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  • Letter
  • Open Access

Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros

Chandan Setty1,*,†, Shouvik Sur1,*,‡, Lei Chen1, Fang Xie1, Haoyu Hu1,2, Silke Paschen1,3, Jennifer Cano4,5, and Qimiao Si1

  • *These authors contributed equally to this work.
  • †Contact author: csetty@rice.edu
  • ‡Contact author: shouvik.sur@rice.edu
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Phys. Rev. Research 6, L032018 – Published 26 July, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032018

Abstract

Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless topological states even when quasiparticles are absent. Here we demonstrate the profundity of the framework in the extreme case, when interactions lead to a Mott insulator, through a solvable model with long-range interactions. We find that both Mott poles and zeros are subject to the symmetry constraints, and relate the symmetry-enforced spectral crossings to degeneracies of the original noninteracting eigenstates. Our results lead to new understandings of topological quantum materials and highlight the utility of interacting Green's functions toward their symmetry-based design.

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References (54)

  1. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  2. N. Nagaosa, T. Morimoto, and Y. Tokura, Transport, magnetic and optical properties of Weyl materials, Nat. Rev. Mater. 5, 621 (2020).
  3. B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Topological quantum chemistry, Nature (London) 547, 298 (2017).
  4. J. Cano, B. Bradlyn, Z. Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. A. Bernevig, Building blocks of topological quantum chemistry: Elementary band representations, Phys. Rev. B 97, 035139 (2018).
  5. H. C. Po, A. Vishwanath, and H. Watanabe, Symmetry-based indicators of band topology in the 230 space groups, Nat. Commun. 8, 50 (2017).
  6. H. Watanabe, H. C. Po, M. P. Zaletel, and A. Vishwanath, Filling-enforced gaplessness in band structures of the 230 space groups, Phys. Rev. Lett. 117, 096404 (2016).
  7. J. Cano and B. Bradlyn, Band representations and topological quantum chemistry, Annu. Rev. Condens. Matter Phys. 12, 225 (2021).
  8. D. T. Son, Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction, Phys. Rev. B 75, 235423 (2007).
  9. K. Sun, H. Yao, E. Fradkin, and S. A. Kivelson, Topological insulators and nematic phases from spontaneous symmetry breaking in 2d Fermi systems with a quadratic band crossing, Phys. Rev. Lett. 103, 046811 (2009).
  10. O. Vafek and K. Yang, Many-body instability of Coulomb interacting bilayer graphene: Renormalization group approach, Phys. Rev. B 81, 041401(R) (2010).
  11. I. F. Herbut, V. Juričić, and B. Roy, Theory of interacting electrons on the honeycomb lattice, Phys. Rev. B 79, 085116 (2009).
  12. S. Sur and R. Nandkishore, Instabilities of Weyl loop semimetals, New J. Phys. 18, 115006 (2016).
  13. Y. Huh, E.-G. Moon, and Y. B. Kim, Long-range Coulomb interaction in nodal-ring semimetals, Phys. Rev. B 93, 035138 (2016).
  14. B. Roy, Interacting nodal-line semimetal: Proximity effect and spontaneous symmetry breaking, Phys. Rev. B 96, 041113(R) (2017).
  15. S. Sur and B. Roy, Unifying interacting nodal semimetals: A new route to strong coupling, Phys. Rev. Lett. 123, 207601 (2019).
  16. Z. Wang and S.-C. Zhang, Simplified topological invariants for interacting insulators, Phys. Rev. X 2, 031008 (2012).
  17. Z. Wang and B. Yan, Topological Hamiltonian as an exact tool for topological invariants, J. Phys.: Condens. Matter 25, 155601 (2013).
  18. D. Lessnich, S. M. Winter, M. Iraola, M. G. Vergniory, and R. Valentí, Elementary band representations for the single-particle Green's function of interacting topological insulators, Phys. Rev. B 104, 085116 (2021).
  19. M. O. Soldini, N. Astrakhantsev, M. Iraola, A. Tiwari, M. H. Fischer, R. Valentí, M. G. Vergniory, G. Wagner, and T. Neupert, Interacting topological quantum chemistry of Mott atomic limits, Phys. Rev. B 107, 245145 (2023).
  20. H. H. Hu, L. Chen, C. Setty, M. Garcia-Diez, S. E. Grefe, X. Yan, M. Lužnik, N. Reumann, A. Prokofiev, S. Kirchner, M. G. Vergniory, S. Paschen, J. Cano, and Q. Si, Topological semimetals without quasiparticles, arXiv:2110.06182.
  21. L. Chen, C. Setty, H. Hu, M. G. Vergniory, S. E. Grefe, L. Fischer, X. Yan, G. Eguchi, A. Prokofiev, S. Paschen et al., Topological semimetal driven by strong correlations and crystalline symmetry, Nat. Phys. 18, 1341 (2022).
  22. H.-H. Lai, S. E. Grefe, S. Paschen, and Q. Si, Weyl-Kondo semimetal in heavy-Fermion systems, Proc. Natl. Acad. Sci. USA 115, 93 (2018).
  23. S. Dzsaber, L. Prochaska, A. Sidorenko, G. Eguchi, R. Svagera, M. Waas, A. Prokofiev, Q. Si, and S. Paschen, Kondo insulator to semimetal transformation tuned by spin-orbit coupling, Phys. Rev. Lett. 118, 246601 (2017).
  24. S. Dzsaber, X. Yan, M. Taupin, G. Eguchi, A. Prokofiev, T. Shiroka, P. Blaha, O. Rubel, S. E. Grefe, H.-H. Lai, Q. Si, and S. Paschen, Giant spontaneous Hall effect in a nonmagnetic Weyl Kondo semimetal, Proc. Natl. Acad. Sci. USA 118, e2013386118 (2021).
  25. T. Morimoto and N. Nagaosa, Weyl Mott insulator, Sci. Rep. 6, 1 (2016).
  26. A. A. Abrikosov, L. P. Gor'kov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewood Cliffs, NJ, 1963).
  27. See the Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L032018 for details of the 2D and 3D models, their symmetries, and the Green's function methodology.
  28. S. M. Young and C. L. Kane, Dirac semimetals in two dimensions, Phys. Rev. Lett. 115, 126803 (2015).
  29. Y. Hatsugai and M. Kohmoto, Exactly solvable model of correlated lattice electrons in any dimensions, J. Phys. Soc. Jpn. 61, 2056 (1992).
  30. P. W. Phillips, C. Setty, and S. Zhang, Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in d dimensions, Phys. Rev. B 97, 195102 (2018).
  31. C. Setty, Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual, Phys. Rev. B 101, 184506 (2020).
  32. C. Setty, Superconductivity from Luttinger surfaces: Emergent Sachdev-Ye-Kitaev physics with infinite-body interactions, Phys. Rev. B 103, 014501 (2021).
  33. P. W. Phillips, L. Yeo, and E. W. Huang, Exact theory for superconductivity in a doped Mott insulator, Nat. Phys. 16, 1175 (2020).
  34. E. W. Huang, G. L. Nave, and P. W. Phillips, Discrete symmetry breaking defines the Mott quartic fixed point, Nat. Phys. 18, 511 (2022).
  35. K. Yang, Exactly solvable model of Fermi arcs and pseudogap, Phys. Rev. B 103, 024529 (2021).
  36. H.-S. Zhu, Z. Li, Q. Han, and Z. D. Wang, Topological s-wave superconductors driven by electron correlation, Phys. Rev. B 103, 024514 (2021).
  37. C. Setty, Dilute magnetic moments in an exactly solvable interacting host, arXiv:2105.15205.
  38. M. Fabrizio, Emergent quasiparticles at Luttinger surfaces, Nat. Commun. 13, 1561 (2022).
  39. S. Raghu, X.-L. Qi, C. Honerkamp, and S.-C. Zhang, Topological Mott insulators, Phys. Rev. Lett. 100, 156401 (2008).
  40. D. Sheng, Z.-C. Gu, K. Sun, and L Sheng, Fractional quantum Hall effect in the absence of Landau levels, Nat. Commun. 2, 389 (2011).
  41. J. Kang and O. Vafek, Strong coupling phases of partially filled twisted bilayer graphene narrow bands, Phys. Rev. Lett. 122, 246401 (2019).
  42. L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98, 106803 (2007).
  43. L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76, 045302 (2007).
  44. C. Setty, F. Xie, S. Sur, L. Chen, S. Paschen, M. G. Vergniory, J. Cano, and Q. Si, Topological diagnosis of strongly correlated electron systems, arXiv:2311.12031.
  45. C. Setty, F. Xie, S. Sur, L. Chen, M. G. Vergniory, and Q. Si, Electronic properties, correlated topology and Green's function zeros, arXiv:2309.14340.
  46. B. J. Wieder, Y. Kim, A. M. Rappe, and C. L. Kane, Double Dirac semimetals in three dimensions, Phys. Rev. Lett. 116, 186402 (2016).
  47. B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. Andrei Bernevig, Beyond Dirac and Weyl Fermions: Unconventional quasiparticles in conventional crystals, Science 353, aaf5037 (2016).
  48. D. Di Sante, A. Hausoel, P. Barone, J. M. Tomczak, G. Sangiovanni, and R. Thomale, Realizing double Dirac particles in the presence of electronic interactions, Phys. Rev. B 96, 121106(R) (2017).
  49. A. Goldoni, U. del Pennino, F. Parmigiani, L. Sangaletti, and A. Revcolevschi, Electronic structure of Bi2CuO4, Phys. Rev. B 50, 10435 (1994).
  50. J. L. Garcia-Munoz, J. Rodriguez-Carvajal, F. Sapina, M. J. Sanchis, R. Ibanez, and D. Beltran-Porter, Crystal and magnetic structures of Bi2CuO4, J. Phys.: Condens. Matter 2, 2205 (1990).
  51. L. Chen, F. Xie, S. Sur, H. Hu, S. Paschen, J. Cano, and Q. Si, Emergent flat band and topological Kondo semimetal driven by orbital-selective correlations, Nat. Commun. 15, 5242 (2024).
  52. H. Hu and Q. Si, Coupled topological flat and wide bands: Quasiparticle formation and destruction, Sci. Adv. 9, eadg0028 (2023).
  53. L. Chen, F. Xie, S. Sur, H. Hu, S. Paschen, J. Cano, and Q. Si, Metallic quantum criticality enabled by flat bands in a kagome lattice, arXiv:2307.09431.
  54. N. Wagner, L. Crippa, A. Amaricci, P. Hansmann, M. Klett, E. J. König, T. Schäfer, D. D. Sante, J. Cano, A. J. Millis, A. Georges, and G. Sangiovanni, Mott insulators with boundary zeros, Nat. Commun. 14, 7531 (2023).

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Phys. Rev. Research 6, L032018– Published 26 July, 2024
  • Received 6 March 2023
  • Accepted 29 May 2024
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