- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Insulating Out-of-Plane Transport in Anisotropic Metals: The Case of Sr2RuO4 and Related Layered Oxides

Sophie Beck1,2,*, Matthew Shammami1,3, Lorenzo Van Muñoz4, Jason Kaye1,5, Antoine Georges6,1,7,8, and Jernej Mravlje9,10,†

  • *Contact author: sophie.beck@tuwien.ac.at
  • †Contact author: jernej.mravlje@ijs.si
PDF

Phys. Rev. Lett. 137, 166301 – Published 14 October, 2026

DOI: https://doi.org/10.1103/lch5-7zp4

Abstract

We reveal a mechanism that may explain the nonmetallic out-of-plane resistivity in layered metals. By carefully examining how the Drude-Boltzmann expression for the c-axis conductivity emerges out of the Kubo formula, we find, besides the standard metallic term proportional to the carrier lifetime τ, a non-Drude contribution proportional to 1/τ. The Drude behavior breaks down when 1/τ>2η*, the crossover value η* being small (and hence observable) when the c-axis velocities vary rapidly with the distance from the Fermi surface. We consider the Hund metal Sr2RuO4 as a test case, which we study within a realistic dynamical mean-field theory approach. The non-Drude behavior observed experimentally in c-axis transport is reproduced and explained by our considerations, showing that earlier invoked extrinsic mechanisms that involve either impurities or phonons are unnecessary. Although the small value of η* arises from a peculiar accidental cancellation due to destructive interference, characteristic of body-centered tetragonal lattices, we emphasize and discuss the generality of this mechanism.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (62)

  1. J. A. N. Bruin, H. Sakai, R. S. Perry, and A. P. Mackenzie, Science 339, 804 (2013).
  2. C. M. Varma, Rev. Mod. Phys. 92, 031001 (2020).
  3. A. Ataei, A. Gourgout, G. Grissonnanche, L. Chen, J. Baglo, M.-E. Boulanger, F. Laliberté, S. Badoux, N. Doiron-Leyraud, V. Oliviero, S. Benhabib, D. Vignolles, J.-S. Zhou, S. Ono, H. Takagi, C. Proust, and L. Taillefer, Nat. Phys. 18, 1420 (2022).
  4. I. Terasaki, Y. Sasago, and K. Uchinokura, Phys. Rev. B 56, R12685 (1997).
  5. A. W. Tyler, A. P. Mackenzie, S. NishiZaki, and Y. Maeno, Phys. Rev. B 58, R10107 (1998).
  6. I. Nagai, N. Shirakawa, N. Umeyama, and S.-I. Ikeda, J. Phys. Soc. Jpn. 79, 114719 (2010).
  7. T. Valla, P. D. Johnson, Z. Yusof, B. Wells, Q. Li, S. M. Loureiro, R. J. Cava, M. Mikami, Y. Mori, M. Yoshimura, and T. Sasaki, Nature (London) 417, 627 (2002).
  8. S.-C. Wang, H.-B. Yang, A. K. P. Sekharan, H. Ding, J. R. Engelbrecht, X. Dai, Z. Wang, A. Kaminski, T. Valla, T. Kidd, A. V. Fedorov, and P. D. Johnson, Phys. Rev. Lett. 92, 137002 (2004).
  9. A. Millis, Nature (London) 417, 599 (2002).
  10. A. Hunter, S. Beck, E. Cappelli, F. Margot, M. Straub, Y. Alexanian, G. Gatti, M. D. Watson, T. K. Kim, C. Cacho, N. C. Plumb, M. Shi, M. Radović, D. A. Sokolov, A. P. Mackenzie, M. Zingl, J. Mravlje, A. Georges, F. Baumberger, and A. Tamai, Phys. Rev. Lett. 131, 236502 (2023).
  11. M. Radonjić, D. Tanasković, V. Dobrosavljević, and K. Haule, Phys. Rev. B 81, 075118 (2010).
  12. X. Deng, J. Mravlje, R. Žitko, M. Ferrero, G. Kotliar, and A. Georges, Phys. Rev. Lett. 110, 086401 (2013).
  13. R. E. Prange and L. P. Kadanoff, Phys. Rev. 134, A566 (1964).
  14. W. Xu, K. Haule, and G. Kotliar, Phys. Rev. Lett. 111, 036401 (2013).
  15. A. Georges and J. Mravlje, Phys. Rev. Res. 3, 043132 (2021).
  16. A. Gourgout, G. Grissonnanche, F. Laliberté, A. Ataei, L. Chen, S. Verret, J.-S. Zhou, J. Mravlje, A. Georges, N. Doiron-Leyraud, and L. Taillefer, Phys. Rev. X 12, 011037 (2022).
  17. J. Mravlje, M. Aichhorn, T. Miyake, K. Haule, G. Kotliar, and A. Georges, Phys. Rev. Lett. 106, 096401 (2011).
  18. A. Tamai, M. Zingl, E. Rozbicki, E. Cappelli, S. Riccò, A. de la Torre, S. McKeown Walker, F. Y. Bruno, P. D. C. King, W. Meevasana, M. Shi, M. Radović, N. C. Plumb, A. S. Gibbs, A. P. Mackenzie, C. Berthod, H. U. R. Strand, M. Kim, A. Georges, and F. Baumberger, Phys. Rev. X 9, 021048 (2019).
  19. D. J. Abramovitch, J.-J. Zhou, J. Mravlje, A. Georges, and M. Bernardi, Phys. Rev. Mater. 7, 093801 (2023).
  20. U. Lundin and R. H. McKenzie, Phys. Rev. B 68, 081101 (2003).
  21. A. F. Ho and A. J. Schofield, Phys. Rev. B 71, 045101 (2005).
  22. D. B. Gutman and D. L. Maslov, Phys. Rev. Lett. 99, 196602 (2007).
  23. D. B. Gutman and D. L. Maslov, Phys. Rev. B 77, 035115 (2008).
  24. L. B. Ioffe and A. J. Millis, Phys. Rev. B 58, 11631 (1998).
  25. G. D. Mahan, Many-Particle Physics, 3rd ed., Physics of Solids and Liquids (Kluwer Academic/Plenum Publishers, New York, 2000), pp. xii–785.
  26. G. Sordi, P. Sémon, K. Haule, and A.-M. S. Tremblay, Phys. Rev. B 87, 041101(R) (2013).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/lch5-7zp4 for the derivation of Eq. (5), details of the numerical calculations (DFT, DMFT and transport), the tight-binding parameters, additional figures on the DMFT results, and an analysis of the response of related layered oxides, which includes Refs. [28–52].
  28. G. Blesio, S. Beck, O. Gingras, A. Georges, and J. Mravlje, Phys. Rev. Res. 6, 023124 (2024).
  29. S. Coh and D. Vanderbilt, Python tight binding (pythtb), 10.5281/zenodo.12721316 (2022).
  30. H. T. Dang, J. Mravlje, A. Georges, and A. J. Millis, Phys. Rev. Lett. 115, 107003 (2015).
  31. K. F. Garrity, J. W. Bennett, K. M. Rabe, and D. Vanderbilt, Comput. Mater. Sci. 81, 446 (2014).
  32. P. Giannozzi et al., J. Phys. Condens. Matter 21, 395502 (2009).
  33. E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Rev. Mod. Phys. 83, 349 (2011).
  34. K. Held, Adv. Phys. 56, 829 (2007).
  35. J. Karp, M. Bramberger, M. Grundner, U. Schollwöck, A. J. Millis, and M. Zingl, Phys. Rev. Lett. 125, 166401 (2020).
  36. A. Kauch, P. Pudleiner, K. Astleithner, P. Thunström, T. Ribic, and K. Held, Phys. Rev. Lett. 124, 047401 (2020).
  37. J. Kaye, S. Beck, A. Barnett, L. V. Muñoz, and O. Parcollet, SciPost Phys. 15, 062 (2023).
  38. A. Kazemi-Moridani, S. Beck, A. Hampel, A.-M. S. Tremblay, M. Côté, and O. Gingras, Phys. Rev. B 109, 165146 (2024).
  39. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
  40. G. Pizzi et al., J. Phys. Condens. Matter 32, 165902 (2020).
  41. T. Sato and H. Tsunetsugu, Phys. Rev. B 94, 085110 (2016).
  42. L. Van Muñoz, S. Beck, and J. Kaye, J. Open Source Software 9, 7080 (2024).
  43. L. Van Muñoz, J. Kaye, A. Barnett, and S. Beck, Phys. Rev. B 111, 195162 (2025).
  44. J. Vučičević, J. Kokalj, R. Žitko, N. Wentzell, D. Tanasković, and J. Mravlje, Phys. Rev. Lett. 123, 036601 (2019).
  45. G. Zhang and E. Pavarini, Phys. Rev. B 99, 125102 (2019).
  46. M. Aichhorn, L. Pourovskii, P. Seth, V. Vildosola, M. Zingl, O. E. Peil, X. Deng, J. Mravlje, G. J. Kraberger, C. Martins, M. Ferrero, and O. Parcollet, Comput. Phys. Commun. 204, 200 (2016).
  47. K. S. D. Beach, Identifying the maximum entropy method as a special limit of stochastic analytic continuation, arXiv:cond-mat/0403055.
  48. A. Khurana, Phys. Rev. Lett. 64, 1990 (1990).
  49. J. Mravlje and A. Georges, Phys. Rev. Lett. 117, 036401 (2016).
  50. V. S. Oudovenko, G. Pálsson, K. Haule, G. Kotliar, and S. Y. Savrasov, Phys. Rev. B 73, 035120 (2006).
  51. The Materials Project, Materials Data on Sr2MoO4, LBNL Materials Project, 10.17188/1194095(2020).
  52. The Materials Project, Materials Data on Sr2RhO4, LBNL Materials Project, 10.17188/1290707(2020).
  53. M. Kim, J. Mravlje, M. Ferrero, O. Parcollet, and A. Georges, Phys. Rev. Lett. 120, 126401 (2018).
  54. K. Yoshida, F. Nakamura, T. Goko, T. Fujita, Y. Maeno, Y. Mori, and S. NishiZaki, Phys. Rev. B 58, 15062 (1998).
  55. N. Kikugawa, C. Bergemann, A. P. Mackenzie, and Y. Maeno, Phys. Rev. B 70, 134520 (2004).
  56. F. Jerzembeck, H. S. Røising, A. Steppke, H. Rosner, D. A. Sokolov, N. Kikugawa, T. Scaffidi, S. H. Simon, A. P. Mackenzie, and C. W. Hicks, Nat. Commun. 13, 4596 (2022).
  57. N. Shirakawa, K. Murata, S. Nishizaki, Y. Maeno, and T. Fujita, Phys. Rev. B 56, 7890 (1997).
  58. D. J. Abramovitch, J. Coulter, S. Beck, and A. Millis, Phys. Rev. B 112, 075113 (2025).
  59. N. E. Hussey, A. P. Mackenzie, J. R. Cooper, Y. Maeno, S. Nishizaki, and T. Fujita, Phys. Rev. B 57, 5505 (1998).
  60. L. Wang, H. Liu, V. Zimmermann, A. K. Yogi, M. Isobe, M. Minola, M. Hepting, G. Khaliullin, and B. Keimer, Phys. Rev. Lett. 132, 116502 (2024).
  61. D. J. Singh, Phys. Rev. B 61, 13397 (2000).
  62. S. Beck, M. Shammami, L. Van Muñoz, J. Kaye, A. Georges, and J. Mravlje, Data for “Insulating out-of-plane transport in anisotropic metals: The case of Sr2RuO4 and related layered oxides,” Zenodo, 10.5281/zenodo.22214545(2026).

Outline

Information

Phys. Rev. Lett. 137, 166301– Published 14 October, 2026
  • Received 7 October 2025
  • Accepted 31 August 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