The interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many-body physics. Conventional superconductors are insensitive to dilute non-magnetic impurities, known as Anderson’s theorem1. Destruction of superconductivity and even superconductor–insulator transitions2,3,4,5,6,7,8,9,10 occur in the regime of strong disorder. Hence, disorder-enhanced superconductivity is rare and has been observed only in some alloys or granular states11,12,13,14,15,16,17. Owing to the entanglement of various effects, the mechanism of enhancement is still under debate. Here, we report a well-controlled disorder effect in the recently discovered monolayer NbSe2 superconductor. The superconducting transition temperatures of NbSe2 monolayers are substantially increased by disorder. Realistic theoretical modelling shows that the unusual enhancement possibly arises from the multifractality18,19 of electron wavefunctions. This work provides experimental evidence of the multifractal superconducting state.
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
All relevant data are available from the corresponding authors on reasonable request.
All relevant codes or algorithms are available from the corresponding authors on reasonable request.
Anderson, P. W. Theory of dirty superconductors. J. Phys. Chem. Solids 11, 26–30 (1959).
Strongin, M., Thompson, R. S., Kammerer, O. F. & Crow, J. E. Destruction of superconductivity in disordered near-monolayer films. Phys. Rev. B 1, 1078 (1970).
Imry, Y. & Strongin, M. Destruction of superconductivity in granular and highly disordered metals. Phys. Rev. B 24, 6353 (1981).
Graybeal, J. M. & Beasley, M. R. Localization and interaction effects in ultrathin amorphous superconducting films. Phys. Rev. B 29, 4167 (1984).
Maekawa, S. & Fukuyama, H. Localization effects in two-dimensional superconductors. J. Phys. Soc. Jpn 51, 1380–1385 (1982).
Maekawa, S., Ebisawa, H. & Fukuyama, H. Theory of dirty superconductors in weakly localized regime. J. Phys. Soc. Jpn 53, 2681–2687 (1984).
Ma, M., Halperin, B. I. & Lee, P. A. Strongly disordered superfluids: quantum fluctuations and critical behavior. Phys. Rev. B 34, 3136 (1986).
Haviland, D. B., Liu, Y. & Goldman, A. M. Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180 (1989).
Hsu, J. W. P., Park, S. I., Deutscher, G. & Kapitulnik, A. Superconducting transition temperature in a Nb/NbxSi1−x bilayer system. Phys. Rev. B 43, 2648 (1991).
Jisrawi, N. M. et al. Reversible depression in the T c of thin Nb films due to enhanced hydrogen adsorption. Phys. Rev. B 58, 6585 (1998).
Kammerer, O. F. & Strongin, M. Superconductivity in tungsten films. Phys. Lett. 17, 224 (1965).
Abeles, B., Cohen, R. W. & Cullen, G. W. Enhancement of superconductivity in metal films. Phys. Rev. Lett. 17, 632 (1966).
Naugle, D. G. The effect of very thin Ge coating on the superconducting transition of thin Sn and Tl films. Phys. Lett. A 25, 688 (1967).
Garland, J. W., Bennemann, K. H. & Mueller, F. M. Effect of lattice disorder on the superconducting transition temperature. Phys. Rev. Lett. 21, 1315 (1968).
Tsuei, C. C. & Johnson, W. L. Superconductivity in metal-semiconductor eutectic alloys. Phys. Rev. B 9, 4742 (1974).
Parashar, R. S. & Srivastava, V. Superconducting T c enhancement in weakly disordered Ge-covered tin films. Phys. Rev. B 32, 6048 (1985).
Osofsky, M. S. et al. New insight into enhanced superconductivity in metals near the metal-insulator transition. Phys. Rev. Lett. 87, 197004 (2001).
Feigel’man, M. V., Ioffe, L. B., Kravtsov, V. E. & Yuzbashyan, E. A. Eigenfunction fractality and pseudogap state near the superconductor–insulator transition. Phys. Rev. Lett. 98, 027001 (2007).
Burmistrov, I. S., Gornyi, I. V. & Mirlin, A. D. Superconductor–insulator transitions: phase diagram and magnetoresistance. Phys. Rev. B 92, 014506 (2015).
Ugeda, M. M. et al. Characterization of collective ground states in single-layer NbSe2. Nat. Phys. 12, 92–97 (2016).
Tsen, A. W. et al. Nature of the quantum metal in a two-dimensional crystalline superconductor. Nat. Phys. 12, 208–212 (2016).
Xi, X. X., Berger, H., Forró, L., Shan, J. & Mak, K. F. Gate tuning of electronic phase transitions in two-dimensional NbSe2. Phys. Rev. Lett. 117, 106801 (2016).
Xi, X. X. et al. Ising pairing in superconducting NbSe2 atomic layers. Nat. Phys. 12, 139–143 (2016).
Zhou, B. T., Yuan, N. F. Q., Jiang, H. L. & Law, K. T. Ising superconductivity and Majorana fermions in transition-metal dichalcogenides. Phys. Rev. B 93, 180501 (2016).
Ma, M. & Lee, P. A. Localized superconductors. Phys. Rev. B 32, 5658 (1985).
Evers, F. & Mirlin, A. D. Anderson transition. Rev. Mod. Phys. 80, 1355 (2008).
Chalker, J. T. & Daniell, G. J. Scaling, diffusion, and the integer quantized Hall effect. Phys. Rev. Lett. 61, 593 (1988).
Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958).
Abrahams, E., Anderson, P. W., Licciardello, D. C. & Ramakrishnan, T. V. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673 (1979).
Cuevas, E. & Kravtsov, V. E. Two-eigenfunction correlation in a multifractal metal and insulator. Phys. Rev. B 76, 235119 (2007).
Guillamón, I. et al. Superconducting density of states and vortex cores of 2H-NbS2. Phys. Rev. Lett. 101, 166407 (2008).
Staley, N. E. et al. Electric field effect on superconductivity in atomically thin flakes of NbSe2. Phys. Rev. B 80, 184505 (2009).
Beasley, M. R., Mooij, J. E. & Orlando, T. P. Possibility of vortex–antivortex pair dissociation in two-dimensional superconductors. Phys. Rev. Lett. 42, 1165 (1979).
Halperin, B. I. & Nelson, D. R. Resistive transition in superconducting films. J. Low Temp. Phys. 36, 599–616 (1979).
Fiory, A. T., Hebard, A. F. & Glaberson, W. I. Superconducting phase transitions in indium/indium-oxide thin-film composites. Phys. Rev. B 28, 5075 (1983).
Kadin, A. M., Epstein, K. & Goldman, A. M. Renormalization and the Kosterlitz–Thouless transition in a two-dimensional superconductor. Phys. Rev. B 27, 6691 (1983).
Hsu, J. W. P. & Kapitulnik, A. Superconducting transition, fluctuation, and vortex motion in a two-dimensional single-crystal Nb film. Phys. Rev. B 45, 4819 (1992).
Benfatto, L., Castellani, C. & Giamarchi, T. Broadening of the Berezinskii–Kosterlitz–Thouless superconducting transition by inhomogeneity and finite-size effects. Phys. Rev. B 80, 214506 (2009).
König, E. J. et al. Berezinskii–Kosterlitz–Thouless transition in homogeneously disordered superconducting films. Phys. Rev. B 92, 214503 (2015).
Castellani, C. & Peliti, L. Multifractal wavefunction at the localization threshold. J. Phys. A 19, L429 (1986).
Mayoh, J. & García-García, A. M. Global critical temperature in disordered superconductors with weak multifractality. Phys. Rev. B 92, 174526 (2015).
Richardella, A. et al. Visualizing critical correlations near the metal-insulator transition in Ga1–xMnxAs. Science 327, 665–669 (2010).
Sacépé, B. et al. Localization of performed Cooper pairs in disordered superconductors. Nat. Phys. 7, 239–244 (2011).
Sacépé, B. et al. Disorder-induced inhomogeneities of the superconducting state close to the superconductor–insulator transition. Phys. Rev. Lett. 101, 157006 (2008).
Ramakrishnan, T. V. Superconductivity in disordered thin films. Phys. Scr. T27, 24–30 (1989).
Feigel’man, M. V., Ioffe, L. B., Kravtsov, V. E. & Cuevas, E. Fractal superconductivity near localization threshold. Ann. Phys. 325, 1390–1478 (2010).
Chhabra, A. & Jensen, R. V. Direct determination of the f(α) singularity spectrum. Phys. Rev. Lett. 62, 1327 (1989).
Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67. Nat. Phys. 8, 871–876 (2012).
Wagner, K. E. et al. Tuning the charge density wave and superconductivity in CuxTaS2. Phys. Rev. B 78, 104520 (2008).
Sugawara, K., Yokota, K., Takemoto, J., Tanokura, Y. & Sekine, T. Anderson localization and layered superconductor 2H-NbSe2–xSx. J. Low Temp. Phys. 91, 39–47 (1993).
Straub, Th et al. Charge-density-wave mechanism in 2H-NbSe2: photoemission results. Phys. Rev. Lett. 82, 4504 (1999).
Rossnagel, K. et al. Fermi surface of 2H-NbSe2 and its implications on the charge-density-wave mechanism. Phys. Rev. B 64, 235119 (2001).
Borisenko, S. V. et al. Two energy gaps and Fermi-surface “arcs” in NbSe2. Phys. Rev. Lett. 102, 166402 (2009).
Feng, Y. J. et al. Order parameter fluctuations at a buried quantum critical point. Proc. Natl Acad. Sci. USA 109, 7224–7229 (2012).
Rubio-Verdú, C. et al. Multifractal superconductivity in a two-dimensional transition metal dichalcogenide. Preprint at https://arxiv.org/abs/1810.08222 (2018).
Berger, C. et al. Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B 108, 19912–19916 (2004).
Horcas, I. et al. WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev. Sci. Instrum. 78, 013705 (2007).
We thank A. M. García-García for stimulating discussions. This work is supported by the Ministry of Science and Technology of China (grant nos. 2018YFA0305600, 2016YFA0301002, 2017YFA0303302, 2013CB934600), the National Natural Science Foundation of China (grant nos. 51561145005, 11622433, 11574175, 51522212, 11774008, 11704414). K.T.L. would like to acknowledge the support of HKRGC (grants 16324216, 16309718, 6307117 and C6026-16W), Croucher Foundation and Dr. Tai-Chin Lo Foundation. L.G. is partially supported by Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB07030200). M.S.B. and N.N. gratefully acknowledge support from the CREST, JST (no. JPMJCR16F1). N.N. is also supported by JSPS KAKENHI grant numbers 18H03676 and 26103006. M.S.B. is also supported by the Japan Society for Promotion of Science (Grant-in-Aid for Scientific Research (S) no. 24224009).
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Zhao, K., Lin, H., Xiao, X. et al. Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides. Nat. Phys. 15, 904–910 (2019). https://doi.org/10.1038/s41567-019-0570-0
Communications Physics (2021)
Communications Physics (2020)
Nature Communications (2020)
Nature Physics (2020)