- 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
  • Open Access

Impact of spin-orbit coupling on electron correlation corrections to the density of states in anisotropic conductors

Bahruz Suleymanli*

B. Tanatar†

  • *Contact author: bahruz.suleymanli@gmail.com
  • †Contact author: tanatar@fen.bilkent.edu.tr
PDF

Phys. Rev. B 114, 074202 – Published 18 August, 2026

DOI: https://doi.org/10.1103/fc6k-t79j

Abstract

We study Altshuler-Aronov-type interaction corrections to the single-particle density of states (DOS) in a strongly anisotropic two-dimensional conductor with an open Fermi surface and weak disorder, in the presence of coexisting Rashba and Dresselhaus spin-orbit couplings (SOCs) constrained to the longitudinal direction. The low-energy band consists of two warped sheets weakly tunnel-coupled transversely; the SOC splits the sheets into helicity branches with a fixed spin axis. Working in a Matsubara space, we compute the exchange contribution in the diffusion channel with dynamically screened Coulomb interaction and an impurity ladder. The resulting DOS anomaly exhibits a dimensional crossover governed by the transverse coupling scale ɛc. Close to the Fermi level (|ɛ−ɛF|<ɛc), the system behaves two dimensionally, featuring a logarithmic DOS dip whose magnitude is enhanced by intrinsic SOCs. Further from the Fermi level (|ɛ−ɛF|>ɛc), the system behaves quasi-one-dimensionally, featuring a sharper square-root singularity whose amplitude is remarkably enhanced by the SOCs. Notably, we identify a critical SOC strength at which these spin-orbit effects exactly cancel the electron-correlation correction, perfectly restoring the unperturbed density of states. Furthermore, increasing the SOC beyond this critical point inverts the sign of the anomaly entirely, yielding a positive DOS correction. This sign reversal fundamentally alters the energy dependence, such that at energies beyond ɛF+ɛc, the positive correction decays to smaller values as energy increases, opposite to the standard negative correction. This contrasting trend provides a distinct spectroscopic signature of SOC-modulated correlation effects.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (57)

  1. J. B. Miller, D. M. Zumbühl, C. M. Marcus, Y. B. Lyanda-Geller, D. Goldhaber-Gordon, K. Campman, and A. C. Gossard, Gate-controlled spin-orbit quantum interference effects in lateral transport, Phys. Rev. Lett. 90, 076807 (2003).
  2. A. D. Caviglia, M. Gabay, S. Gariglio, N. Reyren, C. Cancellieri, and J.-M. Triscone, Tunable Rashba spin-orbit interaction at oxide interfaces, Phys. Rev. Lett. 104, 126803 (2010).
  3. L. Guo, Y. Yan, R. Xu, J. Li, and C. Zeng, Zero-bias conductance peaks effectively tuned by gating-controlled Rashba spin-orbit coupling, Phys. Rev. Lett. 126, 057701 (2021).
  4. E. Mariani, L. I. Glazman, A. Kamenev, and F. von Oppen, Zero-bias anomaly in the tunneling density of states of graphene, Phys. Rev. B 76, 165402 (2007).
  5. Z. Wang, D.-K. Ki, H. Chen, H. Berger, A. H. MacDonald, and A. F. Morpurgo, Strong interface-induced spin-orbit interaction in graphene on WS2, Nat. Commun. 6, 8339 (2015).
  6. T. Wakamura, F. Reale, P. Palczynski, S. Guéron, C. Mattevi, and H. Bouchiat, Strong anisotropic spin-orbit interaction induced in graphene by monolayer WS2, Phys. Rev. Lett. 120, 106802 (2018).
  7. B. Fülöp, A. Márffy, S. Zihlmann, M. Gmitra, E. Tóvári, B. Szentpéteri, M. Kedves, K. Watanabe, T. Taniguchi, J. Fabian, C. Schönenberger, P. Makk, and S. Csonka, Boosting proximity spin orbit coupling in graphene/WSe2 heterostructures via hydrostatic pressure, npj 2D Mater. Appl. 5, 82 (2021).
  8. L. Sun, L. Rademaker, D. Mauro, A. Scarfato, Á. Pásztor, I. Gutiérrez-Lezama, Z. Wang, J. Martinez-Castro, A. F. Morpurgo, and C. Renner, Determining spin-orbit coupling in graphene by quasiparticle interference imaging, Nat. Commun. 14, 3771 (2023).
  9. A. Endo and Y. Iye, Origin of positive magnetoresistance in small-amplitude unidirectional lateral superlattices, Phys. Rev. B 72, 235303 (2005).
  10. A. Endo, S. Katsumoto, and Y. Iye, Commensurability oscillations in the Hall resistance of unidirectional lateral superlattices, Phys. Rev. B 103, 235303 (2021).
  11. C. Blumenstein, J. Schäfer, S. Mietke, S. Meyer, A. Dollinger, M. Lochner, X. Y. Cui, L. Patthey, R. Matzdorf, and R. Claessen, Atomically controlled quantum chains hosting a Tomonaga-Luttinger liquid, Nat. Phys. 7, 776 (2011).
  12. C. Tegenkamp, D. Lükermann, H. Pfnür, B. Slomski, G. Landolt, and J. H. Dil, Fermi nesting between atomic wires with strong spin-orbit coupling, Phys. Rev. Lett. 109, 266401 (2012).
  13. J. Park, S. W. Jung, M.-C. Jung, H. Yamane, N. Kosugi, and H. W. Yeom, Self-assembled nanowires with giant Rashba split bands, Phys. Rev. Lett. 110, 036801 (2013).
  14. N. Ossi, L. Bitton, D. B. Gutman, and A. Frydman, Zero-bias anomaly in a two-dimensional granular insulator, Phys. Rev. B 87, 115137 (2013).
  15. Z. Ovadyahu, Interaction-induced spatial correlations in a disordered glass, Phys. Rev. B 105, 235101 (2022).
  16. B. L. Altshuler and A. G. Aronov, Zero bias anomaly in tunnel resistance and electron-electron interaction, Solid State Commun. 30, 115 (1979).
  17. A. L. Efros and B. I. Shklovskii, Coulomb gap and low temperature conductivity of disordered systems, J. Phys. C 8, L49 (1975).
  18. M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, Luttinger-liquid behaviour in carbon nanotubes, Nature (London) 397, 598 (1999).
  19. E. Turco, M. Aapro, S. C. Ganguli, N. Krane, R. Drost, N. Sobrino, A. Bernhardt, M. Juríček, R. Fasel, P. Ruffieux, P. Liljeroth, and D. Jacob, Demonstrating Kondo behavior by temperature-dependent scanning tunneling spectroscopy, Phys. Rev. Res. 6, L022061 (2024).
  20. J. H. Pixley, D. A. Huse, and S. Das Sarma, Rare-region-induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals, Phys. Rev. X 6, 021042 (2016).
  21. H. Li, R. Hanus, C. A. Polanco, A. Zeidler, G. Koblmüller, Y. K. Koh, and L. Lindsay, GaN thermal transport limited by the interplay of dislocations and size effects, Phys. Rev. B 102, 014313 (2020).
  22. Y. Yao, S. Huang, R. Cao, Z. Zhang, et al., Dislocation-assisted electron and hole transport in GaN epitaxial layers, Nat. Commun. 16, 6448 (2025).
  23. M. Reiche and M. Kittler, Electronic and optical properties of dislocations in silicon, Crystals 6, 74 (2016).
  24. L.-J. Yin, H. Jiang, J.-B. Qiao, and L. He, Direct imaging of topological edge states at a bilayer graphene domain wall, Nat. Commun. 7, 11760 (2016).
  25. S. Thiel, C. W. Schneider, L. F. Kourkoutis, D. A. Muller, N. Reyren, A. D. Caviglia, S. Gariglio, J.-M. Triscone, and J. Mannhart, Electron scattering at dislocations in LaAlO3/SrTiO3 interfaces, Phys. Rev. Lett. 102, 046809 (2009).
  26. H. Xue, D. Jia, Y. Ge, Y. j. Guan, Q. Wang, S.-q. Yuan, H.-x. Sun, Y. D. Chong, and B. Zhang, Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator, Phys. Rev. Lett. 127, 214301 (2021).
  27. G. Bergmann, Weak localization in thin films: A time-of-flight experiment with conduction electrons, Phys. Rep. 107, 1 (1984).
  28. A. Altland, B. Simons, and M. Zirnbauer, Theories of low-energy quasi-particle states in disordered d-wave superconductors, Phys. Rep. 359, 283 (2002).
  29. B. L. Altshuler and A. Aronov, Contribution to the theory of disordered metals in strongly doped semiconductors, Zh. Eksp. Teor. Fiz. 77, 2028 (1979) [Sov. Phys. JETP 50, 968 (1979)].
  30. B. L. Altshuler, A. G. Aronov, and P. A. Lee, Interaction effects in disordered Fermi systems in two dimensions, Phys. Rev. Lett. 44, 1288 (1980).
  31. B. Altshuler and A. Aronov, Electron-electron interaction in disordered conductors, in Electron-Electron Interactions in Disordered Systems, edited by A. Efros and M. Pollak, Modern Problems in Condensed Matter Sciences, Vol. 10 (Elsevier, Amsterdam, 1985), Chap. 1, pp. 1–153.
  32. A. M. Finkel'shtein, Influence of Coulomb interaction on the properties of disordered metals, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)].
  33. H. Fukuyama, Interaction effects in the weakly localized regime of two- and three-dimensional disordered systems, in Electron–Electron Interactions in Disordered Systems, edited by A. Efros and M. Pollak, Modern Problems in Condensed Matter Sciences, Vol. 10 (Elsevier, Amsterdam, 1985), Chap. 2, pp. 155–230.
  34. Y. A. Firsov, E. P. Nakhmebov, V. N. Prigodin, and W. Weller, Corrections from electron-electron interaction to the one-particle density of states in strongly anisotropic two-dimensional systems, Physica Status Solidi B 141, 111 (1987).
  35. Y. A. Firsov, E. P. Nakhmedov, V. N. Prigodin, and W. Weller, Low-temperature conductivity of a weakly disordered, strongly anisotropic two-dimensional system with electron-electron interaction. Application to germanium bicrystals and to surface superlattices, Physica Status Solidi B 145, 625 (1988).
  36. S. Caliskan and M. Kumru, High-order perturbation corrections to the density of states of disordered metals in a magnetic field, Phys. Rev. B 85, 205148 (2012).
  37. C. Zhou and H. Guo, Altshuler-Aronov effects in nonequilibrium disordered nanostructures, Phys. Rev. B 100, 045413 (2019).
  38. C. Carbillet, V. Cherkez, M. A. Skvortsov, M. V. Feigel'man, F. Debontridder, L. B. Ioffe, V. S. Stolyarov, K. Ilin, M. Siegel, D. Roditchev, T. Cren, and C. Brun, Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler-Aronov density of states suppression in ultrathin NbN films, Phys. Rev. B 102, 024504 (2020).
  39. M. Kuzmiak, M. Kopčík, F. Košuth, V. Vaňo, J. Haniš, T. Samuely, V. Latyshev, O. Onufriienko, V. Komanický, J. Kačmarčík, M. Žemlička, M. Gmitra, P. Szabó, and P. Samuely, Disorder- and magnetic field-tuned fermionic superconductor-insulator transition in MoN thin films: Transport and scanning tunneling microscopy, Phys. Rev. B 108, 184511 (2023).
  40. M. Lizée, M. Stosiek, I. Burmistrov, T. Cren, and C. Brun, Local density of states fluctuations in a two-dimensional superconductor as a probe of quantum diffusion, Phys. Rev. B 107, 174508 (2023).
  41. G. Shi, F. Gao, Z. Li, R. Zhang, I. Gornyi, D. Gutman, and Y. Li, Quantum corrections to the magnetoconductivity of surface states in three-dimensional topological insulators, Nat. Commun. 14, 2596 (2023).
  42. A. Mošková and M. Moško, States-conserving density of states for Altshuler-Aronov effect: Heuristic derivation, Solid State Commun. 284-286, 56 (2018).
  43. Y. Huang and S. Das Sarma, Electronic transport, metal-insulator transition, and Wigner crystallization in transition metal dichalcogenide monolayers, Phys. Rev. B 109, 245431 (2024).
  44. J. Rollbühler and H. Grabert, Tunneling density of states of the interacting two-dimensional electron gas, Phys. Rev. Lett. 91, 166402 (2003).
  45. C. L. Romano, S. E. Ulloa, and P. I. Tamborenea, Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures, Phys. Rev. B 71, 035336 (2005).
  46. B. Suleymanli, E. Nakhmedov, F. Tatardar, and B. Tanatar, The diagrammatic method of Berezinskii for one-dimensional disordered wire with spin–orbit interaction, Physica E 146, 115550 (2023).
  47. C. L. Kane, R. Mukhopadhyay, and T. C. Lubensky, Fractional quantum Hall effect in an array of quantum wires, Phys. Rev. Lett. 88, 036401 (2002).
  48. J. Klinovaja and D. Loss, Topological edge states and fractional quantum Hall effect from umklapp scattering, Phys. Rev. Lett. 111, 196401 (2013).
  49. A. A. Burkov, A. S. Núñez, and A. H. MacDonald, Theory of spin-charge-coupled transport in a two-dimensional electron gas with Rashba spin-orbit interactions, Phys. Rev. B 70, 155308 (2004).
  50. A. Abrikosov, L. Gorkov, and I. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 2012).
  51. G. B. Arfken, H. J. Weber, and F. E. Harris, Complex variable theory, in Mathematical Methods for Physicists (Seventh Edition), edited by G. B. Arfken, H. J. Weber, and F. E. Harris (Academic, Boston, 2013), Chap. 11, pp. 469–550.
  52. C. Hamaguchi, Basic Semiconductor Physics (Springer, Berlin, 2009).
  53. A. Altland and B. Simons, Condensed Matter Field Theory (Cambridge University Press, Cambridge, 2010).
  54. E. Şaşıoğlu, S. Çalışkan, and M. Kumru, Critical behavior of density of states near Fermi energy in low-dimensional disordered metals, Phys. Rev. B 79, 035123 (2009).
  55. C. Niu, G. Qiu, Y. Wang, Z. Zhang, M. Si, W. Wu, and P. D. Ye, Gate-tunable strong spin-orbit interaction in two-dimensional tellurium probed by weak antilocalization, Phys. Rev. B 101, 205414 (2020).
  56. B. Geldiyev, M. Ünzelmann, P. Eck, T. Kißlinger, J. Schusser, T. Figgemeier, P. Kagerer, N. Tezak, M. Krivenkov, A. Varykhalov, et al., Strongly anisotropic spin and orbital Rashba effect at a tellurium – noble metal interface, Phys. Rev. B 108, L121107 (2023).
  57. L. Liu, J. Niu, L. Xiang, J. Wei, D.-L. Li, J.-F. Feng, X.-F. Han, X.-G. Zhang, and J. M. D. Coey, Symmetry-dependent electron-electron interaction in coherent tunnel junctions resolved by measurements of zero-bias anomaly, Phys. Rev. B 90, 195132 (2014).

Outline

Information

Phys. Rev. B 114, 074202– Published 18 August, 2026
  • Received 26 November 2025
  • Revised 12 June 2026
  • Accepted 24 July 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