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

Orbital Magnetic Field Driven Metal-Insulator Transition in Strongly Correlated Electron Systems

Georg Rohringer1,2 and Anton Markov3,4

  • 1Theory and Simulation of Condensed Matter, Department of Physics, King’s College London, The Strand, London WC2R 2LS, United Kingdom
  • 2I. Institute of Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany
  • 3Russian Quantum Center, Skolkovo Innovation City, 121205 Moscow, Russia
  • 4Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium

Phys. Rev. Lett. 135, 196503 – Published 6 November, 2025

DOI: https://doi.org/10.1103/bw7f-p8mp

Abstract

We study the effects of an orbital magnetic field on the Mott metal-insulator transition in the Hubbard-Hofstadter model. We demonstrate that sufficiently large magnetic fields induce a Mott insulator-to-metal phase transition supporting our claim with dynamical mean field theory (DMFT) numerical results. For both competing phases (metal and insulator) we observe a magnetic-field-induced metallization reflected in an enhancement of kinetic and potential energy. The kinetic energy of the Mott insulator increases due to the Aharonov-Bohm effect experienced by electrons virtually tunneling around an elementary plaquette which is, however, suppressed by strong correlations. The kinetic energy of the metallic phase, on the other hand, is more strongly affected by the magnetic field through a field-driven redistribution of spectral weight due to the formation of magnetic minibands. This leads to an increase of the kinetic energy which tends to stabilize the metallic state. Our theoretical results might be relevant for recent experimental studies on magnetic field driven insulator-to-metal transitions in strongly correlated materials such as VO2, λ-type organic conductors, and moiré multilayers.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (74)

  1. N. Ashcroft and N. Mermin, Solid State Physics (Hartcourt College Publishers, New York, 1976).
  2. T. Schäfer, F. Geles, D. Rost, G. Rohringer, E. Arrigoni, K. Held, N. Blümer, M. Aichhorn, and A. Toschi, Phys. Rev. B 91, 125109 (2015).
  3. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  4. F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008).
  5. R. E. Peierls, Quantum Theory of Solids (Clarendon Press, New York, 1996).
  6. J. Zaanen, G. A. Sawatzky, and J. W. Allen, Phys. Rev. Lett. 55, 418 (1985).
  7. N. F. Mott, Rev. Mod. Phys. 40, 677 (1968).
  8. S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, Nat. Rev. Mater. 2, 17033 (2017).
  9. B. H. Moon, Emergent Mater. 4, 989 (2021).
  10. K. Haule and G. L. Pascut, Sci. Rep. 7, 10375 (2017).
  11. Y. Fei, Z. Wu, W. Zhang, and Y. Yin, AAPPS Bull. 32, 20 (2022).
  12. K. L. Gurunatha, S. Sathasivam, J. Li, M. Portnoi, I. P. Parkin, and I. Papakonstantinou, Adv. Funct. Mater. 30, 2005311 (2020).
  13. C. Ling, Z. Zhao, X. Hu, J. Li, X. Zhao, Z. Wang, Y. Zhao, and H. Jin, ACS Appl. Nano Mater. 2, 6738 (2019).
  14. G. Mazza, A. Amaricci, M. Capone, and M. Fabrizio, Phys. Rev. Lett. 117, 176401 (2016).
  15. F. Kagawa, T. Itou, K. Miyagawa, and K. Kanoda, Phys. Rev. Lett. 93, 127001 (2004).
  16. Z. L. Sun, A. F. Wang, H. M. Mu, H. H. Wang, Z. F. Wang, T. Wu, Z. Y. Wang, X. Y. Zhou, and X. H. Chen, npj Quantum Mater. 6, 94 (2021).
  17. A. P. Ramirez, J. Phys. Condens. Matter 9, 8171 (1997).
  18. E. Dagotto, T. Hotta, and A. Moreo, Phys. Rep. 344, 1 (2001).
  19. M. B. Salamon and M. Jaime, Rev. Mod. Phys. 73, 583 (2001).
  20. Y. H. Matsuda, D. Nakamura, A. Ikeda, S. Takeyama, Y. Suga, H. Nakahara, and Y. Muraoka, Nat. Commun. 11, 3591 (2020).
  21. Y. H. Matsuda, Y. Muraoka, D. Nakamura, A. Ikeda, Y. Ishii, X.-G. Zhou, H. Sawabe, and S. Takeyama, J. Phys. Soc. Jpn. 91, 101008 (2022).
  22. S. Fukuoka, T. Oka, Y. Ihara, A. Kawamoto, S. Imajo, and K. Kindo, Phys. Rev. B 109, 195142 (2024).
  23. Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, Nature (London) 556, 80 (2018).
  24. J. M. Pizarro, M. J. Calderón, and E. Bascones, J. Phys. Comm. 3, 035024 (2019).
  25. Y. H. Kwan, S. A. Parameswaran, and S. L. Sondhi, Phys. Rev. B 101, 205116 (2020).
  26. K. Czajka, A. Gorczyca, M. M. Maśka, and M. Mierzejewski, Phys. Rev. B 74, 125116 (2006).
  27. S. Acheche, L.-F. Arsenault, and A.-M. S. Tremblay, Phys. Rev. B 96, 235135 (2017).
  28. A. A. Markov, G. Rohringer, and A. N. Rubtsov, Phys. Rev. B 100, 115102 (2019).
  29. J. Vučičević and R. Žitko, Phys. Rev. Lett. 127, 196601 (2021).
  30. J. Vučičević and R. Žitko, Phys. Rev. B 104, 205101 (2021).
  31. J. K. Ding, W. O. Wang, B. Moritz, Y. Schattner, E. W. Huang, and T. P. Devereaux, Commun. Phys. 5, 204 (2022).
  32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/bw7f-p8mp for technical details of the numerical calculations and additional numerical results.
  33. M. Wallerberger, A. Hausoel, P. Gunacker, A. Kowalski, N. Parragh, F. Goth, K. Held, and G. Sangiovanni, Comput. Phys. Commun. 235, 388 (2019).
  34. F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
  35. J. Sherman and W. J. Morrison, Ann. Math. Stat. 21, 124 (1950).
  36. W. W. Hager, SIAM Rev. 31, 221 (1989).
  37. D. A. Harville, Matrix Algebra From a Statistician’s Perspective (Springer-Verlag, New York, 1997), https://doi.org/10.1007/b98818.
  38. I. M. Niven, H. S. Zuckerman, and H. L. Montgomery, An Introduction to the Theory of Numbers, 5th ed. (John Wiley and Sons, New York, 1991).
  39. W. R. Inc., Mathematica, version 14.1 (1988–2025), Champaign, IL, 2024.
  40. D. Vollhardt and P. Wölfe, Electronic Phase Transitions (Elsevier Science Publishers B.V., New York, 1992), Chap. 1, pp. 1–78.
  41. A. Georges and W. Krauth, Phys. Rev. Lett. 69, 1240 (1992).
  42. A. Georges and G. Kotliar, Phys. Rev. B 45, 6479 (1992).
  43. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
  44. L. Laloux, A. Georges, and W. Krauth, Phys. Rev. B 50, 3092 (1994).
  45. J. Bauer and A. C. Hewson, Phys. Rev. B 76, 035118 (2007).
  46. P. G. van Dongen and C. Leinung, Ann. Phys. (Berlin) 509, 45 (1997).
  47. D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984).
  48. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
  49. G. Sangiovanni, A. Toschi, E. Koch, K. Held, M. Capone, C. Castellani, O. Gunnarsson, S.-K. Mo, J. W. Allen, H.-D. Kim, A. Sekiyama, A. Yamasaki, S. Suga, and P. Metcalf, Phys. Rev. B 73, 205121 (2006).
  50. X. Wang, E. Gull, L. de’ Medici, M. Capone, and A. J. Millis, Phys. Rev. B 80, 045101 (2009).
  51. J. Fei, C.-N. Yeh, and E. Gull, Phys. Rev. Lett. 126, 056402 (2021).
  52. K. Nogaki, J. Fei, E. Gull, and H. Shinaoka, SciPost Phys. Codebases 19 (2023).
  53. K. Nogaki, J. Fei, E. Gull, and H. Shinaoka, SciPost Phys. Codebases 19-r1.0 (2023).
  54. M. Jarrell and J. E. Gubernatis, Phys. Rep. 269, 133 (1996).
  55. J. Kaufmann and K. Held, Comput. Phys. Commun. 282, 108519 (2023).
  56. Larger magnetic fields (B>0.5) are not meaningful in our model, as it is symmetric under the transformation B→1−B.

  57. Y. Hatsugai and M. Kohmoto, Phys. Rev. B 42, 8282 (1990).
  58. N. Hyttrek, Topological quantization of the Hall conductivity in superconducting cuprates—A Hubbard-Hofstadter model study, Master’s thesis, University of Hamburg, 2024.
  59. R. Bulla and M. Potthoff, Eur. Phys. J. B 13, 257 (2000).
  60. M. C. Gutzwiller, Phys. Rev. 137, A1726 (1965).
  61. W. F. Brinkman and T. M. Rice, Phys. Rev. B 2, 4302 (1970).
  62. D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984).
  63. M. M. Wysokiński and M. Fabrizio, Phys. Rev. B 95, 161106(R) (2017).
  64. The improved treatment of fluctuations in Ref. [63] reduces Uc by a factor of ∼0.822. Moreover, according to our phase diagram the critical Uc=2.71 at T=0 is reduced to Uc=2.45 at T=0.01. Hence, we have Uc=(2.45/2.71)×0.822×8|Ekin0|=5.945|Ekin0|∼6|Ekin0|.

  65. G. G. Naumis, Phys. Lett. A 380, 1772 (2016).
  66. S. Pairault, D. Sénéchal, and A.-M. S. Tremblay, Phys. Rev. Lett. 80, 5389 (1998).
  67. S. Pairault, D. Sénéchal, and A.-M. S. Tremblay, Eur. Phys. J. B 16, 85 (2000).
  68. D. Sen and R. Chitra, Phys. Rev. B 51, 1922 (1995).
  69. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
  70. S. Choi, G. Ahn, S. J. Moon, and S. Lee, Sci. Rep. 10, 9721 (2020).
  71. H. Lu and J. Robertson, Phys. Status Solidi (b) 256, 1900210 (2019).
  72. J. Dalibard, in Proceedings of the International School of Physics “Enrico Fermi” 2014 (2015), arXiv:1504.05520.
  73. J. Kang, B. A. Bernevig, and O. Vafek, Phys. Rev. Lett. 127, 266402 (2021).
  74. C. R. Kometter, J. Yu, T. Devakul, A. P. Reddy, Y. Zhang, B. A. Foutty, K. Watanabe, T. Taniguchi, L. Fu, and B. E. Feldman, Nat. Phys. 19, 1861 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation