- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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
  • Letter
  • Open Access

Type-II heavy Fermi liquids and the magnetic memory of 4Hb−TaS2

Elio J. König

  • Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany

PDF

Phys. Rev. Research 6, L012058 – Published 13 March, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012058

Abstract

The interplay of quantum spin liquids with itinerant conduction electrons is of crucial interest for understanding layered structures composed of frustrated magnet and metal monolayers. Using parton-mean-field theory, we demonstrate here that a type-II heavy Fermi liquid, which is characterized by a vortex lattice in the slave boson condensate, can occur in the vicinity of the quantum phase transition separating fractionalized and heavy Fermi liquid phases. The magnetic flux threading each such vortex is about vf/137c times smaller than the magnetic flux threading vortices in type-II superconductors, where vf is the speed of magnetic excitations and c the speed of light. This makes a magnetic observation of this effect challenging. We propose scanning tunneling spectroscopy instead and investigate its signatures. If a type-II heavy Fermi liquid is cooled into a type-II superconductor, vortices in the slave boson condensate and in the superconducting condensate mutually attract. We argue that the type-II heavy Fermi liquid thereby provides a compelling explanation for the magnetic memory observed recently [Persky et al., Nature (London) 607, 692 (2022)] in thermal cycles of 4Hb−TaS2.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (75)

  1. F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schäfer, Superconductivity in the presence of strong Pauli paramagnetism: CeCu2Si2, Phys. Rev. Lett. 43, 1892 (1979).
  2. J. G. Bednorz and K. A. Müller, Possible high Tc superconductivity in the Ba- La- Cu- O system, Z. Phys. B 64, 189 (1986).
  3. A. K. Geim and I. V. Grigorieva, Van der Waals heterostructures, Nature (London) 499, 419 (2013).
  4. S. Nagata, T. Aochi, T. Abe, S. Ebisu, T. Hagino, Y. Seki, and K. Tsutsumi, Superconductivity in the layered compound 2H-TaS2, J. Phys. Chem. Solids 53, 1259 (1992).
  5. S. C. De la Barrera, M. R. Sinko, D. P. Gopalan, N. Sivadas, K. L. Seyler, K. Watanabe, T. Taniguchi, A. W. Tsen, X. Xu, D. Xiao et al., Tuning Ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalcogenides, Nat. Commun. 9, 1427 (2018).
  6. P. Fazekas and E. Tosatti, Electrical, structural and magnetic properties of pure and doped 1T-TaS2, Philos. Mag. B 39, 229 (1979).
  7. A. Ribak, I. Silber, C. Baines, K. Chashka, Z. Salman, Y. Dagan, and A. Kanigel, Gapless excitations in the ground state of 1T−TaS2, Phys. Rev. B 96, 195131 (2017).
  8. I. Lutsyk, M. Rogala, P. Dabrowski, P. Krukowski, P. J. Kowalczyk, A. Busiakiewicz, D. A. Kowalczyk, E. Lacinska, J. Binder, N. Olszowska, M. Kopciuszynski, K. Szalowski, M. Gmitra, R. Stepniewski, M. Jalochowski, J. J. Kolodziej, A. Wysmolek, and Z. Klusek, Electronic structure of commensurate, nearly commensurate, and incommensurate phases of 1T−TaS2 by angle-resolved photoelectron spectroscopy, scanning tunneling spectroscopy, and density functional theory, Phys. Rev. B 98, 195425 (2018).
  9. H. Murayama, Y. Sato, T. Taniguchi, R. Kurihara, X. Z. Xing, W. Huang, S. Kasahara, Y. Kasahara, I. Kimchi, M. Yoshida, Y. Iwasa, Y. Mizukami, T. Shibauchi, M. Konczykowski, and Y. Matsuda, Effect of quenched disorder on the quantum spin liquid state of the triangular-lattice antiferromagnet 1T−TaS2, Phys. Rev. Res. 2, 013099 (2020).
  10. V. Vaňo, M. Amini, S. C. Ganguli, G. Chen, J. L. Lado, S. Kezilebieke, and P. Liljeroth, Artificial heavy fermions in a van der Waals heterostructure, Nature (London) 599, 582 (2021).
  11. C. G. Ayani, M. Pisarra, I. M. Ibarburu, M. Garnica, R. Miranda, F. Calleja, F. Martín, and A. L. V. de Parga, Probing the phase transition to a coherent 2D Kondo lattice, Small 20, 2303275 (2024).
  12. S. Qiao, X. Li, N. Wang, W. Ruan, C. Ye, P. Cai, Z. Hao, H. Yao, X. Chen, J. Wu, Y. Wang, and Z. Liu, Mottness collapse in 1T–TaS2−xSex transition-metal dichalcogenide: An interplay between localized and itinerant orbitals, Phys. Rev. X 7, 041054 (2017).
  13. Y. Chen, W. Ruan, M. Wu, S. Tang, H. Ryu, H.-Z. Tsai, R. L. Lee, S. Kahn, F. Liou, C. Jia et al., Strong correlations and orbital texture in single-layer 1T-TaSe2, Nat. Phys. 16, 218 (2020).
  14. W. Ruan, Y. Chen, S. Tang, J. Hwang, H.-Z. Tsai, R. L. Lee, M. Wu, H. Ryu, S. Kahn, F. Liou et al., Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe2 from scanning tunnelling microscopy, Nat. Phys. 17, 1154 (2021).
  15. W. Wan, R. Harsh, A. Meninno, P. Dreher, S. Sajan, H. Guo, I. Errea, F. de Juan, and M. M. Ugeda, Evidence for ground state coherence in a two-dimensional Kondo lattice, Nat. Commun. 14, 7005 (2023).
  16. Y. Chen, W.-Y. He, W. Ruan, J. Hwang, S. Tang, R. L. Lee, M. Wu, T. Zhu, C. Zhang, H. Ryu et al., Evidence for a spinon Kondo effect in cobalt atoms on single-layer 1T-TaSe2, Nat. Phys. 18, 1335 (2022).
  17. M. Liu, J. Leveillee, S. Lu, J. Yu, H. Kim, C. Tian, Y. Shi, K. Lai, C. Zhang, F. Giustino et al., Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator, Sci. Adv. 7, eabi6339 (2021).
  18. M. Kratochvilova, A. D. Hillier, A. R. Wildes, L. Wang, S.-W. Cheong, and J.-G. Park, The low-temperature highly correlated quantum phase in the charge-density-wave 1T−TaS2 compound, npj Quantum Mater. 2, 42 (2017).
  19. M. Klanjšek, A. Zorko, R. Žitko, J. Mravlje, Z. Jaglicić, P. K. Biswas, P. Prelovsek, D. Mihailovic, and D. Arcon, A high-temperature quantum spin liquid with polaron spins, Nat. Phys. 13, 1130 (2017).
  20. K. T. Law and P. A. Lee, 1T−TaS2 as a quantum spin liquid, Proc. Natl. Acad. Sci. USA 114, 6996 (2017).
  21. W.-Y. He, X. Y. Xu, G. Chen, K. T. Law, and P. A. Lee, Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T−TaS2, Phys. Rev. Lett. 121, 046401 (2018).
  22. L. Savary and L. Balents, Quantum spin liquids: a review, Rep. Prog. Phys. 80, 016502 (2017).
  23. Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017).
  24. A. Ribak, R. M. Skiff, M. Mograbi, P. Rout, M. Fischer, J. Ruhman, K. Chashka, Y. Dagan, and A. Kanigel, Chiral superconductivity in the alternate stacking compound 4Hb-TaS2, Sci. Adv. 6, eaax9480 (2020).
  25. A. K. Nayak, A. Steinbok, Y. Roet, J. Koo, G. Margalit, I. Feldman, A. Almoalem, A. Kanigel, G. A. Fiete, B. Yan et al., Evidence of topological boundary modes with topological nodal-point superconductivity, Nat. Phys. 17, 1413 (2021).
  26. I. Silber, S. Mathimalar, I. Mangel, A. K. Nayak, O. Green, N. Avraham, H. Beidenkopf, I. Feldman, A. Kanigel, A. Klein, M. Goldstein et al., Two-component nematic superconductivity in 4Hb-TaS2, Nat. Commun. 15, 824 (2024).
  27. A. Almoalem, I. Feldman, M. Shlafman, Y. E. Yaish, M. H. Fischer, M. Moshe, J. Ruhman, and A. Kanigel, Evidence of a two-component order parameter in 4Hb-TaS2 in the Little-Parks effect, arXiv:2208.13798.
  28. E. Persky, A. V. Bjørlig, I. Feldman, A. Almoalem, E. Altman, E. Berg, I. Kimchi, J. Ruhman, A. Kanigel, and B. Kalisky, Magnetic memory and spontaneous vortices in a van der Waals superconductor, Nature (London) 607, 692 (2022).
  29. We note in passing that a scenario of a non-Abelian chiral spin liquid with gauge group SU(2) is also conceivable. The authors of the experimental paper [28] did not elaborate in detail which CSL they envisioned.
  30. S.-Z. Lin, Kondo enabled transmutation between spinons and superconducting vortices: origin of magnetic memory in 4Hb-TaS2, arXiv:2210.06550.
  31. G. Chen, Is spontaneous vortex generation in superconducting 4Hb-TaS2 from vison-vortex nucleation with Z2 topological order?, arXiv:2208.03995.
  32. R. M. Fernandes, P. P. Orth, and J. Schmalian, Intertwined vestigial order in quantum materials: Nematicity and beyond, Annu. Rev. Condens. Matter Phys. 10, 133 (2019).
  33. T. A. Bojesen, E. Babaev, and A. Sudbø, Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems, Phys. Rev. B 88, 220511(R) (2013).
  34. T. A. Bojesen, E. Babaev, and A. Sudbø, Phase transitions and anomalous normal state in superconductors with broken time-reversal symmetry, Phys. Rev. B 89, 104509 (2014).
  35. V. Grinenko, D. Weston, F. Caglieris, C. Wuttke, C. Hess, T. Gottschall, I. Maccari, D. Gorbunov, S. Zherlitsyn, J. Wosnitza, A. Rydh, K. Kihou, C.-H. Lee, R. Sarkar, S. Dengre, J. Garaud, A. Charnukha, R. Hühne, K. Nielsch, B. Büchner et al., State with spontaneously broken time-reversal symmetry above the superconducting phase transition, Nat. Phys. 17, 1254 (2021).
  36. L. Crippa, H. Bae, P. Wunderlich, I. I. Mazin, B. Yan, G. Sangiovanni, T. Wehling, and R. Valentí, Heavy fermions vs doped Mott physics in heterogeneous Ta-dichalcogenide bilayers, Nat. Commun. 15, 1357 (2024).
  37. C. Wen, J. Gao, Y. Xie, Q. Zhang, P. Kong, J. Wang, Y. Jiang, X. Luo, J. Li, W. Lu, Y.-P. Sun, and S. Yan, Roles of the narrow electronic band near the Fermi level in 1T−TaS2-related layered materials, Phys. Rev. Lett. 126, 256402 (2021).
  38. A. K. Nayak, A. Steinbok, Y. Roet, J. Koo, I. Feldman, A. Almoalem, A. Kanigel, B. Yan, A. Rosch, N. Avraham et al., First order quantum phase transition in the hybrid metal-Mott insulator transition metal dichalcogenide 4Hb-TaS2, arXiv:2303.01447.
  39. P. Coleman, J. B. Marston, and A. J. Schofield, Transport anomalies in a simplified model for a heavy-electron quantum critical point, Phys. Rev. B 72, 245111 (2005).
  40. P. Coleman, Introduction to Many-Body Physics (Cambridge University Press, Cambridge, UK, 2015).
  41. T. Senthil and M. P. A. Fisher, Fractionalization in the cuprates: Detecting the topological order, Phys. Rev. Lett. 86, 292 (2001).
  42. Pinned V vortices may also be induced by field cooling to T∈[Tc,TK]. Subsequent zero field cooling below Tc, as in the thermal cycles of Fig. 2(c) of Ref. [28], would then nucleate spontaneous Δ vortices.
  43. T. Cookmeyer, J. Motruk, and J. E. Moore, Four-spin terms and the origin of the chiral spin liquid in Mott insulators on the triangular lattice, Phys. Rev. Lett. 127, 087201 (2021).
  44. O. I. Motrunich, Orbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to κ−(ET)2Cu2(CN)3, Phys. Rev. B 73, 155115 (2006).
  45. E. J. König, P. Coleman, and Y. Komijani, Frustrated Kondo impurity triangle: A simple model of deconfinement, Phys. Rev. B 104, 115103 (2021).
  46. A. A. Abrikosov, On the magnetic properties of superconductors of the second group, Sov. Phys. JETP 5, 1174 (1957).
  47. J. N. Rjabinin and L. W. Shubnikow, Magnetic properties and critical currents of supra-conducting alloys, Nature (London) 135, 581 (1935).
  48. N. Read and D. M. Newns, On the solution of the Coqblin-Schreiffer Hamiltonian by the large-N expansion technique, J. Phys. C 16, 3273 (1983).
  49. P. Coleman, 1N expansion for the Kondo lattice, Phys. Rev. B 28, 5255 (1983).
  50. S. E. Barnes, New method for the Anderson model, J. Phys. F 6, 1375 (1976).
  51. P. Coleman, New approach to the mixed-valence problem, Phys. Rev. B 29, 3035 (1984).
  52. T. Senthil, S. Sachdev, and M. Vojta, Fractionalized Fermi liquids, Phys. Rev. Lett. 90, 216403 (2003).
  53. T. Senthil, M. Vojta, and S. Sachdev, Weak magnetism and non-Fermi liquids near heavy-fermion critical points, Phys. Rev. B 69, 035111 (2004).
  54. X. G. Wen and A. Zee, Effective theory of the T- and P-breaking superconducting state, Phys. Rev. Lett. 62, 2873 (1989).
  55. S. Sachdev, Stable hc/e vortices in a gauge theory of superconductivity in strongly correlated systems, Phys. Rev. B 45, 389 (1992).
  56. N. Nagaosa and P. A. Lee, Ginzburg-Landau theory of the spin-charge-separated system, Phys. Rev. B 45, 966 (1992).
  57. A. M. Tsvelik and P. Coleman, Order fractionalization in a Kitaev-Kondo model, Phys. Rev. B 106, 125144 (2022).
  58. A. Wugalter, Y. Komijani, and P. Coleman, Large-N approach to the two-channel Kondo lattice, Phys. Rev. B 101, 075133 (2020).
  59. M. Kornjača, V. L. Quito, and R. Flint, Mobile Majorana zero-modes in two-channel Kondo insulators, arXiv:2104.11173.
  60. Y. Ge and Y. Komijani, Emergent spinon dispersion and symmetry breaking in two-channel Kondo lattices, Phys. Rev. Lett. 129, 077202 (2022).
  61. S. Saremi, P. A. Lee, and T. Senthil, Kondo vortices, zero modes, and magnetic ordering in a Kondo lattice model, arXiv:0903.4195.
  62. S. Saremi, P. A. Lee, and T. Senthil, Unifying Kondo coherence and antiferromagnetic ordering in the honeycomb lattice, Phys. Rev. B 83, 125120 (2011).
  63. S. Iimura, M. Hirayama, and S. Hoshino, Vortex bound state of a Kondo lattice coupled to a compensated metal, Phys. Rev. B 102, 064505 (2020).
  64. The possibility of vortex solutions in the Kondo hybridization was also mentioned in Ref. [30], but not further pursued.
  65. A. Ramires, P. Coleman, A. H. Nevidomskyy, and A. M. Tsvelik, β− YbAlB4: A critical nodal metal, Phys. Rev. Lett. 109, 176404 (2012).
  66. S. Elitzur, Impossibility of spontaneously breaking local symmetries, Phys. Rev. D 12, 3978 (1975).
  67. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L012058 for a discussion of vortex solutions in the heavy Fermi liquid, for a microscopic derivation of Ginzburg-Landau parameters, for a discussion of the magnetic fields configurations in the heavy Fermi liquid, and for a discussion of subgap states trapped in the V vortices, which includes Refs. [74, 75].
  68. C. Pépin, Selective Mott transition and heavy fermions, Phys. Rev. B 77, 245129 (2008).
  69. P. M. Cônsoli and M. Vojta, Kondo breakdown transitions and phase-separation tendencies in valence-fluctuating heavy-fermion metals, Phys. Rev. B 106, 235127 (2022).
  70. M. Maltseva, M. Dzero, and P. Coleman, Electron cotunneling into a Kondo lattice, Phys. Rev. Lett. 103, 206402 (2009).
  71. C. Caroli, P. G. De Gennes, and J. Matricon, Bound fermion states on a vortex line in a type II superconductor, Phys. Lett. 9, 307 (1964).
  72. G 't Hooft, The topological mechanism for permanent quark confinement in a non-Abelian gauge theory, Phys. Scr. 25, 133 (1982).
  73. R. Jackiw and P. Rossi, Zero modes of the vortex-fermion system, Nucl. Phys. B 190, 681 (1981).
  74. E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics: Theory of the Condensed State, Course of Theoretical Physics, Vol. 9 (Elsevier Science, Amsterdam, 2013).
  75. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer Science & Business Media, New York, 1998).

Outline

Information

Phys. Rev. Research 6, L012058– Published 13 March, 2024
  • Received 16 June 2023
  • Revised 31 October 2023
  • Accepted 8 February 2024
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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation