Strain-induced stripe phase in charge-ordered single layer NbSe2
Source abstract
Abstract
Abstract Charge density waves are ubiquitous phenomena in metallic transition metal dichalcogenides. In NbSe2, a triangular 3 × 3 structural modulation is coupled to a charge modulation. Recent experiments reported evidence for a triangular-stripe transition at the surface, due to strain or accidental doping and associated to a 4 × 4 modulation. We employ ab initio calculations to investigate the strain-induced structural instabilities in a pristine single layer and analyse the energy hierarchy of the structural and charge modulations. Our results support the observation of phase separation between triangular and stripe phases in 1H-NbSe2, relating the stripe phase to compressive isotropic strain, favouring the 4 × 4 modulation. The observed wavelength of the charge modulation is also reproduced with a good accuracy.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: 2D Materials and Applications · Perovskite Materials and Applications · Organic and Molecular Conductors Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (74)
Show source-provided references
1. Saito, Y., Nojima, T. & Iwasa, Y. Highly crystalline 2d superconductors. Nat. Rev. Mater. 2, 16094 (2016).10.1038/natrevmats.2016.94 ↗
2. Wilson, J. A., DiSalvo, F. J. & Mahajan, S. Charge-density waves in metallic, layered, transition-metal dichalcogenides. Phys. Rev. Lett. 32, 882–885 (1974).10.1103/PhysRevLett.32.882 ↗
3. Wilson, J. A., Salvo, F. J. D. & Mahajan, S. Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides. Adv. Phys. 50, 1171–1248 (2001).10.1080/00018730110102718 ↗
4. Moncton, D. E., Axe, J. D. & DiSalvo, F. J. Study of superlattice formation in 2H -NbSe2 and 2H-TaSe2 by neutron scattering. Phys. Rev. Lett. 34, 734–737 (1975).10.1103/PhysRevLett.34.734 ↗
5. Revolinsky, E., Spiering, G. A. & J, B. D. Superconductivity in the niobium–selenium system. J. Phys. Chem. Solids 26, 1029 (1965).10.1016/0022-3697(65)90190-3 ↗
6. Kiss, T. et al. Charge-order-maximized momentum-dependent superconductivity. Nat. Phys. 3, 720 (2007).10.1038/nphys699 ↗
7. Rice, T. M. & Scott, G. K. New mechanism for a charge-density-wave instability. Phys. Rev. Lett. 35, 120–123 (1975).10.1103/PhysRevLett.35.120 ↗
8. Liu, R., Olson, C. G., Tonjes, W. C. & Frindt, R. F. Momentum dependent spectral changes induced by the charge density wave in 2H-TaSe2 and the implication on the CDW mechanism. Phys. Rev. Lett. 80, 5762–5765 (1998).10.1103/PhysRevLett.80.5762 ↗
9. Straub, T. et al. Charge-density-wave mechanism in 2H -NbSe2: photoemission results. Phys. Rev. Lett. 82, 4504–4507 (1999).10.1103/PhysRevLett.82.4504 ↗
10. Rahn, D. J. et al. Gaps and kinks in the electronic structure of the superconductor 2H-NbSe2 from angle-resolved photoemission at 1 k. Phys. Rev. B 85, 224532 (2012).10.1103/PhysRevB.85.224532 ↗
11. CastroNeto, A. H. Charge density wave, superconductivity, and anomalous metallic behavior in 2d transition metal dichalcogenides. Phys. Rev. Lett. 86, 4382–4385 (2001).10.1103/PhysRevLett.86.4382 ↗
12. Cho, K. et al. Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2. Nat. Commun. 9, 2796 (2018).
13. Inosov, D. S. et al. Fermi surface nesting in several transition metal dichalcogenides. New J. Phys. 10, 125027 (2008).10.1088/1367-2630/10/12/125027 ↗
14. Rossnagel, K. et al. Fermi surface of 2H-NbSe2 and its implications on the charge-density-wave mechanism. Phys. Rev. B 64, 235119 (2001).10.1103/PhysRevB.64.235119 ↗
15. Rossnagel, K. & Smith, N. V. Spin-orbit splitting, fermi surface topology, and charge-density-wave gapping in 2H -TaSe2. Phys. Rev. B 76, 073102 (2007).10.1103/PhysRevB.76.073102 ↗
16. Johannes, M. D., Mazin, I. I. & Howells, C. A. Fermi-surface nesting and the origin of the charge-density wave in NbSe2. Phys. Rev. B 73, 205102 (2006).10.1103/PhysRevB.73.205102 ↗
17. Johannes, M. D. & Mazin, I. I. Fermi surface nesting and the origin of charge density waves in metals. Phys. Rev. B 77, 165135 (2008).10.1103/PhysRevB.77.165135 ↗
18. Zhu, X., Cao, Y., Zhang, J., Plummer, E. W. & Guo, J. Classification of charge density waves based on their nature. Proc. Natl. Acad. Sci. USA 112, 2367–2371 (2015).10.1073/pnas.1424791112 ↗
19. ÁngelSilva-Guillén, J., Ordejón, P., Guinea, F. & Canadell, E. Electronic structure of 2H-NbSe2 single-layers in the CDW state. 2D Materials 3, 035028 (2016).10.1088/2053-1583/3/3/035028 ↗
20. Calandra, M., Mazin, I. I. & Mauri, F. Effect of dimensionality on the charge-density wave in few-layer 2H-NbSe2. Phys. Rev. B 80, 241108 (2009).10.1103/PhysRevB.80.241108 ↗
21. Valla, T. et al. Quasiparticle spectra, charge-density waves, superconductivity, and electron-phonon coupling in 2H-NbSe2. Phys. Rev. Lett. 92, 086401 (2004).10.1103/PhysRevLett.92.086401 ↗
22. Zheng, F., Zhou, Z., Liu, X. & Feng, J. First-principles study of charge and magnetic ordering in monolayer NbSe2. Phys. Rev. B 97, 081101 (2018).10.1103/PhysRevB.97.081101 ↗
23. Arguello, C. J. et al. Visualizing the charge density wave transition in 2H-NbSe2 in real space. Phys. Rev. B 89, 235115 (2014).10.1103/PhysRevB.89.235115 ↗
24. Flicker, F. & van Wezel, J. Charge order from orbital-dependent coupling evidenced by NbSe2. Nat. Commun. 6, 7034 (2015).10.1038/ncomms8034 ↗
25. Galvis, J. A. et al. Tilted vortex cores and superconducting gap anisotropy in 2H -NbSe2. Commun. Phys. 1, 30 (2018).10.1038/s42005-018-0028-1 ↗
26. Fu, Z.-G. et al. Doping stability and charge-density-wave transition of strained 1T -TiSe2. Europhys. Lett. 120, 17006 (2017).10.1209/0295-5075/120/17006 ↗
27. Wei, M. J. et al. Manipulating charge density wave order in monolayer 1T -TiSe2 by strain and charge doping: a first-principles investigation. Phys. Rev. B 96, 165404 (2017).10.1103/PhysRevB.96.165404 ↗
28. DiSalvo, F. J., Wilson, J. A., Bagley, B. G. & Waszczak, J. V. Effects of doping on charge-density waves in layer compounds. Phys. Rev. B 12, 2220–2235 (1975).10.1103/PhysRevB.12.2220 ↗
29. Chatterjee, U. et al. Emergence of coherence in the charge-density wave state of 2H-NbSe2. Nat. Commun. 6, 6313 (2015).10.1038/ncomms7313 ↗
30. Cossu, F. et al. Unveiling hidden charge density waves in single-layer NbSe2 by impurities. Phys. Rev. B 98, 195419 (2018).10.1103/PhysRevB.98.195419 ↗
31. Shao, D. F. et al. Manipulating charge density waves in 1T-TaS2 by charge-carrier doping: a first-principles investigation. Phys. Rev. B 94, 125126 (2016).10.1103/PhysRevB.94.125126 ↗
32. Kotov, V. N., Uchoa, B., Pereira, V. M., Guinea, F. & CastroNeto, A. H. Electron-electron interactions in graphene: current status and perspectives. Rev. Mod. Phys. 84, 1067–1125 (2012).10.1103/RevModPhys.84.1067 ↗
33. Guinea, F., Katsnelson, M. I. & Wehling, T. O. Two-dimensional materials: electronic structure and many-body effects. Ann. Phys. 526, A81–A82 (2014).10.1002/andp.201470096 ↗
34. Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater. 12, 207–211 (2012).10.1038/nmat3505 ↗
35. Frindt, R. F. Superconductivity in ultrathin NbSe2 layers. Phys. Rev. Lett. 28, 299–301 (1972).10.1103/PhysRevLett.28.299 ↗
36. Xi, X. et al. Strongly enhanced charge-density-wave order in monolayer NbSe2. Nat Nano 10, 765–769 (2015).10.1038/nnano.2015.143 ↗
37. Ugeda, M. M. et al. Characterization of collective ground states in single-layer NbSe2. Nat. Phys. 12, 92–97 (2016).10.1038/nphys3527 ↗
38. Butler, S. Z. et al. Progress, challenges, and opportunities in two-dimensional materials beyond graphene. ACS Nano. 7, 2898–2926 (2013).10.1021/nn400280c ↗
39. Geim, A. K. & Grigorieva, I. V. Van der waals heterostructures. Nature 499, 419 (2013).10.1038/nature12385 ↗
40. Novoselov, K. S., Mishchenko, A., Carvalho, A. & CastroNeto, A. H. 2d materials and van der waals heterostructures. Science 353, aac9439 (2016).10.1126/science.aac9439 ↗
41. Ge, Y. & Liu, A. Y. Effect of dimensionality and spin–orbit coupling on charge-density-wave transition in 2H-TaSe2. Phys. Rev. B 86, 104101 (2012).10.1103/PhysRevB.86.104101 ↗
42. Menard, G. C. et al. Coherent long-range magnetic bound states in a superconductor. Nat. Phys. 11, 1013–1016 (2015).10.1038/nphys3508 ↗
43. Weber, F. et al. Extended phonon collapse and the origin of the charge-density wave in 2H-NbSe2. Phys. Rev. Lett. 107, 107403 (2011).10.1103/PhysRevLett.107.107403 ↗
44. Riley, J. M. et al. Direct observation of spin-polarized bulk bands in an inversion-symmetric semiconductor. Nat. Phys. 10, 835–839 (2014).10.1038/nphys3105 ↗
45. Bawden, L. et al. Spin-valley locking in the normal state of a transition-metal dichalcogenide superconductor. Nat. Commun. 7, 11711 (2016).10.1038/ncomms11711 ↗
46. Kadijk, F. & Jellinek, F. On the polymorphism of niobium diselenide. J. Less Common Metals 23, 437–441 (1971).10.1016/0022-5088(71)90053-1 ↗
47. Nakata, Y. et al. Monolayer 1T-NbSe2 as a mott insulator. NPG Asia Mater. 8, e321 (2016).10.1038/am.2016.157 ↗
48. Bischoff, F. et al. Nanoscale phase engineering of niobium diselenide. Chem. Mater. 29, 9907–9914 (2017).10.1021/acs.chemmater.7b03061 ↗
49. Liu, Y. et al. Nature of charge density waves and superconductivity in 1T -TaSe2−x Tex. Phys. Rev. B 94, 045131 (2016).10.1103/PhysRevB.94.045131 ↗
50. Börner, P. C. et al. Observation of charge density waves in free-standing 1T -TaSe2 monolayers by transmission electron microscopy. Appl. Phys. Lett. 113, 173103 (2018).10.1063/1.5052722 ↗
51. Law, K. T. & Lee, P. A.1T -TaS2 as a quantum spin liquid. Proc. Natl. Acad. Sci. USA 114, 6996–7000 (2017).10.1073/pnas.1706769114 ↗
52. Fazekas, P. & Tosatti, E. Charge carrier localization in pure and doped 1T -TaS2. Physica B+C 99, 183–187 (1980).10.1016/0378-4363(80)90229-6 ↗
53. Soumyanarayanan, A. et al. Quantum phase transition from triangular to stripe charge order in NbSe2. Proc. Natl. Acad. Sci. USA 110, 1623–1627 (2013).10.1073/pnas.1211387110 ↗
54. Gao, S. et al. Atomic-scale strain manipulation of a charge density wave. Proc. Natl. Acad. Sci. USA 115, 6986–6990 (2018).10.1073/pnas.1718931115 ↗
55. Gye, G., Oh, E. & Yeom, H. W. Topological landscape of competing charge density waves in 2H-NbSe2. Phys. Rev. Lett. 122, 016403 (2019).10.1103/PhysRevLett.122.016403 ↗
56. Lian, C.-S., Si, C. & Duan, W. Unveiling charge-density wave, superconductivity, and their competitive nature in two-dimensional NbSe2. Nano Lett. 18, 2924–2929 (2018).10.1021/acs.nanolett.8b00237 ↗
57. Flicker, F. & van Wezel, J. Charge ordering geometries in uniaxially strained NbSe2. Phys. Rev. B 92, 201103 (2015).10.1103/PhysRevB.92.201103 ↗
58. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953 ↗
59. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).10.1103/PhysRevB.59.1758 ↗
60. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 21, 395502 (2009).
61. Giannozzi, P. et al. Advanced capabilities for materials modelling with quantum ESPRESSO. J. Phys.: Condens. Matter 29, 465901 (2017).
62. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
63. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 78, 1396–1396 (1997).10.1103/PhysRevLett.78.1396 ↗
64. Popescu, V. & Zunger, A. Extracting E versus $$\overrightarrow{k}$$ effective band structure from supercell calculations on alloys and impurities. Phys. Rev. B 85, 085201 (2012).10.1103/PhysRevB.85.085201 ↗
65. Hofer, W. Challenges and errors: interpreting high resolution images in scanning tunneling microscopy. Prog. Surf. Sci. 71, 147–183 (2003).10.1016/S0079-6816(03)00005-4 ↗
66. Palotás, K. & Hofer, W. A. Multiple scattering in a vacuum barrier obtained from real-space wavefunctions. J. Phys.: Condens. Matter 17, 2705–2713 (2005).
67. Mándi, G. & Palotás, K. Chen’s derivative rule revisited: role of tip-orbital interference in stm. Phys. Rev. B 91, 165406 (2015).10.1103/PhysRevB.91.165406 ↗
68. Tersoff, J. & Hamann, D. R. Theory of the scanning tunneling microscope. Phys. Rev. B 31, 805–813 (1985).10.1103/PhysRevB.31.805 ↗
69. Fang, A. et al. Bursting at the seams: rippled monolayer bismuth on NbSe2. Sci. Adv. 4, eaaq0330 (2018).10.1126/sciadv.aaq0330 ↗
70. Kamil, E. et al. Electronic structure of single layer 1T -NbSe2: interplay of lattice distortions, non-local exchange, and Mott–Hubbard correlations. J. Phys.: Condens. Matter 30, 325601 (2018).
71. Komori, F., Iwaki, T., Hattori, K., Shiino, O. & Hasegawa, T. New superstructure on the surface of 2H-NbSe2 and tunneling spectra at 4.2 K. J. Phys. Soc. Jpn. 66, 298–301, https://doi.org/10.1143/JPSJ.66.298 (1997).10.1143/JPSJ.66.298 ↗
72. Wang, H., Lee, J., Dreyer, M. & Barker, B. I. A scanning tunneling microscopy study of a new superstructure around defects created by tip-sample interaction on 2H-NbSe2. J. Phys.: Condens. Matter 21, 265005 (2009).
73. Malliakas, C. D. & Kanatzidis, M. G. Nb–Nb interactions define the charge density wave structure of 2H-NbSe2. J. Am. Chem. Soc. 135, 1719–1722 (2013).10.1021/ja3120554 ↗
74. Kim, S. & Son, Y.-W. Quasiparticle energy bands and Fermi surfaces of monolayer nbse2. Phys. Rev. B 96, 155439 (2017).10.1103/PhysRevB.96.155439 ↗