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Highly crystalline 2D superconductors

Nature Reviews Materials volume 2, Article number: 16094 (2017) Cite this article

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Abstract

Recent advances in materials fabrication have enabled the manufacturing of ordered 2D electron systems, such as heterogeneous interfaces, atomic layers grown by molecular beam epitaxy, exfoliated thin flakes and field-effect devices. These 2D electron systems are highly crystalline, and some of them, despite their single-layer thickness, exhibit a sheet resistance more than an order of magnitude lower than that of conventional amorphous or granular thin films. In this Review, we explore recent developments in the field of highly crystalline 2D superconductors and highlight the unprecedented physical properties of these systems. In particular, we explore the quantum metallic state (or possible metallic ground state), the quantum Griffiths phase observed in out-of-plane magnetic fields and the superconducting state maintained in anomalously large in-plane magnetic fields. These phenomena are examined in the context of weakened disorder and/or broken spatial inversion symmetry. We conclude with a discussion of how these unconventional properties make highly crystalline 2D systems promising platforms for the exploration of new quantum physics and high-temperature superconductors.

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Figure 1: Evolution of the thickness of 2D superconductors since 1980.
Figure 2: 2D superconductivity in deposited metallic thin films.
Figure 3: Superconductivity at oxide interfaces.
Figure 4: Superconducting atomic layers of Pb, In and FeSe grown by molecular beam epitaxy.
Figure 5: Atomically thin superconductors based on exfoliated 2D crystals.
Figure 6: Electric-field-induced superconductivity in 2D crystals.
Figure 7: Metallic ground state in ion-gated ZrNCl.
Figure 8: Quantum Griffiths singularity in a superconducting Ga crystalline thin film.
Figure 9: Superconductivity protected by spin–valley locking in ion-gated MoS2 and NbSe2 bilayers.

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References

  1. Shal'nikov, A. Superconducting thin films. Nature 142, 74 (1938).

    CAS  Google Scholar 

  2. Buckel, W. & Hilsch, R. Einfluss der Kondensation bei tiefen Temperaturen auf den elektrischen Widerstand und die Supraleitung für verschiedene Metalle. Z. Phys. 138, 109–120 (in German) (1954).

    CAS  Google Scholar 

  3. Hilsh, R. Non-crystalline Solids (ed. Frechette, V. D. ) (Wiley, 1958).

    Google Scholar 

  4. Ginsberg, D. M. & Shier, J. S. in Basic Problems in Thin Films Physics (eds Niedermayer, R. & Mayer, H. ) 543 (Vandenhoeck and Ruprecht, 1966).

    Google Scholar 

  5. Strongin, M. & Kammerer, O. F. Superconductive phenomena in ultrathin films. J. Appl. Phys. 39, 2509–2514 (1968).

    CAS  Google Scholar 

  6. Graybeal, J. M. & Beasley, M. R. Localization and interaction effects in ultrathin amorphous superconducting films. Phys. Rev. B 29, 4167–4169 (1984).

    CAS  Google Scholar 

  7. Orr, B. G., Jaeger, H. M. & Goldman, A. M. Local superconductivity in ultrathin Sn films. Phys. Rev. B 32, 7586–7589 (1985).

    CAS  Google Scholar 

  8. Jaeger, H. M., Haviland, D. B., Goldman, A. M. & Orr, B. G. Threshold for superconductivity in ultrathin amorphous gallium films. Phys. Rev. B 34, 4920–4923 (1986).

    CAS  Google Scholar 

  9. Jaeger, H. M., Haviland, D. B., Orr, B. G. & Goldman, A. M. Onset of superconductivity in ultrathin granular metal films. Phys. Rev. B 40, 182–196 (1989).

    CAS  Google Scholar 

  10. Haviland, D. B., Liu, Y. & Goldman, A. M. Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989).

    CAS  Google Scholar 

  11. Hebard, A. F. & Paalanen, M. A. Magnetic-field-tuned superconductor–insulator transition in two-dimensional films. Phys. Rev. Lett. 65, 927–930 (1990).

    CAS  Google Scholar 

  12. Liu, Y., Haviland, D. B., Nease, B. & Goldman, A. M. Insulator-to-superconductor transition in ultrathin films. Phys. Rev. B 47, 5931–5946 (1993).

    CAS  Google Scholar 

  13. Qin, Y., Vicente, C. L. & Yoon, J. Magnetically induced metallic phase in superconducting tantalum films. Phys. Rev. B 73, 100505 (2006).

    Google Scholar 

  14. Terashima, T., Shimura, K. & Bando, Y. Superconductivity of one-unit-cell thick YBa2Cu3O7 thin film. Phys. Rev. Lett. 67, 1362–1365 (1991).

    CAS  Google Scholar 

  15. Dekker, C. & Woltgens, P. J. M. Absence of a finite-temperature vortex-glass phase transition in two-dimensional YBa2Cu3O7 − δ films. Phys. Rev. Lett. 69, 2717–2720 (1992).

    CAS  Google Scholar 

  16. Guo, Y. et al. Superconductivity modulated by quantum size effects. Science 306, 1915–1918 (2004).

    CAS  Google Scholar 

  17. Nishio, T., Ono, M., Eguchi, T., Sakata, H. & Hasegawa, Y. Superconductivity of nanometer-size Pb islands studied by low-temperature scanning tunneling microscopy. Appl. Phys. Lett. 88, 113115 (2006).

    Google Scholar 

  18. Eom, D., Qin, S., Chou, M. Y. & Shih, C. K. Persistent superconductivity in ultrathin Pb films: a scanning tunneling spectroscopy study. Phys. Rev. Lett. 96, 27005 (2006).

    Google Scholar 

  19. Qin, S., Kim, J., Niu, Q. & Shih, C.-K. Superconductivity at the two-dimensional limit. Science 324, 1314–1317 (2009).

    CAS  Google Scholar 

  20. Zhang, T. et al. Superconductivity in one-atomic-layer metal films grown on Si(111). Nat. Phys. 6, 104–108 (2010).

    CAS  Google Scholar 

  21. Reyren, N. et al. Superconducting interfaces between insulating oxides. Science 317, 1196–1199 (2007).

    CAS  Google Scholar 

  22. Gozar, A. et al. High-temperature interface superconductivity between metallic and insulating copper oxides. Nature 455, 782–785 (2008).

    CAS  Google Scholar 

  23. Wang, Q.-Y. et al. Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3 . Chin. Phys. Lett. 29, 37402 (2012).

    Google Scholar 

  24. Staley, N. E. et al. Electric field effect on superconductivity in atomically thin flakes of NbSe2 . Phys. Rev. B 80, 184505 (2009).

    Google Scholar 

  25. Jiang, D. et al. High-Tc superconductivity in ultrathin Bi2Sr2CaCu2O8 + x down to half-unit-cell thickness by protection with graphene. Nat. Commun. 5, 5708 (2014).

    CAS  Google Scholar 

  26. Cao, Y. et al. Quality heterostructures from two-dimensional crystals unstable in air by their assembly in inert atmosphere. Nano Lett. 15, 4914–4921 (2015).

    CAS  Google Scholar 

  27. Xi, X. et al. Strongly enhanced charge-density-wave order in monolayer NbSe2 . Nat. Nanotechnol. 10, 765–769 (2015).

    CAS  Google Scholar 

  28. Ueno, K. et al. Electric-field-induced superconductivity in an insulator. Nat. Mater. 7, 855–858 (2008).

    CAS  Google Scholar 

  29. Ye, J. T. et al. Liquid-gated interface superconductivity on an atomically flat film. Nat. Mater. 9, 125–128 (2010).

    CAS  Google Scholar 

  30. Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).

    CAS  Google Scholar 

  31. Costanzo, D., Jo, S., Berger, H. & Morpurgo, A. F. Gate-induced superconductivity in atomically thin MoS2 crystals. Nat. Nanotechnol. 11, 339–344 (2016).

    CAS  Google Scholar 

  32. Schiller, C. K. Angular dependence of the critical field of quenched thin Pb and Sn films. J. Appl. Phys. 40, 4179–4183 (1969).

    CAS  Google Scholar 

  33. Tinkham, M. Effect of fluxoid quantization on transitions of superconducting films. Phys. Rev. 129, 2413–2422 (1963).

    Google Scholar 

  34. Mooij, J. E. in Percolation, Localization and Superconductivity (eds Goldman, A. M. & Wolf, S. A. ) 325–370 (Plenum, 1984).

    Google Scholar 

  35. Blatt, J. M. & Thompson, C. J. Shape resonances in superconducting thin films. Phys. Rev. Lett. 10, 332–334 (1963).

    Google Scholar 

  36. Orr, B. G., Jaeger, H. M. & Goldman, A. M. Transition-temperature oscillations in thin superconducting films. Phys. Rev. Lett. 53, 2046–2049 (1984).

    CAS  Google Scholar 

  37. Aslamasov, L. G. & Larkin, A. I. The influence of fluctuation pairing of electrons on the conductivity of normal metal. Phys. Lett. A 26, 238–239 (1968).

    Google Scholar 

  38. Maki, K. The critical fluctuation of the order parameter in type-II superconductors. Prog. Theor. Phys. 39, 897–906 (1968).

    Google Scholar 

  39. Thompson, R. Microwave, flux flow, and fluctuation resistance of dirty type-II superconductors. Phys. Rev. B 1, 327–333 (1970).

    Google Scholar 

  40. Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group. I. Classical systems. Sov. Phys. JETP 32, 493–500 (1971).

    Google Scholar 

  41. Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems. Sov. Phys. JETP 34, 610–616 (1972).

    Google Scholar 

  42. Kosterlitz, J. M. & Thouless, D. J. Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory). J. Phys. C Solid State Phys. 5, 124–126 (1972).

    Google Scholar 

  43. Fisher, M. P. A. Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–927 (1990).

    CAS  Google Scholar 

  44. Goldman, A. M. Superconductor–insulator transitions. Int. J. Mod. Phys. B 24, 4081–4101 (2010).

    CAS  Google Scholar 

  45. Hebard, A. F. & Fiory, A. T. Critical-exponent measurements of a two-dimensional superconductor. Phys. Rev. Lett. 50, 1603–1606 (1983).

    CAS  Google Scholar 

  46. Fisher, M. P. A., Grinstein, G. & Girvin, S. M. Presence of quantum diffusion in two dimensions: universal resistance at the superconductor–insulator transition. Phys. Rev. Lett. 64, 587–590 (1990).

    CAS  Google Scholar 

  47. Krauth, W., Trivedi, N. & Ullah, S. Superfluid-insulator transition in disordered boson systems. Phys. Rev. Lett. 67, 2307–2310 (1991).

    CAS  Google Scholar 

  48. Scalettar, R. T., Batrouni, G. G. & Zimanyi, G. T. Localization in interacting, disordered, Bose systems. Phys. Rev. Lett. 66, 3144–3147 (1991).

    CAS  Google Scholar 

  49. Yazdani, A. & Kapitulnik, A. Superconducting–insulating transition in two-dimensional a-MoGe thin films. Phys. Rev. Lett. 74, 3037–3040 (1995).

    CAS  Google Scholar 

  50. Ephron, D., Yazdani, A., Kapitulnik, A. & Beasley, M. R. Observation of quantum dissipation in the vortex state of a highly disordered superconducting thin film. Phys. Rev. Lett. 76, 1529–1532 (1996).

    CAS  Google Scholar 

  51. Chervenak, J. & Valles, J. Absence of a zero-temperature vortex solid phase in strongly disordered superconducting Bi films. Phys. Rev. B 61, R9245–R9248 (2000).

    CAS  Google Scholar 

  52. Goldman, A. M. & Markovic´, N. Superconductor–insulator transitions in the two-dimensional limit. Phys. Today 51, 39–44 (1998).

    CAS  Google Scholar 

  53. Lin, Y. H., Nelson, J. & Goldman, A. M. Superconductivity of very thin films: the superconductor–insulator transition. Phys. C 514, 130–141 (2015).

    CAS  Google Scholar 

  54. Meservey, R. & Tedrow, P. M. Spin–orbit scattering in superconducting thin films. Phys. Lett. A 58, 131–132 (1976).

    Google Scholar 

  55. Tedrow, P. M. & Meservey, R. Critical magnetic field of very thin superconducting aluminum films. Phys. Rev. B 25, 171–178 (1982).

    CAS  Google Scholar 

  56. Gariglio, S. & Triscone, J. M. Oxide interface superconductivity. C. R. Phys. 12, 591–599 (2011).

    CAS  Google Scholar 

  57. Gariglio, S., Gabay, M., Mannhart, J. & Triscone, J.-M. Interface superconductivity. Phys. C 514, 189–198 (2015).

    CAS  Google Scholar 

  58. Ueno, K. et al. Field-induced superconductivity in electric double layer transistors. J. Phys. Soc. Jpn 83, 32001 (2014).

    Google Scholar 

  59. Xu, C. et al. Large-area high-quality 2D ultrathin Mo2C superconducting crystals. Nat. Mater. 14, 1135–1141 (2015).

    CAS  Google Scholar 

  60. Wang, L. et al. Magnetotransport properties in high-quality ultrathin two-dimensional superconducting Mo2C crystals. ACS Nano 10, 4504–4510 (2016).

    CAS  Google Scholar 

  61. Mizukami, Y. et al. Extremely strong-coupling superconductivity in artificial two-dimensional Kondo lattices. Nat. Phys. 7, 849–853 (2011).

    CAS  Google Scholar 

  62. Xue, M., Chen, G., Yang, H. & Zhu, Y. Superconductivity in potassium-doped few-layer graphene. J. Am. Chem. Soc. 134, 6536–6539 (2012).

    CAS  Google Scholar 

  63. Ludbrook, B. M. et al. Evidence for superconductivity in Li-decorated monolayer graphene. Proc. Natl Acad. Sci. USA 112, 11795–11799 (2015).

    CAS  Google Scholar 

  64. Ichinokura, S., Sugawara, K., Takayama, A., Takahashi, T. & Hasegawa, S. Superconducting calcium-intercalated bilayer graphene. ACS Nano 10, 2761–2765 (2016).

    CAS  Google Scholar 

  65. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    CAS  Google Scholar 

  66. Ohtomo, A. & Hwang, H. Y. A high-mobility electron gas at the LaAlO3/SrTiO3 . Nature 427, 423–426 (2004).

    CAS  Google Scholar 

  67. Caviglia, A. D. et al. Electric field control of the LaAlO3/SrTiO3 interface ground state. Nature 456, 624–627 (2008).

    CAS  Google Scholar 

  68. Hurand, S. et al. Density driven fluctuations in a two-dimensional superconductor. Preprint at https://arxiv.org/abs/1506.06874 (2015).

  69. Richter, C. et al. Interface superconductor with gap behaviour like a high-temperature superconductor. Nature 502, 528–531 (2013).

    CAS  Google Scholar 

  70. Cheng, G. et al. Electron pairing without superconductivity. Nature 521, 196–199 (2015).

    CAS  Google Scholar 

  71. Biscaras, J. et al. Two-dimensional superconductivity at a Mott insulator/band insulator interface LaTiO3/SrTiO3 . Nat. Commun. 1, 89 (2010).

    CAS  Google Scholar 

  72. Biscaras, J. et al. Two-dimensional superconducting phase in LaTiO3/SrTiO3 heterostructures induced by high-mobility carrier doping. Phys. Rev. Lett. 108, 247004 (2012).

    CAS  Google Scholar 

  73. Biscaras, J. et al. Multiple quantum criticality in a two-dimensional superconductor. Nat. Mater. 12, 542–548 (2013).

    CAS  Google Scholar 

  74. Gozar, A. & Bozovic, I. High temperature interface superconductivity. Phys. C 521, 38–49 (2016).

    Google Scholar 

  75. Bozovic, I. Atomic-layer engineering of superconducting oxides: yesterday, today, tomorrow. IEEE Trans Appl. Supercond. 11, 2686–2695 (2001).

    Google Scholar 

  76. Wu, J. et al. Anomalous independence of interface superconductivity from carrier density. Nat. Mater. 12, 877–881 (2013).

    CAS  Google Scholar 

  77. He, Q. L. et al. Two-dimensional superconductivity at the interface of a Bi2Te3/FeTe heterostructure. Nat. Commun. 5, 4247 (2014).

    CAS  Google Scholar 

  78. Ozer, M. M., Thompson, J. R. & Weitering, H. H. Hard superconductivity of a soft metal in the quantum regime. Nat. Phys. 2, 173–176 (2006).

    CAS  Google Scholar 

  79. Nishio, T. et al. Superconducting Pb island nanostructures studied by scanning tunneling microscopy and spectroscopy. Phys. Rev. Lett. 101, 167001 (2008).

    Google Scholar 

  80. Özer, M. M., Jia, Y., Zhang, Z., Thompson, J. R. & Weitering, H. H. Tuning the quantum stability and superconductivity of ultrathin metal alloys. Science 316, 1594–1597 (2007).

    Google Scholar 

  81. Paggel, J. J. Quantum-well states as Fabry–Perot modes in a thin-film electron interferometer. Science 283, 1709–1711 (1999).

    CAS  Google Scholar 

  82. Chiang, T. C. Photoemission studies of quantum well states in thin films. Surf. Sci. Rep. 39, 181–235 (2000).

    CAS  Google Scholar 

  83. Uchihashi, T., Mishra, P., Aono, M. & Nakayama, T. Macroscopic superconducting current through a silicon surface reconstruction with indium adatoms: Si(111)–(√7 × √3)-In. Phys. Rev. Lett. 107, 207001 (2011).

    Google Scholar 

  84. Yamada, M., Hirahara, T. & Hasegawa, S. Magnetoresistance measurements of a superconducting surface state of In-induced and Pb-induced structures on Si(111). Phys. Rev. Lett. 110, 237001 (2013).

    Google Scholar 

  85. Yoshizawa, S. et al. Imaging Josephson vortices on the surface superconductor Si(111)-(√7 × √3)-In using a scanning tunneling microscope. Phys. Rev. Lett. 113, 247004 (2014).

    Google Scholar 

  86. Matetskiy, A. V. et al. Two-dimensional superconductor with a giant Rashba effect: one-atom-layer Tl–Pb compound on Si(111). Phys. Rev. Lett. 115, 147003 (2015).

    CAS  Google Scholar 

  87. Gruznev, D. V. et al. A strategy to create spin-split metallic bands on silicon using a dense alloy layer. Sci. Rep. 4, 4742 (2014).

    Google Scholar 

  88. Sekihara, T., Masutomi, R. & Okamoto, T. Two-dimensional superconducting state of monolayer Pb films grown on GaAs(110) in a strong parallel magnetic field. Phys. Rev. Lett. 111, 57005 (2013).

    Google Scholar 

  89. Fulde, P. & Ferrell, A. R. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550–A563 (1964).

    Google Scholar 

  90. Larkin, A. I. & Ovchinnikov, Y. N. Nonuniform state of superconductors. Sov. Phys. JETP 20, 762–769 (1965).

    Google Scholar 

  91. Kaur, R. P., Agterberg, D. F. & Sigrist, M. Helical vortex phase in the noncentrosymmetric CePt3Si. Phys. Rev. Lett. 94, 137002 (2005).

    CAS  Google Scholar 

  92. Zhang, H.-M. et al. Detection of a superconducting phase in a two-atom layer of hexagonal Ga film grown on semiconducting GaN(0001). Phys. Rev. Lett. 114, 107003 (2015).

    Google Scholar 

  93. Ugeda, M. M. et al. Characterization of collective ground states in single-layer NbSe2 . Nat. Phys. 12, 92–97 (2016).

    CAS  Google Scholar 

  94. Hsu, F.-C. et al. Superconductivity in the PbO-type structure α-FeSe. Proc. Natl Acad. Sci. USA 105, 14262–14264 (2008).

    CAS  Google Scholar 

  95. Ge, J.-F. et al. Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3 . Nat. Mater. 14, 285–289 (2015).

    CAS  Google Scholar 

  96. Lee, J. J. et al. Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3 . Nature 515, 245–248 (2014).

    CAS  Google Scholar 

  97. He, S. et al. Phase diagram and electronic indication of high-temperature superconductivity at 65 K in single-layer FeSe films. Nat. Mater. 12, 605–610 (2013).

    CAS  Google Scholar 

  98. Tan, S. et al. Interface-induced superconductivity and strain-dependent spin density waves in FeSe/SrTiO3 thin films. Nat. Mater. 12, 634–640 (2013).

    CAS  Google Scholar 

  99. Peng, R. et al. Tuning the band structure and superconductivity in single-layer FeSe by interface engineering. Nat. Commun. 5, 5044 (2014).

    CAS  Google Scholar 

  100. Shiogai, J., Ito, Y., Mitsuhashi, T., Nojima, T. & Tsukazaki, A. Electric-field-induced superconductivity in electrochemically etched ultrathin FeSe films on SrTiO3 and MgO. Nat. Phys. 12, 42–46 (2015).

    Google Scholar 

  101. Miyata, Y., Nakayama, K., Sugawara, K., Sato, T. & Takahashi, T. High-temperature superconductivity in potassium-coated multilayer FeSe thin films. Nat. Mater. 14, 775–779 (2015).

    CAS  Google Scholar 

  102. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    CAS  Google Scholar 

  103. Geim, A. & Novoselov, K. The rise of graphene. Nat. Mater. 6, 183–191 (2007).

    CAS  Google Scholar 

  104. Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol. 7, 699–712 (2012).

    CAS  Google Scholar 

  105. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).

    CAS  Google Scholar 

  106. Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photonics 10, 216–226 (2016).

    CAS  Google Scholar 

  107. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010).

    CAS  Google Scholar 

  108. Frindt, R. Superconductivity in ultrathin NbSe2 layers. Phys. Rev. Lett. 28, 299–301 (1972).

    CAS  Google Scholar 

  109. Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005).

    CAS  Google Scholar 

  110. Glover, R. E. & Sherrill, M. D. Changes in superconducting critical temperature produced by electrostatic charging. Phys. Rev. Lett. 5, 248–250 (1960).

    CAS  Google Scholar 

  111. Stadler, H. L. Changing properties of metals by ferroelectric polarization charging. Phys. Rev. Lett. 14, 979–981 (1965).

    CAS  Google Scholar 

  112. Hebard, A. F., Fiory, A. T. & Eick, R. H. Experimental considerations in the quest for a thin-film superconducting field-effect transistor. IEEE Trans Magn. 23, 1279–1282 (1987).

    Google Scholar 

  113. Fiory, A. T. et al. Metallic and superconducting surfaces of YBa2Cu307 probed by electrostatic charge modulation of epitaxial films. Phys. Rev. Lett. 65, 3441–3444 (1990).

    CAS  Google Scholar 

  114. Mannhart, J., Schlom, D., Bednorz, J. & Müller, K. Influence of electric fields on pinning in YBa2Cu3O7 − δ films. Phys. Rev. Lett. 67, 2099–2101 (1991).

    CAS  Google Scholar 

  115. Walkenhorst, A. et al. Electric field effects on vortex dynamics in ultrathin YBa2Cu3O7 − δ films. Phys. Rev. Lett. 69, 2709–2712 (1992).

    CAS  Google Scholar 

  116. Xi, X. X. et al. Effects of field-induced hole-density modulation on normal-state and superconducting transport in YBa2Cu3O7 − x . Phys. Rev. Lett. 68, 1240–1243 (1992).

    CAS  Google Scholar 

  117. Mannhart, J. High-T c transistors. Supercond. Sci. Technol. 9, 49–67 (1996).

    CAS  Google Scholar 

  118. Ahn, C. H. et al. Electrostatic modulation of superconductivity in ultrathin GdBa2Cu3O7 − x films. Science 284, 1152–1155 (1999).

    CAS  Google Scholar 

  119. Matthey, D., Gariglio, S. & Triscone, J. M. Field-effect experiments in NdBa2Cu3O7 − δ ultrathin films using a SrTiO3 single-crystal gate insulator. Appl. Phys. Lett. 83, 3758–3760 (2003).

    CAS  Google Scholar 

  120. Parendo, K. A., Tan, K. H. S. B. & Goldman, A. M. Electrostatic and parallel-magnetic-field tuned two-dimensional superconductor-insulator transitions. Phys. Rev. B 73, 1–11 (2006).

    Google Scholar 

  121. Parendo, K. A. et al. Electrostatic tuning of the superconductor-insulator transition in two dimensions. Phys. Rev. Lett. 94, 197004 (2005).

    Google Scholar 

  122. Misra, R., McCarthy, M. & Hebard, A. F. Electric field gating with ionic liquids. Appl. Phys. Lett. 90, 2006–2008 (2007).

    Google Scholar 

  123. Shimotani, H., Diguet, G. & Iwasa, Y. Direct comparison of field-effect and electrochemical doping in regioregular poly(3-hexylthiophene). Appl. Phys. Lett. 86, 2003–2006 (2005).

    Google Scholar 

  124. Panzer, M. J., Newman, C. R. & Frisbie, C. D. Low-voltage operation of a pentacene field-effect transistor with a polymer electrolyte gate dielectric. Appl. Phys. Lett. 86, 103503 (2005).

    Google Scholar 

  125. Brattain, W. H. & Garrett, C. G. B. Experiments on the interface between germanium and an electrolyte. Bell Syst. Tech. J. 34, 129–176 (1955).

    Google Scholar 

  126. Haupt, S. G., Riley, D. R., Jones, C. T., Zhao, J. & McDevitt, J. T. Reversible modulation of T c in conductive polymer/high temperature superconductor assemblies. J. Am. Chem. Soc. 115, 1196–1198 (1993).

    CAS  Google Scholar 

  127. Ueno, K. et al. Discovery of superconductivity in KTaO3 by electrostatic carrier doping. Nat. Nanotechnol. 6, 408–412 (2011).

    CAS  Google Scholar 

  128. Biscaras, J., Chen, Z., Paradisi, A. & Shukla, A. Onset of two-dimensional superconductivity in space charge doped few-layer molybdenum disulfide. Nat. Commun. 6, 8826 (2015).

    CAS  Google Scholar 

  129. Jo, S., Costanzo, D., Berger, H. & Morpurgo, A. F. Electrostatically induced superconductivity at the surface of WS2 . Nano Lett. 15, 1197–1202 (2015).

    CAS  Google Scholar 

  130. Shi, W. et al. Superconductivity series in transition metal dichalcogenides by ionic gating. Sci. Rep. 5, 12534 (2015).

    CAS  Google Scholar 

  131. Bollinger, A. T. et al. Superconductor–insulator transition in La2 − xSrxCuO4 at the pair quantum resistance. Nature 472, 458–460 (2011).

    CAS  Google Scholar 

  132. Leng, X., Garcia-Barriocanal, J., Bose, S., Lee, Y. & Goldman, A. M. Electrostatic control of the evolution from a superconducting phase to an insulating phase in ultrathin YBa2Cu3O7 − x films. Phys. Rev. Lett. 107, 27001 (2011).

    Google Scholar 

  133. Garcia-Barriocanal, J. et al. Electronically driven superconductor–insulator transition in electrostatically doped La2CuO4 + δ thin films. Phys. Rev. B 87, 24509 (2013).

    Google Scholar 

  134. Zeng, S. W. et al. Two-dimensional superconductor–insulator quantum phase transitions in an electron-doped cuprate. Phys. Rev. B 92, 20503 (2015).

    Google Scholar 

  135. Lee, Y. et al. Phase diagram of electrostatically doped SrTiO3 . Phys. Rev. Lett. 106, 136809 (2011).

    Google Scholar 

  136. Gallagher, P., Lee, M., Williams, J. R. & Goldhaber-Gordon, D. Gate-tunable superconducting weak link and quantum point contact spectroscopy on a strontium titanate surface. Nat. Phys. 10, 748–752 (2014).

    CAS  Google Scholar 

  137. Saito, Y., Kasahara, Y., Ye, J., Iwasa, Y. & Nojima, T. Metallic ground state in an ion-gated two-dimensional superconductor. Science 350, 409–413 (2015).

    CAS  Google Scholar 

  138. Yamada, Y., Ueno, K. & Fukumura, T. Electrically induced ferromagnetism at room temperature in cobalt-doped titanium dioxide. Science 332, 1065–1067 (2011).

    CAS  Google Scholar 

  139. Nakano, M. et al. Collective bulk carrier delocalization driven by electrostatic surface charge accumulation. Nature 487, 459–462 (2012).

    CAS  Google Scholar 

  140. Yuan, H. et al. Zeeman-type spin splitting controlled by an electric field. Nat. Phys. 9, 563–569 (2013).

    CAS  Google Scholar 

  141. Zhang, Y. J., Oka, T., Suzuki, R., Ye, J. T. & Iwasa, Y. Electrically switchable chiral light-emitting transistor. Science 344, 725–728 (2014).

    CAS  Google Scholar 

  142. Saito, Y. & Iwasa, Y. Ambipolar insulator-to-metal transition in black phosphorus by ionic-liquid gating. ACS Nano 9, 3192–3198 (2015).

    CAS  Google Scholar 

  143. Yoshida, M. et al. Gate-optimized thermoelectric power factor in ultrathin WSe2 single crystals. Nano Lett. 16, 2061–2065 (2016).

    CAS  Google Scholar 

  144. Tsen, A. W. et al. Nature of the quantum metal in a two-dimensional crystalline superconductor. Nat. Phys. 12, 208–212 (2016).

    CAS  Google Scholar 

  145. Yamanaka, S., Kawaji, H., Hotehama, K. & Ohashi, M. A new layerstructured nitride superconductor. lithium-intercalated β-zirconium nitride chloride, LixZrNCl. Adv. Mater. 8, 771–774 (1996).

    CAS  Google Scholar 

  146. Ito, T. et al. Two-dimensional nature of superconductivity in the intercalated layered systems LixHfNCl and LixZrNCl: muon spin relaxation and magnetization measurements. Phys. Rev. B 69, 134522 (2004).

    Google Scholar 

  147. Taguchi, Y., Kitora, A. & Iwasa, Y. Increase in Tc upon reduction of doping in LixZrNCl superconductors. Phys. Rev. Lett. 97, 107001 (2006).

    CAS  Google Scholar 

  148. Takano, T., Kitora, A., Taguchi, Y. & Iwasa, Y. Modulation-doped-semiconductorlike behavior manifested in magnetotransport measurements of LixZrNCl layered superconductors. Phys. Rev. B 77, 104518 (2008).

    Google Scholar 

  149. Feigel'man, M. V., Geshkenbein, V. B. & Larkin, A. I. Pinning and creep in layered superconductors. Phys. C 167, 177–187 (1990).

    Google Scholar 

  150. Mason, N. & Kapitulnik, A. Dissipation effects on the superconductor–insulator transition in 2D superconductors. Phys. Rev. Lett. 82, 5341–5344 (1999).

    CAS  Google Scholar 

  151. Mason, N. & Kapitulnik, A. True superconductivity in a two-dimensional superconducting-insulating system. Phys. Rev. B 64, 60504 (2001).

    Google Scholar 

  152. Morita, M. & Okuma, S. Magnetoresistance and vortex states below the 2D superconductor–insulator transition near T = 0. Phys. C 392–396, 406–409 (2003).

    Google Scholar 

  153. Vicente, C. L., Qin, Y. & Yoon, J. Evidence of spatial inhomogeneity near the onset of magnetically induced insulating state in superconducting thin films. Phys. Rev. B 74, 100507R (2006).

    Google Scholar 

  154. Seo, Y., Qin, Y., Vicente, C. L., Choi, K. S. & Yoon, J. Origin of nonlinear transport across the magnetically induced superconductor–metal–insulator transition in two dimensions. Phys. Rev. Lett. 97, 57005 (2006).

    CAS  Google Scholar 

  155. Li, Y., Vicente, C. L. & Yoon, J. Transport phase diagram for superconducting thin films of tantalum with homogeneous disorder. Phys. Rev. B 81, 20505 (2010).

    Google Scholar 

  156. Beidenkopf, H. et al. Equilibrium first-order melting and second-order glass transitions of the vortex matter in Bi2Sr2CaCu2O8 . Phys. Rev. Lett. 95, 257004 (2005).

    CAS  Google Scholar 

  157. Galitski, V. M., Refael, G., Fisher, M. P. A. & Senthil, T. Vortices and quasiparticles near the superconductor–insulator transition in thin films. Phys. Rev. Lett. 95, 77002 (2005).

    Google Scholar 

  158. Steiner, M., Breznay, N. & Kapitulnik, A. Approach to a superconductor-to-Bose-insulator transition in disordered films. Phys. Rev. B 77, 212501 (2008).

    Google Scholar 

  159. Shimshoni, E., Auerbach, A. & Kapitulnik, A. Transport through quantum melts. Phys. Rev. Lett. 80, 3352–3355 (1998).

    CAS  Google Scholar 

  160. Das, D. & Doniach, S. Existence of a Bose metal at T = 0. Phys. Rev. B 60, 1261–1275 (1999).

    CAS  Google Scholar 

  161. Das, D. & Doniach, S. Bose metal: gauge-field fluctuations and scaling for field-tuned quantum phase transitions. Phys. Rev. B 64, 134511 (2001).

    Google Scholar 

  162. Dalidovich, D. & Phillips, P. Phase glass is a Bose metal: a new conducting state in two dimensions. Phys. Rev. Lett. 89, 27001 (2002).

    Google Scholar 

  163. Phillips, P. & Dalidovich, D. The elusive Bose metal. Science 302, 243–247 (2003).

    CAS  Google Scholar 

  164. Wu, J. & Phillips, P. Vortex glass is a metal: unified theory of the magnetic-field and disorder-tuned Bose metals. Phys. Rev. B 73, 1–13 (2006).

    Google Scholar 

  165. Reyren, N. et al. Anisotropy of the superconducting transport properties of the LaAlO3/SrTiO3 interface. Appl. Phys. Lett. 94, 112506 (2009).

    Google Scholar 

  166. Harris, A. B. Effect of random defects on the critical behaviour of Ising models. J. Phys. C Solid State Phys. 7, 1671 (1974).

    Google Scholar 

  167. Griffiths, R. B. Non magnetic behavior above the critical point in a random Ising ferromagnet. Phys. Rev. Lett. 23, 17 (1969).

    Google Scholar 

  168. McCoy, B. M. Incompleteness of the critical exponent description for ferromagnetic systems containing random impurities. Phys. Rev. Lett. 23, 383 (1969).

    Google Scholar 

  169. Randeria, M., Sethna, J. P. & Palmer, R. G. Low-frequency relaxation in Ising spin-glasses. Phys. Rev. Lett. 54, 1321–1324 (1985).

    CAS  Google Scholar 

  170. Fisher, D. S. Random transverse field Ising spin chains. Phys. Rev. Lett. 69, 534–537 (1992).

    CAS  Google Scholar 

  171. Fisher, D. S. Critical behavior of random transverse-field Ising spin chains. Phys. Rev. B 53, 1689–1699 (1995).

    Google Scholar 

  172. Ubaid-Kassis, S., Vojta, T. & Schroeder, A. Quantum Griffiths phase in the weak itinerant ferromagnetic alloy N1 − xVx . Phys. Rev. Lett. 104, 66402 (2010).

    Google Scholar 

  173. Demkó, L. et al. Disorder promotes ferromagnetismml_ rounding of the quantum phase transition in Sr1 − xCaxRuO3 . Phys. Rev. Lett. 108, 185701 (2012).

    Google Scholar 

  174. Shi, X., Lin, P. & Sasagawa, T. Two-stage magnetic-field-tuned superconductor–insulator transition in underdoped La2 − xSrxCuO4 . Nat. Phys. 10, 437–443 (2014).

    CAS  Google Scholar 

  175. Xing, Y. et al. Quantum Griffiths singularity of superconductor–metal transition in Ga thin films. Science 350, 542–545 (2015).

    CAS  Google Scholar 

  176. Sachdev, S., Werner, P. & Troyer, M. Universal conductance of nanowires near the superconductor–metal quantum transition. Phys. Rev. Lett. 92, 237003 (2004).

    Google Scholar 

  177. Hoyos, J., Kotabage, C. & Vojta, T. Effects of dissipation on a quantum critical point with disorder. Phys. Rev. Lett. 99, 230601 (2007).

    Google Scholar 

  178. Vojta, T., Kotabage, C. & Hoyos, J. Infinite-randomness quantum critical points induced by dissipation. Phys. Rev. B 79, 24401 (2009).

    Google Scholar 

  179. Del Maestro, A., Rosenow, B., Müller, M. & Sachdev, S. Infinite randomness fixed point of the superconductor-metal quantum phase transition. Phys. Rev. Lett. 101, 35701 (2008).

    Google Scholar 

  180. Del Maestro, A., Rosenow, B., Hoyos, J. A. & Vojta, T. Dynamical conductivity at the dirty superconductor–metal quantum phase transition. Phys. Rev. Lett. 105, 145702 (2010).

    Google Scholar 

  181. Kovács, I. & Iglói, F. Renormalization group study of the two-dimensional random transverse-field Ising model. Phys. Rev. B 82, 54437 (2010).

    Google Scholar 

  182. Vojta, T., Farquhar, A. & Mast, J. Infinite-randomness critical point in the two-dimensional disordered contact process. Phys. Rev. E 79, 011111 (2009).

    Google Scholar 

  183. Shen, S. et al. Observation of quantum Griffiths singularity and ferromagnetism at superconducting LaAlO3/SrTiO3(110) interface. Phys. Rev. B 94, 144517 (2016).

    Google Scholar 

  184. Abrikosov, A. A. & Gorkov, L. P. Theory of superconducting alloys with paramagnetic impurities. Sov. Phys. JETP 12, 1243–1253 (1961).

    Google Scholar 

  185. Scopigno, N. et al. Phase separation from electron confinement at oxide interfaces. Phys. Rev. Lett. 116, 26804 (2016).

    CAS  Google Scholar 

  186. Gantmakher, V. F., Golubkov, M. V., Dolgopolov, V. T., Tsydynzhapov, G. E. & Shashkin, A. A. Superconductor–insulator transition in amorphous In–O films. Phys. B 284, 649–650 (2000).

    Google Scholar 

  187. Spathis, P., Aubin, H., Pourret, A. & Behnia, K. Nernst effect in the phase-fluctuating superconductor InOx . Eur. Phys. Lett. 83, 57005 (2008).

    Google Scholar 

  188. Frigeri, P. A., Agterberg, D. F. & Sigrist, M. Spin susceptibility in superconductors without inversion symmetry. New J. Phys. 6, 115 (2004).

    Google Scholar 

  189. Frigeri, P. A., Agterberg, D. F., Koga, A. & Sigrist, M. Superconductivity without inversion symmetry: MnSi versus CePt3Si. Phys. Rev. Lett. 92, 97001(2004).

    CAS  Google Scholar 

  190. Matsuda, Y. & Shimahara, H. Fulde–Ferrell–Larkin–Ovchinnikov state in heavy fermion superconductors. J. Phys. Soc. Jpn 76, 51005 (2007).

    Google Scholar 

  191. Zhu, Z. Y., Cheng, Y. C. & Schwingenschlögl, U. Giant spin–orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys. Rev. B 84, 153402 (2011).

    Google Scholar 

  192. 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).

    Google Scholar 

  193. Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-vi dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).

    Google Scholar 

  194. Suzuki, R. et al. Valley-dependent spin polarization in bulk MoS2 with broken inversion symmetry. Nat. Nanotechnol. 9, 611–617 (2014).

    CAS  Google Scholar 

  195. Saito, Y. et al. Superconductivity protected by spin–valley locking in ion-gated MoS2 . Nat. Phys. 12, 144–149 (2016).

    CAS  Google Scholar 

  196. Lu, J. M. et al. Evidence for two-dimensional Ising superconductivity in gated MoS2 . Science 350, 1353–1357 (2015).

    CAS  Google Scholar 

  197. Xi, X. et al. Ising pairing in superconducting NbSe2 atomic layers. Nat. Phys. 12, 139–143 (2016).

    CAS  Google Scholar 

  198. Klemm, R., Luther, A. & Beasley, M. Theory of the upper critical field in layered superconductors. Phys. Rev. B 12, 877–891 (1975).

    Google Scholar 

  199. Frigeri, P. A. Superconductivity in crystals without an inversion center. Thesis, ETH Zurich (2005).

  200. Mattheiss, L. F. Band structures of transition-metal–dichalcogenide layer compounds. Phys. Rev. B 8, 3719–3740 (1973).

    CAS  Google Scholar 

  201. 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).

    Google Scholar 

  202. Youn, S. J., Fischer, M. H., Rhim, S. H., Sigrist, M. & Agterberg, D. F. Role of strong spin–orbit coupling in the superconductivity of the hexagonal pnictide SrPtAs. Phys. Rev. B 85, 220505 (2012).

    Google Scholar 

  203. He, W.-Y., T. Zhou, B., J. He, J., Zhang, T. & T. Law, K. Nodal topological superconductivity in monolayer NbSe2. Preprint at http://arXiv:1604.02867 (2016).

  204. Markovic, N. Randomness rules. Science 350, 509–509 (2015).

    CAS  Google Scholar 

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Acknowledgements

The authors thank J. T. Ye, Y. Kasahara, Y. Kohama, M. Tokunaga, Y. Nakagawa and M. Onga for experimental cooperation, and Y. Nakamura, Y. Yanase and M. S. Bahramy for theoretical discussions. Y.S. was supported by the Japan Society for the Promotion of Science (JSPS) through a research fellowship for young scientists (Grant-in-Aid for JSPS Research Fellow: no. 15J07681). This work was supported by the Strategic International Collaborative Research Program (SICORP-LEMSUPER) of the Japan Science and Technology Agency, Grant-in-Aid for Specially Promoted Research (no. 25000003) from JSPS and Grant-in-Aid for Scientific Research on Innovative Areas (no. 22103004) from MEXT of Japan.

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  1. Quantum-Phase Electronics Center (QPEC) and Department of Applied Physics, The University of Tokyo, 113–8656, Tokyo, Japan

    Yu Saito & Yoshihiro Iwasa

  2. Institute for Materials Research, Tohoku University, Sendai, 980–8577, Japan

    Tsutomu Nojima

  3. RIKEN Center for Emergent Matter Science (CEMS, Wako, 0351–0198, Japan

    Yoshihiro Iwasa

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  1. Yu Saito
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Saito, Y., Nojima, T. & Iwasa, Y. Highly crystalline 2D superconductors. Nat Rev Mater 2, 16094 (2017). https://doi.org/10.1038/natrevmats.2016.94

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