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Intertwined orbital distribution of charge density waves in NbSe2

Jyun-Yu Wu1, Yung-Ting Lee2,3, Guan-Hao Chen1,4, Zheng-Hong Li1, Chang-Tsan Lee1, Jie-Yu Hsu1, Chia-Nung Kuo5, Juhn-Jong Lin1, Wen-Hao Chang1,4 et al.

Chin Shan Lue5,6, Noriaki Takagi7, Po-Tuan Chen2, Cheng-Tien Chiang8,9, Chien-Cheng Kuo10, Chien-Te Wu1,11, Chi-Cheng Lee9,*, Ming-Chiang Chung12,†, Hung-Chung Hsueh9,‡, and Chun-Liang Lin1,§

  • *Contact author: cclee.physics@gmail.com
  • †Contact author: mingchiangha@phys.nchu.edu.tw
  • ‡Contact author: hchsueh521@gmail.com
  • §Contact author: clin@nycu.edu.tw
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Phys. Rev. Research 7, 043206 – Published 21 November, 2025

DOI: https://doi.org/10.1103/dn1j-gkjs

Abstract

Charge density wave (CDW) resulting from a periodic distortion in the lattice creates orders beyond the original lattice. In 2H−NbSe2, one of the layered transition metal dichalcogenides, the 3×3 charge order appears in two-dimensional (2D) layers. Although CDW can be observed by different techniques, the spatial distribution within a 2D layer has never been systematically visualized. Here, by using scanning tunneling microscopy and density functional theory, we monitored the evolution of CDW along the c axis and found a strong relation with the orbital charges. The results show that the appearance of the CDW varies while tuning the tunneling current and undergoes a transition from Se orbital charges to Nb orbital charges. The calculation of orbital charge distributions shows that both CDW intensity modulation and the transition are strongly intertwined with the distribution of Se 4p orbitals and Nb 4d orbitals.

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Corrections

15 December, 2025

Correction: Contact author footnotes have been added for the last four authors.

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References (52)

  1. K. Rossnagel, On the origin of charge-density waves in select layered transition-metal dichalcogenides, J. Phys.: Condens. Matter 23, 213001 (2011).
  2. K. Cho, M. Kończykowski, S. Teknowijoyo, M. A. Tanatar, J. Guss, P. B. Gartin, J. M. Wilde, A. Kreyssig, R. J. McQueeney, A. I. Goldman, V. Mishra, P. J. Hirschfeld, and R. Prozorov, Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2, Nat. Commun. 9, 2796 (2018).
  3. 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).
  4. P. Chen, Woei Wu Pai, Y.-H. Chan, A. Takayama, C.-Z. Xu, A. Karn, S. Hasegawa, M. Y. Chou, S.-K. Mo, A.-V. Fedorov, and T.-C. Chiang, Emergence of charge density waves and a pseudogap in single-layer TiTe2, Nat. Commun. 8, 516 (2017).
  5. H. Ryu, Y. Chen, H. Kim, H.-Z. Tsai, S. Tang, J. Jiang, F. Liou, S. Kahn, C. Jia, A. A. Omrani, J. H. Shim, Z. Hussain, Z.-X. Shen, K. Kim, B.-Il Min, C. Hwang, M. F. Crommie, and S.-K. Mo, Persistent charge-density-wave order in single-layer TaSe2, Nano Lett. 18, 689 (2018).
  6. D. L. Bolloc’h, S. Ravy, J. Dumas, J. Marcus, F. Livet, C. Detlefs, F. Yakhou, and L. Paolasini, Charge density wave dislocation as revealed by coherent x-ray diffraction, Phys. Rev. Lett. 95, 116401 (2005).
  7. D. Lin, S. Li, J. Wen, H. Berger, L. Forró, H. Zhou, S. Jia, T. Taniguchi, K. Watanabe, X. Xi, and M. S. Bahramy, Patterns and driving forces of dimensionality-dependent charge density waves in 2H-type transition metal dichalcogenides, Nat. Commun. 11, 2406 (2020).
  8. D. L. Duong, G. Ryu, A. Hoyer, C. Lin, M. Burghard, and K. Kern, Correction to Raman characterization of the charge density wave phase of 1T−TiSe2: From bulk to atomically thin layers, ACS Nano 11, 2304 (2017).
  9. T.-R. T. Han, F. Zhou, C. D. Malliakas, P. M. Duxbury, S. D. Mahanti, M. G. Kanatzidis, and C.-Y. Ruan, Exploration of metastability and hidden phases in correlated electron crystals visualized by femtosecond optical doping and electron crystallography, Sci. Adv. 1, e1400173 (2015).
  10. 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 1T−TaS2, Proc. Natl Acad. Sci. USA 112, 15054 (2015).
  11. H. Zhao, H. Li, B. R. Ortiz, S. M. L. Teicher, T. Park, M. Ye, Z. Wang, L. Balents, S. D. Wilson, and I. Zeljkovic, Cascade of correlated electron states in the kagome superconductor CsV3Sb5, Nature (London) 599, 216 (2021).
  12. M. Spera, A. Scarfato, Á. Pásztor, E. Giannini, D.  R. Bowler, and Ch. Renner, Insight into the charge density wave gap from contrast inversion in topographic STM images, Phys. Rev. Lett. 125, 267603 (2020).
  13. W.-C. Chiu, S. Mardanya, R. Markiewicz, J. Nieminen, B. Singh, T. Hakioglu, A. Agarwal, T.-R. Chang, H. Lin, and A. Bansil, Strain-induced charge density waves with emergent topological states in monolayer NbSe2, ACS Nano 19, 18108 (2025).
  14. D. Lin, A. Ranjbar, X. Li, X. Huang, Y. Huang, H. Berger, L. Forró, K. Watanabe, T. Taniguchi, R. V. Belosludov, T. D. Kühne, H. Ding, M. S. Bahramy, and X. Xi, Axial-bonding-driven dimensionality effect on the charge-density wave in NbSe2, Nano Lett. 22, 9389 (2022).
  15. A. Sanna, C. Pellegrini, E. Liebhaber, K. Rossnagel, K. J. Franke, and E. K. U. Gross, Real-space anisotropy of the superconducting gap in the charge-density wave material 2H−NbSe2, npj Quantum Mater. 7, 6 (2022).
  16. X. Xi, L. Zhao, Z. Wang, H. Berger, L. Forró, J. Shan, and K. F. Mak, Strongly enhanced charge-density-wave order in monolayer NbSe2, Nat. Nanotech. 10, 765 (2015).
  17. M. Leroux, I. Errea, M. Le Tacon, S.-M. Souliou, G. Garbarino, L. Cario, A. Bosak, F. Mauri, M. Calandra, and P. Rodière, Strong anharmonicity induces quantum melting of charge density wave in 2H−NbSe2 under pressure, Phys. Rev. B 92, 140303(R) (2015).
  18. C. Wen, Y. Xie, Y. Wu, S. Shen, P. Kong, H. Lian, J. Li, H. Xing, and S. Yan, Impurity-pinned incommensurate charge density wave and local phonon excitation in 2H−NbS2, Phys. Rev. B 101, 241404(R) (2020).
  19. F. Zheng, Z. Zhou, X. Liu, and J. Feng, First-principles study of charge and magnetic ordering in monolayer NbSe2, Phys. Rev. B 97, 081101(R) (2018).
  20. K. C. Rahnejat, C. A. Howard, N. E. Shuttleworth, S. R. Schofield, K. Iwaya, C. F. Hirjibehedin, Ch. Renner, G. Aeppli, and M. Ellerby, Charge density waves in the graphene sheets of the superconductor CaC6, Nat. Commun. 2, 558 (2011).
  21. B. Guster, C. Rubio-Verdú, R. Robles, J. Zaldívar, P. Dreher, M. Pruneda, J. Á. Silva-Guillén, D.-J. Choi, J. I. Pascual, M. M. Ugeda, P. Ordejón, and E. Canadell, Coexistence of elastic modulations in the charge density wave state of 2H−NbSe2, Nano Lett. 19, 3027 (2019).
  22. Y.-X. Jiang, J.-X. Yin , M. M. Denner, N. Shumiya, B. R. Ortiz, G. Xu, Z. Guguchia , J. He, M. S. Hossain, X. Liu, J. Ruff, L. Kautzsch , S. S. Zhang, G. Chang, I. Belopolski, Q. Zhang, T. A. Cochran, D. Multer, M. Litskevich , Z.-J. Cheng et al., Unconventional chiral charge order in kagome superconductor KV3Sb5, Nat. Mater. 20, 1353 (2021).
  23. T. Neupert, M. M. Denner, J.-X. Yin, R. Thomale, and M. Z. Hasan, Charge order and superconductivity in kagome materials, Nat. Phys. 18, 137 (2022).
  24. G. Zheng, C. Tan, Z. Chen, M. Wang, X. Zhu, S. Albarakati, M. Algarni, J. Partridge, L. Farrar, J. Zhou, W. Ning, M. Tian, M. S. Fuhrer, and L. Wang, Electrically controlled superconductor-to-failed insulator transition and giant anomalous Hall effect in kagome metal CsV3Sb5 nanoflakes, Nat. Commun. 14, 678 (2023).
  25. H. S. Kim, S. Kim, K. Kim, B. I. Min, Y.-H. Cho, L. Wang, S.-W. Cheong, and H. W. Yeom, Nanoscale superconducting honeycomb charge order in IrTe2, Nano Lett. 16, 4260 (2016).
  26. M. M. Ugeda, A. J. Bradley, Y. Zhang, S. Onishi, Y. Chen, W. Ruan, C. O.-Aristizabal, H. Ryu, M. T. Edmonds, H.-Z. Tsai, A. Riss, S.-K. Mo, D. Lee, A. Zettl, Z. Hussain, Z.-X. Shen, and M. F. Crommie, Characterization of collective ground states in single-layer NbSe2, Nat. Phys. 12, 92 (2016).
  27. G. Gye, E. Oh, and H. W. Yeom, Topological landscape of competing charge density waves in 2H−NbSe2, Phys. Rev. Lett. 122, 016403 (2019).
  28. 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−TaS2, Nat. Phys. 16, 218 (2020).
  29. Á. Pásztor, A. Scarfato, M. Spera, F. Flicker, C. Barreteau, E. Giannini, J. van Wezel, and C. Renner, Multiband charge density wave exposed in a transition metal dichalcogenide, Nat. Commun. 12, 6037 (2021).
  30. F. Flicker and J. van Wezel, Charge order from orbital-dependent coupling evidenced by NbSe2, Nat. Commun. 6, 7034 (2015).
  31. T. Ritschel, J. Trinckauf, K. Koepernik, B. Büchner, M. v. Zimmermann, H. Berger, Y. I. Joe, P. Abbamonte, and J. Geck, Orbital textures and charge density waves in transition metal dichalcogenides, Nat. Phys. 11, 328 (2015).
  32. H. Kim, Y. Yoshida, C.-C. Lee, T.-R. Chang, H.-T. Jeng, H. Lin, Y. Haga, Z. Fisk, and Y. Hasegawa, Atomic-scale visualization of surface-assisted orbital order, Sci. Adv. 3, eaao0362 (2017).
  33. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
  34. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  35. T. Ozaki, Variationally optimized atomic orbitals for large-scale electronic structures, Phys. Rev. B 67, 155108 (2003).
  36. T. Ozaki and H. Kino, Efficient projector expansion for the ab initio LCAO method, Phys. Rev. B 72, 045121 (2005).
  37. I. Morrison, D. M. Bylander, and L. Kleinman, Nonlocal Hermitian norm-conserving Vanderbilt pseudopotential, Phys. Rev. B 47, 6728 (1993).
  38. T. Ozaki and H. Kino, Numerical atomic basis orbitals from H to Kr, Phys. Rev. B 69, 195113 (2004).
  39. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  40. J. Tersoff and D. R. Hamann, Theory of the scanning tunneling microscope, Phys. Rev. B 31, 805 (1985).
  41. K. Momma and F. Izumi, VESTA: a three-dimensional visualization system for electronic and structural analysis, J. Appl. Crystallogr. 41, 653 (2008).
  42. Y.-T. Lee and T. Ozaki, OpenMX Viewer: A web-based crystalline and molecular graphical user interface program, J. Mol. Graph. Model. 89, 192 (2019).
  43. C. S. Lian, C. Si, and W. Duan, Unveiling charge-density wave, superconductivity, and their competitive nature in two-dimensional NbSe2, Nano Lett. 18, 2924 (2018).
  44. A. Soumyanarayanan, M. M. Yee, Y. He, J. van Wezel, D. J. Rahn, K. Rossnagel, E. W. Hudson, M. R. Norman, and J. E. Hoffman, Quantum phase transition from triangular to stripe charge order in NbSe2, Proc. Natl Acad. Sci. USA 110, 1623 (2013).
  45. See Supplemental Material at http://link.aps.org/supplemental/10.1103/dn1j-gkjs for I-Z measurement, the partial charge density distribution of a tungsten tip's apex, the charge density distribution at different Se sites in hollow phase, current-modulated 3×3 CDW intensity of filled phase, the comparison of relative 3×3 CDW intensity as function of current, the DFT simulated STM images under the electric field, Fourier-extracted STM images of 1Ã1 lattice at filled phase region under each set point, the partial charge density projected from the top Se and Nb atoms of NbSe2−3×3×1 hollow and filled phases, and more current-dependent STM images measured by the other instrument.
  46. N. S. Sivakumar, J. Aretz, S. Scherb, M. V. M. Mavric, N. Huijgen, U. Kamber, D. Wegner, A. A. Khajetoorians, M. Rösner, and N. Hauptmann, Influence of surface relaxations on scanning probe microscopy images of the charge density wave material 2H−NbSe2, Phys. Rev. B 111, 075409 (2025).
  47. M.-K. Lin, G.-H. Chen, C.-L. Ho, W.-C. Chueh, J. A. Hlevyack, C.-N. Kuo, T.-Y. Fu, J.-J. Lin, C. S. Lue, W.-H. Chang, N. Takagi, R. Arafune, T.-C. Chiang, and C.-L. Lin, Tip-mediated bandgap tuning for monolayer transition metal dichalcogenides, ACS Nano 16, 14918 (2022).
  48. N. E. Staley, J. Wu, P. Eklund, Y. Liu, L. Li, and Z. Xu, Electric field effect on superconductivity in atomically thin flakes of NbSe2, Phys. Rev. B 80, 184505 (2009).
  49. F. Liu, J. Zhou, C. Zhu, and Z. Liu, Electric field effect in two-dimensional transition metal dichalcogenides, Adv. Funct. Mater. 27, 1602404 (2017).
  50. X. Song, L. Liu, Y. Chen, H. Yang, Z. Huang, B. Hou, Y. Hou, X. Han, H. Yang, Q. Zhang, T. Zhang, J. Zhou, Y. Huang, Y. Zhang, H.-J. Gao, and Y. Wang, Atomic-scale visualization of chiral charge density wave superlattices and their reversible switching, Nat. Commun. 13, 1843 (2022).
  51. X. Ma, T. Dai, S. Dang, S. Kang, X. Chen, W. Zhou, G. Wang, H. Li, P. Hu, Z. He, Y. Sun, D. Li, F. Yu, X. Zhou, H. Chen, X. Chen, S. Wu, and S. Li, Charge density wave phase transitions in large-scale few-layer 1T−VTe2 grown by molecular beam epitaxy, ACS Appl. Mater. Interfaces 11, 10729 (2019).
  52. C. Lin, NbSe2 Tomography (2024), https://osf.io/hbqup/overview?view_only=8766af69c0a44ac5b0491ac5b540c5f9.

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Phys. Rev. Research 7, 043206– Published 21 November, 2025
  • Received 31 January 2024
  • Accepted 18 September 2025
  • Corrected 15 December 2025
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