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Nonlinearities in the Hall resistance by retroreflective scattering

Frederik Bartels1, Beate Horn-Cosfeld1,*, Jakob Schluck1,†, Mihai Cerchez1, Dominique Mailly2, Klaus Pierz3, Hans W. Schumacher3, Benjamin Sanvee4, Jürgen Horbach4 et al.

Thomas Heinzel1,‡

  • *Present address: MWIKE des Landes Nordrhein-Westfalen, Berger Allee 25, 40213 Düsseldorf, Germany.
  • †Present address: II. Physikalisches Institut, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany.
  • ‡Contact author: Thomas.Heinzel@hhu.de
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Phys. Rev. B 113, 165306 – Published 21 April, 2026

DOI: https://doi.org/10.1103/lg7z-nrjy

Abstract

Nonlinearities in the classical Hall resistance of two-dimensional electron gases exposed to retroreflective obstacles at random positions are reported. The Hall slope develops a nonmonotonic component, which increases strongly in amplitude and shifts to larger magnetic fields as the obstacle density increases. At small magnetic fields, the relation between the longitudinal and transverse conductivity remains in qualitative agreement with the Drude-Boltzmann equations, although the characteristic timescale can no longer be interpreted as a momentum relaxation time. The corresponding Hall conductivity develops a marked minimum at a characteristic magnetic field outside the interval where the data agree qualitatively with the Drude-Boltzmann model. With the help of classical event-driven simulations, this minimum is attributed to successive retroreflections which lead to inverted transverse deflection.

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References (43)

  1. E. H. Hall, On a new action of the magnet on electric currents, American Journal of Mathematics 2, 287 (1879).
  2. K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494 (1980).
  3. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-dimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48, 1559 (1982).
  4. J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin Hall effects, Rev. Mod. Phys. 87, 1213 (2015).
  5. B. L. Altshuler, D. Khmel'nitskii, A. I. Larkin, and P. A. Lee, Magnetoresistance and Hall effect in a disordered two-dimensional electron gas, Phys. Rev. B 22, 5142 (1980).
  6. M. A. Khodas and A. M. Finkel'stein, Hall coefficient in an interacting electron gas, Phys. Rev. B 68, 155114 (2003).
  7. H. Fukuyama, Hall effect in two-dimensional disorderd systems, J. Phys. Soc. Jpn. 49, 644 (1980).
  8. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang, et al., Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science 340, 167 (2013).
  9. V. J. Goldman, M. Shayegan, and H. D. Drew, Anomalous Hall effect below the magnetic-field-induced metal-insulator transition in narrow-gap semiconductors, Phys. Rev. Lett. 57, 1056 (1986).
  10. X. P. A. Gao, G. S. Boebinger, A. P. Mills, A. P. Ramirez, L. N. Pfeiffer, and K. W. West, Temperature and magnetic-field-enhanced Hall slope of a dilute 2D hole system in the ballistic regime, Phys. Rev. Lett. 93, 256402 (2004).
  11. J. Jung, F. Zhang, and A. H. MacDonald, Lattice theory of pseudospin ferromagnetism in bilayer graphene: Competing interaction-induced quantum Hall states, Phys. Rev. B 83, 115408 (2011).
  12. R. Fleischmann, T. Geisel, and R. Ketzmerick, Quenched and negative Hall effect in periodic media: Application to antidot superlattices, Europhys. Lett. 25, 219 (1994).
  13. A. M. Ortiz de Zevallos, N. C. Mamani, G. M. Gusev, A. A. Quivy, T. E. Lamas, and J. C. Portal, Enhanced Hall slope in wide AlxGa1−xAs parabolic wells, Phys. Rev. B 75, 205324 (2007).
  14. A. Y. Kuntsevich, A. V. Shupletsov, and A. L. Rakhmanov, Simple mechanism that breaks the Hall-effect linearity at low temperatures, Phys. Rev. B 102, 155426 (2020).
  15. Z. Z. Du, H.-Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nat. Rev. Phys. 3, 744 (2021).
  16. B. Sanvee, J. Schluck, M. Cerchez, D. Mailly, H. W. Schumacher, K. Pierz, T. Heinzel, and J. Horbach, Hall effect in a two-dimensional disordered Lorentz gas, Phys. Rev. B 108, 035301 (2023).
  17. P. Ehrenfest and T. Ehrenfest, The Conceptual Foundations of the Statistical Approach in Mechanics (Courier, Mineola, NY, 1990).
  18. E. H. Hauge and E. G. D. Cohen, Normal and abnormal diffusion in Ehrenfests' wind‐tree model, J. Math. Phys. 10, 397 (1969).
  19. H. Van Beyeren and E. H. Hauge, Abnormal diffusion in Ehrenfest's wind-tree model, Phys. Lett. A 39, 397 (1972).
  20. B. A. Sanvee, R. Lohmann, and J. Horbach, Normal and anomalous diffusion in the disordered wind-tree model, Phys. Rev. E 106, 024104 (2022).
  21. R. Lohmann, B. Horn-Cosfeld, J. Schluck, D. Mailly, N. H. Siboni, H. W. Schumacher, K. Pierz, T. Heinzel, and J. Horbach, Anomalous transport due to retroreflection, Phys. Rev. B 102, 081302(R) (2020).
  22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/lg7z-nrjy for the calculated Hall resistances from numerical simulations, which includes Refs. [40, 41, 42, 43].
  23. T. Ando, Theory of quantum transport in a two-dimensional electron system under magnetic fields II. Single-site approximation under strong fields, J. Phys. Soc. Jpn. 36, 1521 (1974).
  24. J. Schluck, S. Fasbender, T. Heinzel, K. Pierz, H. W. Schumacher, D. Kazazis, and U. Gennser, Commensurability resonances in two-dimensional magnetoelectric lateral superlattices, Phys. Rev. B 91, 195303 (2015).
  25. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 2017).
  26. L. Bockhorn, P. Barthold, D. Schuh, W. Wegscheider, and R. J. Haug, Magnetoresistance in a high-mobility two-dimensional electron gas, Phys. Rev. B 83, 113301 (2011).
  27. A. T. Hatke, M. A. Zudov, J. L. Reno, L. N. Pfeiffer, and K. W. West, Giant negative magnetoresistance in high-mobility two-dimensional electron systems, Phys. Rev. B 85, 081304(R) (2012).
  28. L. Bockhorn, A. Velieva, S. Hakim, T. Wagner, E. P. Rugeramigabo, D. Schuh, C. Reichl, W. Wegscheider, and R. J. Haug, Influence of oval defects on transport properties in high-mobility two-dimensional electron gases, Appl. Phys. Lett. 108, 092103 (2016).
  29. L. Bockhorn, D. Schuh, C. Reichl, W. Wegscheider, and R. J. Haug, Influence of the electron density on the giant negative magnetoresistance in two-dimensional electron gases, Phys. Rev. B 109, 205416 (2024).
  30. A. D. Mirlin, D. G. Polyakov, F. Evers, and P. Wölfle, Quasiclassical negative magnetoresistance of a 2d electron gas: Interplay of strong scatterers and smooth disorder, Phys. Rev. Lett. 87, 126805 (2001).
  31. I. V. Gornyi and D. G. Polyakov, Two-dimensional electron hydrodynamics in a random array of impenetrable obstacles: Magnetoresistivity, Hall viscosity, and the Landauer dipole, Phys. Rev. B 108, 165429 (2023).
  32. P. S. Alekseev and A. P. Dmitriev, Hydrodynamic magnetotransport in two-dimensional electron systems with macroscopic obstacles, Phys. Rev. B 108, 205413 (2023).
  33. J. Schluck, M. Hund, T. Heckenthaler, T. Heinzel, N. H. Siboni, J. Horbach, K. Pierz, H. W. Schumacher, D. Kazazis, U. Gennser, and D. Mailly, Linear negative magnetoresistance in two-dimensional Lorentz gases, Phys. Rev. B 97, 115301 (2018).
  34. A. V. Bobylev, F. A. Maaø, A. Hansen, and E. H. Hauge, Two-dimensional magnetotransport according to the classical Lorentz model, Phys. Rev. Lett. 75, 197 (1995).
  35. B. Horn-Cosfeld, J. Schluck, J. Lammert, M. Cerchez, T. Heinzel, K. Pierz, H. W. Schumacher, and D. Mailly, Relevance of weak and strong classical scattering for the giant negative magnetoresistance in two-dimensional electron gases, Phys. Rev. B 104, 045306 (2021).
  36. N. H. Siboni, J. Schluck, K. Pierz, H. W. Schumacher, D. Kazazis, J. Horbach, and T. Heinzel, Nonmonotonic classical magnetoconductivity of a two-dimensional electron gas in a disordered array of obstacles, Phys. Rev. Lett. 120, 056601 (2018).
  37. C. L. Yang, J. Zhang, R. R. Du, J. A. Simmons, and J. L. Reno, Zener tunneling between Landau orbits in a high-mobility two-dimensional electron gas, Phys. Rev. Lett. 89, 076801 (2002).
  38. F. Bartels, J. Strobel, B. Horn-Cosfeld, M. Cerchez, K. Pierz, H. W. Schumacher, D. Mailly, and T. Heinzel, Hall field induced resistance oscillations by designed random obstacle arrays, Phys. Rev. B 111, 165301 (2025).
  39. F. Bartels, B. Horn-Cosfeld, J. Schluck, M. Cerchez, D. Mailly, K. Pierz, H. W. Schumacher, B. Sanvee, J. Horbach, and T. Heinzel, Nonlinearities in the Hall resistance by retroreflective scattering [data set], Zenodo (2025), 10.5281/zenodo.17702106.
  40. T. Ando, Theory of quantum transport in a two-dimensional electron system under magnetic fields. I. Characteristics of level broadening and transport under strong field, J. Phys. Soc. Jpn. 36, 959 (1974).
  41. T. Ando, Theory of oscillatory g factor in an MOS inversion layer under strong magnetic fields, J. Phys. Soc. Jpn. 37, 1044 (1974).
  42. T. Ando, Theory of quantum transport in a two-dimensional electron system under magnetic fields. IV. Oscillatory conductivity, J. Phys. Soc. Jpn. 37, 1233 (1974).
  43. T. Heinzel, Mesoscopic Electronics in Solid State Nanostructures (Wiley-VCH, New York, 2007).

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Phys. Rev. B 113, 165306– Published 21 April, 2026
  • Received 2 December 2025
  • Revised 11 March 2026
  • Accepted 30 March 2026
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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.

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