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arxiv: 2605.13274 · v1 · pith:5VDASTMJnew · submitted 2026-05-13 · ❄️ cond-mat.mes-hall

Electron - acoustic phonons scattering in quantum wells in a tilted quantizing magnetic field

M.P. Telenkov , Yu.A. Mityagin This is my paper

Pith reviewed 2026-05-14 18:41 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords electron-phonon scatteringacoustic phononsquantum wellstilted magnetic fieldquantizing magnetic fieldLandau levelsscattering rate
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0 comments X

The pith

Expressions for electron-acoustic phonon scattering rates are derived for quantum wells in tilted quantizing magnetic fields, showing trends with field strength, tilt, and well potential.

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

The paper derives explicit expressions for the rate at which electrons scatter from longitudinal acoustic phonons in a quantum well placed in a strong magnetic field applied at an angle to the layers. These expressions are analyzed to identify how the rate changes when the field strength increases, when the tilt angle varies, and when the shape of the confining potential is adjusted. A reader would care because scattering rates govern electron mobility and relaxation times that limit the performance of devices relying on quantizing magnetic fields. The derivation stays within the framework of perturbation theory and focuses on analytical trends rather than specific numerical simulations.

Core claim

Expressions for the scattering rate in a magnetic field tilted to the quantum well layers are derived. By analyzing these expressions, trends in the behavior of the scattering rate are established with changes in the magnetic field strength and orientation, as well as the potential profile of the quantum well.

What carries the argument

Analytical expressions for the electron-acoustic phonon scattering rate obtained via perturbation theory in the tilted magnetic field geometry, accounting for the Landau level structure.

Load-bearing premise

Standard perturbation theory for electron-phonon scattering remains valid in the tilted-field geometry without significant higher-order corrections or breakdown of the Landau-level picture.

What would settle it

Measurement of electron mobility or scattering times in a quantum well sample while systematically varying the magnetic field tilt angle and comparing results against the predicted trends from the expressions would test the claim.

read the original abstract

Electron scattering by longitudinal acoustic phonons in a quantizing magnetic field is considered. Expressions for the scattering rate in a magnetic field tilted to the quantum well layers are derived. By analyzing these expressions, trends in the behavior of the scattering rate are established with changes in the magnetic field strength and orientation, as well as the potential profile of the quantum well.

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 derives expressions for the scattering rate of electrons by longitudinal acoustic phonons in quantum wells subjected to a tilted quantizing magnetic field. Using these expressions, trends are established in the scattering rate as functions of magnetic field strength, tilt angle (orientation), and the quantum well potential profile.

Significance. If the central derivations are valid, the work offers useful qualitative trends for electron-phonon scattering in tilted-field geometries, which are relevant to magnetotransport studies in quantum Hall systems and mesoscopic devices. The application of standard perturbation theory to this geometry is a reasonable extension, but the significance depends on confirming that the unperturbed basis remains appropriate.

major comments (2)
  1. [Section on electron wave functions and Hamiltonian] The single-particle states are taken as products of Landau-level wavefunctions (perpendicular component) and subband envelope functions without explicit diagonalization of the Hamiltonian to include subband mixing from the parallel magnetic-field component. This choice is load-bearing for all reported trends with tilt angle, yet no estimate or bound on the mixing matrix elements is given to justify neglecting them for the considered well widths and tilt ranges.
  2. [Derivation of scattering rate] The scattering-rate expressions (obtained via Fermi's golden rule) insert the tilt angle directly into the phonon wave-vector components and overlap integrals while retaining the unperturbed basis. If the parallel vector-potential term induces non-perturbative mixing, the matrix elements and resulting trends with field orientation become uncontrolled.
minor comments (2)
  1. The abstract is terse; a sentence summarizing the key qualitative trends (e.g., how the rate varies with tilt) would improve accessibility.
  2. [Notation and definitions] Notation for the tilt angle and the decomposition of the magnetic-field vector should be introduced once and used consistently throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments on the validity of the unperturbed basis. We address the points below and will revise the manuscript to include the requested estimates and discussion of the approximation's range of validity.

read point-by-point responses

  1. Referee: [Section on electron wave functions and Hamiltonian] The single-particle states are taken as products of Landau-level wavefunctions (perpendicular component) and subband envelope functions without explicit diagonalization of the Hamiltonian to include subband mixing from the parallel magnetic-field component. This choice is load-bearing for all reported trends with tilt angle, yet no estimate or bound on the mixing matrix elements is given to justify neglecting them for the considered well widths and tilt ranges.

    Authors: We agree that an explicit bound on subband mixing would strengthen the presentation. In the revised manuscript we will add a short estimate (or appendix) of the mixing matrix elements for the well widths (typically 10–20 nm) and tilt angles (up to ~60°) considered in the figures. For the lowest subbands the off-diagonal terms remain ≪ subband separation, keeping the product basis accurate to leading order. The reported trends with tilt arise mainly from the explicit dependence of the phonon wave-vector components and overlap integrals on the tilt angle; these geometric factors survive even when weak mixing is included perturbatively. revision: yes

  2. Referee: [Derivation of scattering rate] The scattering-rate expressions (obtained via Fermi's golden rule) insert the tilt angle directly into the phonon wave-vector components and overlap integrals while retaining the unperturbed basis. If the parallel vector-potential term induces non-perturbative mixing, the matrix elements and resulting trends with field orientation become uncontrolled.

    Authors: The scattering-rate formulas are derived within the unperturbed product basis. We will add a paragraph clarifying the validity condition (mixing ≪ subband spacing) and noting that the dominant tilt dependence enters through the phonon wave-vector projection and the form-factor integrals, both of which are insensitive to small admixtures of higher subbands. Should mixing become appreciable at extreme tilts or wider wells, the trends would receive quantitative corrections but the qualitative suppression of the rate with increasing tilt angle is expected to persist. We will also state the parameter window in which the present expressions remain controlled. revision: yes

Circularity Check

0 steps flagged

Standard derivation of scattering rates shows no circularity

full rationale

The paper applies Fermi's golden rule to electron-acoustic phonon scattering in a tilted magnetic field using the standard Landau-level basis with tilt incorporated via wave-vector components and form factors. No equations reduce by construction to fitted inputs, no self-definitional loops appear, and no load-bearing self-citations or imported uniqueness theorems are invoked. The derivation chain remains independent of its target results and rests on explicit matrix-element evaluation rather than renaming or smuggling ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions of quantum mechanics for electrons in magnetic fields and phonon scattering; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Standard quantum mechanical treatment of electrons in quantizing magnetic fields and longitudinal acoustic phonon scattering applies without modification for the tilted geometry.
    Typical background assumption for scattering-rate calculations in mesoscopic systems.

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Works this paper leans on

59 extracted references · 59 canonical work pages

  1. [1]

    T. Ando, B. Fowler, and F. Stern, Rev. Mod. Phys., 54, 437 (1982). https://doi.org/10.1103/RevModPhys.54.437

    work page doi:10.1103/revmodphys.54.437 1982

  2. [2]

    Blank, and S

    A. Blank, and S. Feng, J. Appl. Phys., 74, 4795 (1993). https://doi.org/10.1063/1.354354

    work page doi:10.1063/1.354354 1993

  3. [3]

    Smirnov, O

    D. Smirnov, O. Drachenko, J. Leotin, H. Page, C. Becker, C. Sirtori, V . Apalkov, and T. Chakraborty, Phys. Rev. B, 66, 125317 (2002). https://doi.org/10.1103/PhysRevB.66.125317

    work page doi:10.1103/physrevb.66.125317 2002

  4. [4]

    Kempa, Y

    K. Kempa, Y . Zhou, J. R. Engelbrecht, and P. Bakshi, Phys. Rev. B, 68, 085302 (2003). https://doi.org/10.1103/PhysRevB.68.085302

    work page doi:10.1103/physrevb.68.085302 2003

  5. [5]

    Becker, A

    C. Becker, A. Vasanelli, C. Sirtori, and G. Bastard, Phys. Rev. B, 69, 115328 (2004). https://doi.org/10.1103/PhysRevB.69.115328

    work page doi:10.1103/physrevb.69.115328 2004

  6. [6]

    Leuliet, A

    A. Leuliet, A. Vasanelli, A. Wade, G. Fedorov, D. Smirnov, G. Bastard, and C. Sirtori, Phys. Rev. B, 73, 085311 (2006). https://doi.org/10.1103/PhysRevB.73.085311

    work page doi:10.1103/physrevb.73.085311 2006

  7. [7]

    Savić, Z

    I. Savić, Z. Ikonić, V . Milanović, N. Vukmirović, V .D. Jovanović, D. Indjin, and P. Harrison, Phys. Rev. B, 73, 075321 (2006). https://doi.org/10.1103/PhysRevB.73.075321

    work page doi:10.1103/physrevb.73.075321 2006

  8. [8]

    Novaković, J

    B. Novaković, J. Radovanović, A. Mirčetić, V . Milanović, Z. Ikonić, and D. Indjin, Optics Commun., 279, 330 (2007). https://doi.org/10.1016/j.optcom.2007.07.028

    work page doi:10.1016/j.optcom.2007.07.028 2007

  9. [9]

    Péré-Laperne, L

    N. Péré-Laperne, L. A. de Vaulchier, Y. Guldner, G. Bastard, G. Scalari, M. Giovannini, J. Faist, A. Vasanelli, S. Dhillon, and C. Sirtori, Appl. Phys. Lett., 91, 062102 (2007). https://doi.org/10.1063/1.2766862

    work page doi:10.1063/1.2766862 2007

  10. [10]

    A. Wade, G. Fedorov, D. Smirnov, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, Nature Photonics, 3, 41 (2009). https://doi.org/10.1038/nphoton.2008.251

    work page doi:10.1038/nphoton.2008.251 2009

  11. [11]

    Telenkov, Yu.A

    M.P. Telenkov, Yu.A. Mityagin, and P.F. Kartsev, JETP Lett., 92, 401 (2010)] https://doi.org/10.1134/S0021364010180086 24

    work page doi:10.1134/s0021364010180086 2010

  12. [12]

    Daničić, J

    A. Daničić, J. Radovanović, V . Milanović, D. Indjin, and Z. Ikonić, J. Phys. D: Appl. Phys. 43, 045101 (2010). https://doi.org/10.1088/0022-3727/43/4/045101

    work page doi:10.1088/0022-3727/43/4/045101 2010

  13. [13]

    Milanović, J

    M.Žeželj, V . Milanović, J. Radovanović, and I. Stanković, J. Phys. D: Appl. Phys., 44, 325105 (2011). https://doi.org/10.1088/0022-3727/44/32/325105

    work page doi:10.1088/0022-3727/44/32/325105 2011

  14. [14]

    Timotijević, J

    D. Timotijević, J. Radovanović, and V. Milanović, Semicond. Sci. Technol., 27, 045006 (2012). https://doi.org/10.1088/0268-1242/27/4/045006

    work page doi:10.1088/0268-1242/27/4/045006 2012

  15. [15]

    Daničić, J

    A. Daničić, J. Radovanović, D. Indjin, and Z. Ikonić, Phys. Scripta, 2012, 014017 (2012). https://doi.org/10.1088/0031-8949/2012/T149/014017

    work page doi:10.1088/0031-8949/2012/t149/014017 2012

  16. [16]

    Arapov, S.V

    Yu.G. Arapov, S.V . Gudina, A.S. Klepikova, V .N. Neverov, S.M. Podgornykh, M.V . Yakunin, and B.N. Zvonkov, Semiconductors, 47, 1447 (2013)]. https://doi.org/10.1134/S1063782613110055

    work page doi:10.1134/s1063782613110055 2013

  17. [17]

    M. P. Telenkov, Yu. A. Mityagin, and P.F. Kartsev, Opt. Quant. Electron., 46, 759 (2014). https://doi.org/10.1007/s11082-013-9784-z

    work page doi:10.1007/s11082-013-9784-z 2014

  18. [18]

    Telenkov, Yu.A

    M.P. Telenkov, Yu.A. Mityagin, A.A. Kutsevol,V .V . Agafonov, and K.K. Nagaraja, JETP Letters, 102, 678 (2015)]. https://doi.org/10.1134/S0021364015220129

    work page doi:10.1134/s0021364015220129 2015

  19. [19]

    Daničić, J

    A. Daničić, J. Radovanović, V. Milanović, D. Indjin, and Z. Ikonić, Physica E, 81, 275 (2016). https://doi.org/10.1016/j.physe.2016.03.019

    work page doi:10.1016/j.physe.2016.03.019 2016

  20. [20]

    Telenkov, Yu.A

    M.P. Telenkov, Yu.A. Mityagin, T.N.V . Doan, and K.K. Nagaraja, Physica E, 104, 11 (2018). https://doi.org/10.1016/j.physe.2018.07.007

    work page doi:10.1016/j.physe.2018.07.007 2018

  21. [21]

    Mityagin, M.P

    Yu.A. Mityagin, M.P. Telenkov, Sh. Amiri, and K.K. Nagaraja, Physica E, 122, 114104 (2020). https://doi.org/10.1016/j.physe.2020.114104 25

    work page doi:10.1016/j.physe.2020.114104 2020

  22. [22]

    Gajić, J

    A. Gajić, J. Radovanović, N. Vuković, V. Milanović, and D.L. Boiko, Phys. Letters A, 387 127007 (2021). https://doi.org/10.1016/j.physleta.2020.127007

    work page doi:10.1016/j.physleta.2020.127007 2021

  23. [23]

    Mityagin, M.P

    Yu.A. Mityagin, M.P. Telenkov; I.A. Bulygina, Ravi Kumar, and K.K. Nagaraja, Physica E, 142, 115288 (2022). https://doi.org/10.1016/j.physe.2022.115288

    work page doi:10.1016/j.physe.2022.115288 2022

  24. [24]

    Telenkov and Yu.A

    M.P. Telenkov and Yu.A. Mityagin, Zh.Exp.Teor.Fiz., 168 (9). 425 (2025). https://journals.rcsi.science/0044-4510/article/view/317336 [https://doi.org/10.48550/arXiv.2505.08028]

    work page doi:10.48550/arxiv.2505.08028 2025

  25. [25]

    Telenkov and Yu.A

    M.P. Telenkov and Yu.A. Mityagin, Zh.Exp.Teor.Fiz., 168 (10), 537 (2025). https://journals.rcsi.science/0044-4510/article/view/317105 https://doi.org/10.48550/arXiv.2510.09787 ]

    work page doi:10.48550/arxiv.2510.09787 2025

  26. [26]

    Telenkov, Yu.A

    M.P. Telenkov, Yu.A. Mityagin, and D.S. Korchagin, Physica E, 174, 116351 (2025). https://doi.org/10.1016/j.physe.2025.116351

    work page doi:10.1016/j.physe.2025.116351 2025

  27. [27]

    Telenkov and Yu.A

    M.P. Telenkov and Yu.A. Mityagin, Physica E, 116555 (2026). https://doi.org/10.1016/j.physe.2026.116555

    work page doi:10.1016/j.physe.2026.116555 2026

  28. [28]

    P. J. Price, Ann. Phys., 133, 217 (1981). https://doi.org/10.1016/0003-4916(81)90250-5

    work page doi:10.1016/0003-4916(81)90250-5 1981

  29. [29]

    Karpus, Fiz

    V . Karpus, Fiz. Techn. Poluprov., 20, 12 (1986) https://www.mathnet.ru/rus/phts/v20/i1/p12

    work page 1986

  30. [30]

    Ferreira and G

    R. Ferreira and G. Bastard, Phys. Rev. B, 40, 1074 (1989). https://doi.org/10.1103/PhysRevB.40.1074

    work page doi:10.1103/physrevb.40.1074 1989

  31. [31]

    Kawamura, S

    T. Kawamura, S. Das Sarma, R. Jalabert, and J. K. Jain, Phys. Rev. B, 42, 5407 (1990) https://doi.org/10.1103/PhysRevB.42.5407

    work page doi:10.1103/physrevb.42.5407 1990

  32. [32]

    J. S. Bhat, S. S. Kubakaddi, and B. G. Mulimani, J. Appl. Phys., 70, 2216 (1991) https://doi.org/10.1063/1.349432

    work page doi:10.1063/1.349432 1991

  33. [33]

    Kawamura and S

    T. Kawamura and S. Das Sarma, Phys. Rev .B, 45, 3612 (1992). https://doi.org/10.1103/PhysRevB.45.3612 26

    work page doi:10.1103/physrevb.45.3612 1992

  34. [34]

    Murzin, Yu.A

    V .N. Murzin, Yu.A. Mityagin,and V.A. Chuenkov, Bulletin of Russian Academy of Sciences: Physics, 64, 235 (2000)

    work page 2000

  35. [35]

    Takeya Unuma, Masahiro Yoshita, Takeshi Noda, Hiroyuki Sakaki, and Hidefumi Akiyama, J. Appl. Phys. 93,1586 (2003). https://doi.org/10.1063/1.1535733

    work page doi:10.1063/1.1535733 2003

  36. [36]

    Pshenai-Severin and Y .I

    D.A. Pshenai-Severin and Y .I. Ravich, Semiconductors, 36, 908 (2002). https://doi.org/10.1134/1.1500470

    work page doi:10.1134/1.1500470 2002

  37. [37]

    Borisenko, Semiconductors, 38, 824 (2004)

    S.I. Borisenko, Semiconductors, 38, 824 (2004). https://doi.org/10.1134/1.1777608

    work page doi:10.1134/1.1777608 2004

  38. [38]

    https://doi.org/10.1016/j.ijleo.2020.164348

    Nguyen Dinh Hien, Optik, 206, 164348 (2020). https://doi.org/10.1016/j.ijleo.2020.164348

    work page doi:10.1016/j.ijleo.2020.164348 2020

  39. [39]

    https://doi.org/10.1039/D3NA00274H

    Tran Cong Phong, Le Ngoc Minh, and Nguyen Dinh Hie, Nanoscale Adv., 6, 832 (2024). https://doi.org/10.1039/D3NA00274H

    work page doi:10.1039/d3na00274h 2024

  40. [40]

    Drichko, I.Yu

    I.L. Drichko, I.Yu. Smirnov, M.O. Safonchik et.al., Zh.Exp.Teor.Fiz., 167, 226 (2025). https://jetpras.ru/s3034641xs0044451025020087-1

    work page 2025

  41. [41]

    L Leadbeater, F.W

    M. L Leadbeater, F.W. Sheard, and L. Eaves, Semicond. Sci. Technol., 6, 1021 (1991). https://doi.org/10.1088/0268-1242/6/10/012

    work page doi:10.1088/0268-1242/6/10/012 1991

  42. [42]

    Telenkov and Yu.A

    M.P. Telenkov and Yu.A. Mityagin, Int. J. of Mod. Phys. B, 21, 1594, (2007). https://doi.org/10.1142/S0217979207043269

    work page doi:10.1142/s0217979207043269 2007

  43. [43]

    V . M. Apalkov and T. Chakraborty, Appl. Phys. Lett., 78, 1973 (2001). https://doi.org/10.1063/1.1359488

    work page doi:10.1063/1.1359488 1973

  44. [44]

    Chakraborty and V .M

    T. Chakraborty and V .M. Apalkov, Advances in Physics, 52, 455 (2003). https://doi.org/10.1080/0001873031000119619

    work page doi:10.1080/0001873031000119619 2003

  45. [45]

    Telenkov and Yu.A

    M.P. Telenkov and Yu.A. Mityagin, T.N.V . Doan, K.K. Nagaraja, J. Phys. Commun., 2, 085019 (2018). https://doi.org/10.1088/2399-6528/aad885

    work page doi:10.1088/2399-6528/aad885 2018

  46. [46]

    Bastard, Wave Mechanic Applied to Semiconductor Heterostructures

    G. Bastard, Wave Mechanic Applied to Semiconductor Heterostructures. Les Editions de Physique, Les Ulis Cedex, France, 1988. 27

    work page 1988

  47. [47]

    Madelung, Landolt -Bornstein, New Series, Group III, V ol

    Numerical Data and Functional Relationships in Science and Technology, edited by O. Madelung, Landolt -Bornstein, New Series, Group III, V ol. 17, Pt. 2.10.1, Springer - Verlag, Berlin, 1982

    work page 1982

  48. [48]

    Bockelmann and G

    U. Bockelmann and G. Bastard, Phys. Rev. B, 45, 1700 (1992). https://doi.org/10.1103/PhysRevB.45.1700

    work page doi:10.1103/physrevb.45.1700 1992

  49. [49]

    D. M. Mitrinović, V .Milanović, and Z. Ikonić. Phys. Rev. B, 54, 7666 (1996). https://doi.org/10.1103/PhysRevB.54.7666

    work page doi:10.1103/physrevb.54.7666 1996

  50. [50]

    Živanović, V

    S. Živanović, V . Milanović, and Z. Ikonić, Phys. Rev. B, 52, 8305 (1995). https://doi.org/10.1103/PhysRevB.52.8305

    work page doi:10.1103/physrevb.52.8305 1995

  51. [51]

    Kapaev, Yu.V

    V .V . Kapaev, Yu.V . Kopaev, and I.V . Tokatly, Phys. Usp., 40, 538 (1997) https://doi.org/10.1070/PU1997v040n05ABEH001568

    work page doi:10.1070/pu1997v040n05abeh001568 1997

  52. [52]

    Telenkov and Yu.A

    M.P. Telenkov and Yu.A. Mityagin, Semiconductors, 40, 581 (2006). https://doi.org/10.1134/S1063782606050125

    work page doi:10.1134/s1063782606050125 2006

  53. [53]

    Hu and A

    J. Hu and A. H. MacDonald, Phys. Rev. B, 46, 12554 (1992). https://doi.org/10.1103/PhysRevB.46.12554

    work page doi:10.1103/physrevb.46.12554 1992

  54. [54]

    Lyo, N.E

    S.K. Lyo, N.E. Harff, and J.A. Simmons, Phys. Rev. B, 58, 1572 (1998). https://doi.org/10.1103/PhysRevB.58.1572

    work page doi:10.1103/physrevb.58.1572 1998

  55. [55]

    Vurgaftman, J

    I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, J. Appl. Phys., 89, 5815 (2001). https://doi.org/10.1063/1.1368156

    work page doi:10.1063/1.1368156 2001

  56. [56]

    Lyo, Phys

    S.K. Lyo, Phys. Rev. B, 40, 8418 (1989), https://doi.org/10.1103/PhysRevB.40.8418

    work page doi:10.1103/physrevb.40.8418 1989

  57. [57]

    Kempa, P

    K. Kempa, P. Bakshi, J. Engelbrecht and Y . Zhou, Phys. Rev. B, 61, 11083 (2000). https://doi.org/10.1103/PhysRevB.61.11083

    work page doi:10.1103/physrevb.61.11083 2000

  58. [58]

    Golovach and M

    V .N. Golovach and M. E. Portnoi, Phys. Rev. B, 74, 085321 (2006). https://doi.org/10.1103/PhysRevB.74.085321

    work page doi:10.1103/physrevb.74.085321 2006

  59. [59]

    Uenoyama and L J

    T. Uenoyama and L J. Sham, Phys. Rev. B, 39, 11044 (1989). https://doi.org/10.1103/PhysRevB.39.11044

    work page doi:10.1103/physrevb.39.11044 1989