- Letter
- Open Access
Unconventional orbital charge density wave mechanism in the transition metal dichalcogenide
Phys. Rev. Research 3, L032053 – Published 27 August, 2021
DOI: https://doi.org/10.1103/PhysRevResearch.3.L032053
Abstract
The transition metal dichalcogenide is attracting growing attention because of the formation of rich density wave (DW) and superconducting transitions. However, the origin of the incommensurate DW state at the highest temperature (), which is “the parent state” of the rich physical phenomena, is still uncovered. Here, we present a natural explanation for the triple- incommensurate DW in based on the first-principles Hubbard model with on-site . We apply the paramagnon interference mechanism that gives the nematic order in Fe-based superconductors. The derived order parameter has very unique characters: (i) an orbital-selective nature, and (ii) an unconventional sign reversal in both momentum and energy spaces. The present Letter will be useful for understanding the rich physics in , , and other transition metal dichalcogenides.
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References (55)
- Y. Yu, F. Yang, X. F. Lu, Y. J. Yan, Y.-H. Cho, L. Ma, X. Niu, S. Kim, Y.-W. Son, D. Feng, S. Li, S.-W. Cheong, X. H. Chen, and Y. Zhang, Gate-tunable phase transitions in thin flakes of , Nat. Nanotechnol. 10, 270 (2015).
- L. J. Li, E. C. T. O'Farrell, K. P. Loh, G. Eda, B. Özyilmaz, and A. H. Castro Neto, Controlling many-body states by the electric-field effect in a two-dimensional material, Nature (London) 529, 185 (2016).
- M. Yoshida, R. Suzuki, Y. Zhang, M. Nakano, and Y. Iwasa, Memristive phase switching in two-dimensional crystals, Sci. Adv. 1, e1500606 (2015).
- A. W. Tsen, R. Hovden, D. Wang, Y. D. Kim, J. Okamoto, K. A. Spoth, Y. Liu, W. Lu, Y. Sun, J. C. Hone, L. F. Kourkoutis, P. Kim, and A. N. Pasupathy, Structure and control of charge density waves in two-dimensional , Proc. Natl. Acad. Sci. U.S.A. 112, 15054 (2015).
- P. C. Börner, M. K. Kinyanjui, T. Björkman, T. Lehnert, A. V. Krasheninnikov, and U. Kaiser, Observation of charge density waves in free-standing monolayers by transmission electron microscopy, Appl. Phys. Lett. 113, 173103 (2018).
- 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 , Nat. Commun. 11, 4215 (2020).
- B. Wang, Y. Liu, X. Luo, K. Ishigaki, K. Matsubayashi, W. Lu, Y. Sun, J. Cheng, and Y. Uwatoko, Universal phase diagram of superconductivity and charge density wave versus high hydrostatic pressure in pure and Se-doped , Phys. Rev. B 97, 220504(R) (2018).
- T. Ritschel, J. Trinckauf, G. Garbarino, M. Hanfland, M. v. Zimmermann, H. Berger, B. Büchner, and J. Geck Pressure dependence of the charge density wave in and its relation to superconductivity, Phys. Rev. B 87, 125135 (2013).
- Q. Stahl, M. Kusch, F. Heinsch, G. Garbarino, N. Kretzschmar, K. Hanff, K. Rossnagel, J. Geck, and T. Ritschel, Collapse of layer dimerization in the photo-induced hidden state of , Nat. Commun. 11, 1247 (2020).
- B. Sipos, A. F. Kusmartseva, A. Akrap, H. Berger, L. Forró, and E. Tutis, From Mott state to superconductivity in , Nat. Mater. 7, 960 (2008).
- K. Sun, S. Sun, C. Zhu, H. Tian, H. Yang, and J. Li, Hidden CDW states and insulator-to-metal transition after a pulsed femtosecond laser excitation in layered chalcogenide , Sci. Adv. 4, eaas9660 (2018).
- R. Ang, Z. C. Wang, C. L. Chen, J. Tang, N. Liu, Y. Liu, W. J. Lu, Y. P. Sun, T. Mori, and Y. Ikuhara, Atomistic origin of an ordered superstructure induced superconductivity in layered chalcogenides, Nat. Commun. 6, 6091 (2015).
- M. Klanjsek, A. Zorko, R. Zitko, J. Mravlje, Z. Jaglicic, P. K. Biswas, P. Prelovsek, D. Mihailovic, and D. Arcon, A high-temperature quantum spin liquid with polaron spins, Nat. Phys. 13, 1130 (2017).
- L. Ma, C. Ye, Y. Yu, X. F. Lu, X. Niu, S. Kim, D. Feng, D. Tománek, Y.-W. Son, X. H. Chen, and Y. Zhang, A metallic mosaic phase and the origin of Mott-insulating state in , Nat. Commun. 7, 10956 (2016).
- 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 et al., Strong correlations and orbital texture in single-layer , Nat. Phys. 16, 218 (2020).
- C. J. Butler, M. Yoshida, T. Hanaguri, and Y. Iwasa, Mottness versus unit-cell doubling as the driver of the insulating state in , Nat. Commun. 11, 2477 (2020).
- 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 Transition-Metal Dichalcogenide: An Interplay between Localized and Itinerant Orbitals, Phys. Rev. X 7, 041054 (2017).
- L. Stojchevska, I. Vaskivskyi, T. Mertelj, P. Kusar, D. Svetin, S. Brazovskii, and D. Mihailovic, Ultrafast switching to a stable hidden quantum state in an electronic crystal, Science 344, 177 (2014).
- I. Vaskivskyi, J. Gospodaric, S. Brazovskii, D. Svetin, P. Sutar, E. Goreshnik, I. A. Mihailovic, T. Mertelj, and D. Mihailovic, Controlling the metal-to-insulator relaxation of the metastable hidden quantum state in , Sci. Adv. 1, e1500168 (2015).
- W. Wang, D. Dietzel, and A. Schirmeisen, Lattice discontinuities of across first order charge density wave phase transitions, Sci. Rep. 9, 7066 (2019).
- C. Zhu, Y. Chen, F. Liu, S. Zheng, X. Li, A. Chaturvedi, J. Zhou, Q. Fu, Y. He, Q. Zeng, H. J. Fan, H. Zhang, W.-J. Liu, T. Yu, and Z. Liu, Light-tunable charge-density-wave oscillators, ACS Nano 12, 11203 (2018).
- M. J. Trott and C. A. Hooley, Can Fermi surface nesting alone drive the charge-density-wave transition in monolayer vanadium diselenide? arXiv:2004.06665.
- A. V. Chubukov, M. Khodas, and R. M. Fernandes, Magnetism, Superconductivity, and Spontaneous Orbital Order in Iron-Based Superconductors: Which Comes First and Why? Phys. Rev. X 6, 041045 (2016).
- R. M. Fernandes and A. V. Chubukov, Low-energy microscopic models for iron-based superconductors: A review, Rep. Prog. Phys. 80, 014503 (2017).
- L. Fanfarillo, G. Giovannetti, M. Capone, and E. Bascones, Nematicity at the Hund's metal crossover in iron superconductors, Phys. Rev. B 95, 144511 (2017).
- S. Onari and H. Kontani, Self-consistent Vertex Correction Analysis for Iron-based Superconductors: Mechanism of Coulomb Interaction-Driven Orbital Fluctuations, Phys. Rev. Lett. 109, 137001 (2012).
- S. Onari, Y. Yamakawa, and H. Kontani, Sign-Reversing Orbital Polarization in the Nematic Phase of FeSe due to the Symmetry Breaking in the Self-Energy, Phys. Rev. Lett. 116, 227001 (2016).
- Y. Yamakawa, S. Onari, and H. Kontani, Nematicity and Magnetism in FeSe and Other Families of Fe-Based Superconductors, Phys. Rev. X 6, 021032 (2016).
- Y. Yamakawa and H. Kontani, Spin-Fluctuation-Driven Nematic Charge-Density Wave in Cuprate Superconductors: Impact of Aslamazov-Larkin Vertex Corrections, Phys. Rev. Lett. 114, 257001 (2015).
- M. Tsuchiizu, Y. Ohno, S. Onari and H. Kontani, Orbital Nematic Instability in the Two-Orbital Hubbard Model: Renormalization-Group+Constrained RPA Analysis, Phys. Rev. Lett. 111, 057003 (2013).
- R. Tazai, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, Functional renormalization group study of orbital fluctuation mediated superconductivity: Impact of the electron-boson coupling vertex corrections, Phys. Rev. B 94, 115155 (2016).
- M. Tsuchiizu, K. Kawaguchi, Y. Yamakawa, and H. Kontani, Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization-group analysis, Phys. Rev. B 97, 165131 (2018).
- K. Kawaguchi, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, Competing unconventional charge-density-wave states in cuprate superconductors: Spin-fluctuation-driven mechanism, J. Phys. Soc. Jpn. 86, 063707 (2017).
- R. Tazai and H. Kontani, Multipole fluctuation theory for heavy fermion systems: Application to multipole orders in , Phys. Rev. B 100, 241103(R) (2019).
- R. Tazai, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, Prediction of pseudogap formation due to bond-order in organic superconductor , Phys. Rev. Research 3, L022014 (2021).
- R. Tazai, Y. Yamakawa, and H. Kontani, Emergence of charge loop current in the geometrically frustrated Hubbard model: A functional renormalization group study, Phys. Rev. B 103, L161112 (2021).
- R. Tazai, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, - and -wave quantum liquid crystal orders in cuprate superconductors, , and coupled chain Hubbard models: functional-renormalization-group analysis, arXiv:2105.01872.
- H. Kontani, Y. Yamakawa, R. Tazai, and S. Onari, Odd-parity spin-loop-current order mediated by transverse spin fluctuations in cuprates and related electron systems, Phys. Rev. Research 3, 013127 (2021).
- S. Onari and H. Kontani, Hidden antiferronematic order in Fe-based superconductor and NaFeAs above , Phys. Rev. Research 2, 042005(R) (2020); Origin of diverse nematic orders in Fe-based superconductors: rotated nematicity in , Phys. Rev. B 100, 020507(R) (2019).
- M. Bovet, D. Popović, F. Clerc, C. Koitzsch, U. Probst, E. Bucher, H. Berger, D. Naumović, and P. Aebi, Pseudogapped Fermi surfaces of and : A charge density wave effect, Phys. Rev. B 69, 125117 (2004).
- C. Sohrt, A. Stange, M. Bauer, and K. Rossnagel, How fast can a Peierls-Mott insulator be melted? Faraday Discuss. 171, 243 (2014).
- W. L. McMillan, Landau theory of charge-density waves in transition-metal dichalcogenides, Phys. Rev. B 12, 1187 (1975).
- K. Nakanishi and H. Shiba, Domain-like incommensurate charge-density-wave states and the first-order incommensurate-commensurate transitions in layered tantalum dichalcogenides. I. 1T-polytype, J. Phys. Soc. Jpn. 43, 1839 (1977).
- K. Nakanishi and H. Shiba, Theory of three-dimensional orderings of charge-density waves in (X: S, Se), J. Phys. Soc. Jpn. 53, 1103 (1984).
- X.-L. Yu, D.-Y. Liu, Y.-M. Quan, J. Wu, H.-Q. Lin, K. Chang, and L.-J. Zou, Electronic correlation effects and orbital density wave in the layered compound , Phys. Rev. B 96, 125138 (2017).
- T. N. Ikeda, H. Tsunetsugu, and K. Yonemitsu, Photoinduced dynamics of commensurate charge density wave in based on three-orbital Hubbard model, Appl. Sci. 9, 70 (2019).
- 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).
- C. Chen, L. Su, A. H. Castro Neto, and V. M. Pereira, Discommensuration-driven superconductivity in the charge density wave phases of transition-metal dichalcogenides, Phys. Rev. B 99, 121108(R) (2019).
- T. Ritschel, H. Berger, and J. Geck, Stacking-driven gap formation in layered , Phys. Rev. B 98, 195134 (2018).
- L. F. Mattheiss, Band structures of transition-metal-dichalcogenide layer compounds, Phys. Rev. B 8, 3719 (1973).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032053 for model Hamiltonian, details of spin susceptibilities and form-factors, unfolded band spectrum, kernel function, and Ginzburg-Landau equations.
- H. Kontani, Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations, Rep. Prog. Phys. 71, 026501 (2008).
- H. Kontani, T. Saito, and S. Onari, Origin of orthorhombic transition, magnetic transition, and shear-modulus softening in iron pnictide superconductors: Analysis based on the orbital fluctuations theory, Phys. Rev. B 84, 024528 (2011).
- Y. Suzuki, T. Shimojima, T. Sonobe, A. Nakamura, M. Sakano, H. Tsuji, J. Omachi, K. Yoshioka, M. Kuwata-Gonokami, T. Watashige, R. Kobayashi, S. Kasahara, T. Shibauchi, Y. Matsuda, Y. Yamakawa, H. Kontani, and K. Ishizaka, Momentum-dependent sign inversion of orbital order in superconducting FeSe, Phys. Rev. B 92, 205117 (2015).
- W. Ku, T. Berlijn, and C.-C. Lee, Unfolding First-Principles Band Structures, Phys. Rev. Lett. 104, 216401 (2010).