- 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

Catalog of cubic, symmetry-protected, non-Fermi liquid, Kondo-type exchange models for doublet impurities

Anna I. Tóth* and Andrew D. Huxley

  • School of Physics and Astronomy, Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom

  • *Contact author: atoth2@ed.ac.uk
PDF

Phys. Rev. B 112, 205120 – Published 18 November, 2025

DOI: https://doi.org/10.1103/j67z-1lj4

Abstract

To identify what types of non-Fermi liquid (NFL) behavior are most likely to occur in cubic metals due to doublet impurities, we derive every cubic symmetry-allowed, NFL, Kondo-type exchange coupling that does not need accidental degeneracy for its realization. We find three distinct types of NFL behavior: two-channel Kondo (2CK) behavior for a non-Kramers doublet impurity coupled to local Γ8 conduction electrons; topological Kondo physics for a Kramers doublet impurity and Γ4 or Γ5 conduction electrons; and lastly, spin-half impurity spin-32 conduction electron Kondo behavior for a Kramers doublet impurity and Γ8 conduction electrons. The first two critical behaviors are not straightforward to realize. In the first case, 2CK physics is not guaranteed, since cubic symmetry does not prevent an effective spatial anisotropy from exceeding the 2CK coupling, which restores a Fermi liquid behavior. In the second case, the topological Kondo interaction is guaranteed to dominate; however, the spin degeneracy of the conduction electrons needs to be lifted, e.g., by a magnetic field—so that they can be represented by Γ4 or Γ5 triplets—which then also lifts the degeneracy of the Kramers doublet. We find that the spin-half impurity spin-32 conduction electron, NFL, Kondo behavior has the greatest chance of existing in diluted, cubic compounds. We compute the thermodynamics of the topological Kondo model using the numerical renormalization group, and we discuss the thermodynamics of the spin-half impurity spin-32 conduction electron Kondo model. We also identify candidate materials where the corresponding NFL behaviors could be observed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (59)

  1. H. R. Ott, H. Rudigier, Z. Fisk, and J. L. Smith, UBe13: An unconventional actinide superconductor, Phys. Rev. Lett. 50, 1595 (1983).
  2. C. L. Seaman, M. B. Maple, B. W. Lee, S. Ghamaty, M. S. Torikachvili, J.-S. Kang, L. Z. Liu, J. W. Allen, and D. L. Cox, Evidence for non-Fermi liquid behavior in the Kondo alloy Y1−xUxPd3, Phys. Rev. Lett. 67, 2882 (1991).
  3. M. Suzuki and T. Murakami, Hall effect in superconducting (La1−xSrx)2CuO4 single crystal thin films, Jpn. J. Appl. Phys. 26, L524 (1987).
  4. M. Gurvitch and A. T. Fiory, Resistivity of La1.825Sr0.175CuO4 and YBa2Cu3O7 to 1100 K: Absence of saturation and its implications, Phys. Rev. Lett. 59, 1337 (1987).
  5. P. Giraldo-Gallo, J. A. Galvis, Z. Stegen, K. A. Modic, F. F. Balakirev, J. B. Betts, X. Lian, C. Moir, S. C. Riggs, A. T. Bollinger et al., Scale-invariant magnetoresistance in a cuprate superconductor, Science 361, 479 (2018).
  6. R. H. Liu, G. Wu, T. Wu, D. F. Fang, H. Chen, S. Y. Li, K. Liu, Y. L. Xie, X. F. Wang, R. L. Yang et al., Anomalous transport properties and phase diagram of the FeAs-based SmFeAsO1−xFx superconductors, Phys. Rev. Lett. 101, 087001 (2008).
  7. L. Fang, H. Luo, P. Cheng, Z. Wang, Y. Jia, G. Mu, B. Shen, I. I. Mazin, L. Shan, C. Ren et al., Roles of multiband effects and electron-hole asymmetry in the superconductivity and normal-state properties of Ba(Fe1−xCox)2As2, Phys. Rev. B 79, 140508(R) (2009).
  8. S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata et al., Evolution from non-Fermi- to Fermi-liquid transport via isovalent doping in BaFe2(As1−xPx)2 superconductors, Phys. Rev. B 81, 184519 (2010).
  9. P. B. Allen, R. M. Wentzcovitch, W. W. Schulz, and P. C. Canfield, Resistivity of the high-temperature metallic phase of VO2, Phys. Rev. B 48, 4359 (1993).
  10. M. M. Qazilbash, K. S. Burch, D. Whisler, D. Shrekenhamer, B. G. Chae, H. T. Kim, and D. N. Basov, Correlated metallic state of vanadium dioxide, Phys. Rev. B 74, 205118 (2006).
  11. P. Kostic, Y. Okada, N. C. Collins, Z. Schlesinger, J. W. Reiner, L. Klein, A. Kapitulnik, T. H. Geballe, and M. R. Beasley, Non-fermi-liquid behavior of SrRuO3: Evidence from infrared conductivity, Phys. Rev. Lett. 81, 2498 (1998).
  12. P. Khalifah, K. D. Nelson, R. Jin, Z. Q. Mao, Y. Liu, Q. Huang, X. P. A. Gao, A. P. Ramirez, and R. J. Cava, Non-Fermi-liquid behaviour in La4Ru6O19, Nature (London) 411, 669 (2001).
  13. Y. S. Lee, J. Yu, J. S. Lee, T. W. Noh, T.-H. Gimm, H.-Y. Choi, and C. B. Eom, Non-Fermi liquid behavior and scaling of the low-frequency suppression in the optical conductivity spectra of CaRuO3, Phys. Rev. B 66, 041104(R) (2002).
  14. S. Nakatsuji, Y. Machida, Y. Maeno, T. Tayama, T. Sakakibara, J. van Duijn, L. Balicas, J. N. Millican, R. T. Macaluso, and J. Y. Chan, Metallic spin-liquid behavior of the geometrically frustrated Kondo lattice Pr2Ir2O7, Phys. Rev. Lett. 96, 087204 (2006).
  15. G. Cao, V. Durairaj, S. Chikara, L. E. DeLong, S. Parkin, and P. Schlottmann, Non-Fermi-liquid behavior in nearly ferromagnetic SrIrO3 single crystals, Phys. Rev. B 76, 100402(R) (2007).
  16. C. Pfleiderer, S. R. Julian, and G. G. Lonzarich, Non-Fermi-liquid nature of the normal state of itinerant-electron ferromagnets, Nature (London) 414, 427 (2001).
  17. M. J. Steiner, F. Beckers, P. G. Niklowitz, and G. G. Lonzarich, Non-Fermi liquid form of the low temperature resistivity in the low moment ferromagnets Ni3Al and YNi3, Phys. B: Condens. Matter 329-333, 1079 (2003).
  18. M. Brando, W. J. Duncan, D. Moroni-Klementowicz, C. Albrecht, D. Grüner, R. Ballou, and F. M. Grosche, Logarithmic fermi-liquid breakdown in NbFe2, Phys. Rev. Lett. 101, 026401 (2008).
  19. G. R. Stewart, Non-Fermi-liquid behavior in d− and f-electron metals, Rev. Mod. Phys. 73, 797 (2001); 78, 743 (2006).
  20. B. Dardel, D. Malterre, M. Grioni, P. Weibel, Y. Baer, J. Voit, and D. Jérôme, Possible observation of a Luttinger-liquid behaviour from photoemission spectroscopy of one-dimensional organic conductors, Europhys. Lett. 24, 687 (1993).
  21. J. Moser, M. Gabay, P. Auban-Senzier, D. Jérome, K. Bechgaard, and J. M. Fabre, Transverse transport in (TM)2X organic conductors: Possible evidence for a Luttinger liquid, Eur. Phys. J. B 1, 39 (1998).
  22. 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).
  23. A. Jaoui, I. Das, G. D. Battista, J. Díez-Mérida, X. Lu, K. Watanabe, T. Taniguchi, H. Ishizuka, L. Levitov, and D. K. Efetov, Quantum critical behaviour in magic-angle twisted bilayer graphene, Nat. Phys. 18, 633 (2022).
  24. S. Tomonaga, Remarks on Bloch's method of sound waves applied to many-fermion problems, Prog. Theor. Phys. 5, 544 (1950).
  25. J. M. Luttinger, An exactly soluble model of a many-Fermion system, J. Math. Phys. 4, 1154 (1963).
  26. S. Lee, Recent developments in non-Fermi Liquid theory, Annu. Rev. Condens. Matter Phys. 9, 227 (2018).
  27. Fractional Quantum Hall Effects: New Developments, edited by B. I. Halperin and J. K. Jain (World Scientific, Singapore, 2020).
  28. D. Chowdhury, A. Georges, O. Parcollet, and S. Sachdev, Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids, Rev. Mod. Phys. 94, 035004 (2022).
  29. Ph. Nozières and A. Blandin, Kondo effect in real metals, J. Phys. Lett. 41, 193 (1980).
  30. K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47, 773 (1975).
  31. I. Affleck and A. W. W. Ludwig, The Kondo effect, conformal field theory and fusion rules, Nucl. Phys. B 352, 849 (1991); Critical theory of overscreened Kondo fixed points, 360, 641 (1991); I. Affleck, A. W. W. Ludwig, H. B. Pang, and D. L. Cox, Relevance of anisotropy in the multichannel Kondo effect: Comparison of conformal field theory and numerical renormalization-group results, Phys. Rev. B 45, 7918 (1992).
  32. D. L. Cox, Quadrupolar Kondo effect in uranium heavy-electron materials? Phys. Rev. Lett. 59, 1240 (1987).
  33. F. G. Aliev, H. El Mfarrej, S. Vieira, and R. Villar, Anomalous ground state of U0.9Th0.1Be13: Temperature dependence of the resistivity and magnetoresistance, Solid State Commun. 91, 775 (1994).
  34. H. Amitsuka and T. Sakakibara, Single uranium-site properties of the dilute heavy electron system UxTh1−xRu2Si2 (x≤0.07), J. Phys. Soc. Jpn. 63, 736 (1994).
  35. T. Onimaru and H. Kusunose, Exotic quadrupolar phenomena in non-Kramers doublet systems—the cases of PrT2Zn20 (T = Ir, Rh) and PrT2Al20 (T = V, Ti), J. Phys. Soc. Jpn. 85, 082002 (2016).
  36. Y. Yamane, T. Onimaru, K. Wakiya, K. T. Matsumoto, K. Umeo, and T. Takabatake, Single-site non-fermi-liquid behaviors in a diluted 4f2 system Y1−xPrxIr2Zn20, Phys. Rev. Lett. 121, 077206 (2018).
  37. T. Yanagisawa, H. Hidaka, H. Amitsuka, S. Zherlitsyn, J. Wosnitza, Y. Yamane, and T. Onimaru, Evidence for the single-site quadrupolar Kondo effect in the dilute non-Kramers system Y1−xPrxIr2Zn20, Phys. Rev. Lett. 123, 067201 (2019).
  38. D. L. Cox, Selection rules for two-channel Kondo models of U4+ and Ce3+ ions in metals, Phys. B Condens. Matter 186, 312 (1993).
  39. D. L. Cox and A. Zawadowski, Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunneling centers, Adv. Phys. 47, 599 (1998).
  40. A. I. Tóth and G. Kotliar, Hexadecapolar Kondo effect in URu2Si2? Phys. Rev. Lett. 107, 266405 (2011).
  41. A. S. Patri and Y. B. Kim, Critical theory of non-Fermi liquid fixed point in multipolar Kondo problem, Phys. Rev. X 10, 041021 (2020).
  42. A. I. Tóth, Three types of non-Fermi-liquid fixed point for a triplet quantum impurity in a cubic metal, arXiv:2510.15163.
  43. G. F. Koster et al., Properties of the Thirty-Two Point Groups (MIT Press, Cambridge, MA, 1963).
  44. R. A. Satten and J. S. Margolis, f2 Configuration in a crystalline field, J. Chem. Phys. 32, 573 (1960).
  45. R. Pappalardo, Cubic-field splitting and cubic-symmetry orthonormal sets of wave functions for J Manifolds (J Half-Integer), J. Chem. Phys. 34, 1380 (1961).
  46. A. Messiah, Quantum Mechanics (Dover, New York, 1999).
  47. V. J. Emery and S. Kivelson, Mapping of the two-channel Kondo problem to a resonant-level model, Phys. Rev. B 46, 10812 (1992).
  48. A. I. Tóth, One-and-a-half-channel Kondo model and its family of non-Fermi liquids, arXiv:1708.08019.
  49. M. Fabrizio and A. O. Gogolin, Toulouse limit for the overscreened four-channel Kondo problem, Phys. Rev. B 50, 17732(R) (1994).
  50. B. Béri and N. R. Cooper, Topological Kondo effect with Majorana Fermions, Phys. Rev. Lett. 109, 156803 (2012).
  51. M. R. Galpin, A. K. Mitchell, J. Temaismithi, D. E. Logan, B. Béri, and N. R. Cooper, Conductance fingerprint of Majorana fermions in the topological Kondo effect, Phys. Rev. B 89, 045143 (2014).
  52. A. I. Tóth, C. P. Moca, Ö. Legeza, and G. Zaránd, Density matrix numerical renormalization group for non-Abelian symmetries, Phys. Rev. B 78, 245109 (2008).
  53. W. C. Oliveira and L. N. Oliveira, Generalized numerical renormalization-group method to calculate the thermodynamical properties of impurities in metals, Phys. Rev. B 49, 11986 (1994).
  54. S. Barakat, D. Braithwaiteb, P. Alirezaa, K. Grubec, M. Uhlarzd, J. Wilsone, C. Pfleiderer, J. Flouquet, and G. Lonzarich, High-pressure investigations of the itinerant ferromagnet CoS2, Phys. B: Condens. Matter 359-361, 1216 (2005).
  55. L. Paolasini and G. H. Lander, Iron magnetism in cubic Laves phase itinerant ferromagnets, J. Alloys Compd. 303-304, 232 (2000).
  56. H. W. Meul, C. Rossel, M. Decroux, A. Fischer, G. Remenyi, and A. Briggs, Observation of magnetic-field-induced superconductivity, Phys. Rev. Lett. 53, 497 (1984).
  57. T.-S. Kim, L. N. Oliveira, and D. L. Cox, Non-Fermi-liquid fixed point, Phys. Rev. B 55, 12460 (1997).
  58. M. Fabrizio and G. Zaránd, Mapping between multichannel exchange models, Phys. Rev. B 54, 10008 (1996).
  59. A. M. Sengupta and Y. B. Kim, Overscreened single-channel Kondo problem, Phys. Rev. B 54, 14918 (1996).

Outline

Information

Phys. Rev. B 112, 205120– Published 18 November, 2025
  • Received 7 November 2024
  • Revised 8 August 2025
  • Accepted 29 September 2025
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