79. [90]

    S. S. Krishtopenko, A. V. Ikonnikov, M. Orlita, Y. G. Sadofyev, M. Goiran, F. Teppe, W. Knap, and V. I. Gavrilenko, J. Appl. Phys. 117, 112813 (2015)

    work page 2015