Two-dimensional (2D) materials are not expected to be metals at low temperature owing to electron localization1. Consistent with this, pioneering studies on thin films reported only superconducting and insulating ground states, with a direct transition between the two as a function of disorder or magnetic field2, 3, 4, 5, 6. However, more recent works have revealed the presence of an intermediate quantum metallic state occupying a substantial region of the phase diagram7, 8, 9, 10, whose nature is intensely debated11, 12, 13, 14, 15, 16, 17. Here, we observe such a state in the disorder-free limit of a crystalline 2D superconductor, produced by mechanical co-lamination of NbSe2 in an inert atmosphere. Under a small perpendicular magnetic field, we induce a transition from superconductor to the quantum metal. We find a unique power-law scaling with field in this phase, which is consistent with the Bose-metal model where metallic behaviour arises from strong phase fluctuations caused by the magnetic field11, 12, 13, 14.
At a glance
- Scaling theory of localization: Absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979). , , &
- Superconductor–insulator transitions in the two-dimensional limit. Phys. Today 51, 39–44 (1998). &
- Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989). , &
- Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–926 (1990).
- Magnetic-field-tuned superconductor–insulator transition in two-dimensional films. Phys. Rev. Lett. 65, 927–930 (1990). &
- Superconducting–insulating transition in two-dimensional α-MoGe thin films. Phys. Rev. Lett. 74, 3037–3040 (1995). &
- Observation of quantum dissipation in the vortex state of a highly disordered superconducting thin film. Phys. Rev. Lett. 76, 1529–1532 (1996). , , &
- Evidence of collective charge behavior in the insulating state of ultrathin films of superconducting metals. Phys. Rev. Lett. 88, 037004 (2002). , &
- Magnetically induced metallic phase in superconducting tantalum films. Phys. Rev. B 73, 100505 (2006). , &
- Approach to a superconductor-to-Bose-insulator transition in disordered films. Phys. Rev. B 77, 212501 (2008). , &
- Existence of a Bose metal at T = 0. Phys. Rev. B 60, 1261–1275 (1999). &
- Bose metal: Gauge-field fluctuations and scaling for field-tuned quantum phase transitions. Phys. Rev. B 64, 134511 (2001). &
- Phase glass is a Bose metal: A new conducting state in two dimensions. Phys. Rev. Lett. 89, 027001 (2002). &
- The elusive Bose metal. Science 302, 243–247 (2003). &
- Transport through quantum melts. Phys. Rev. Lett. 80, 3352–3355 (1998). , &
- Quantum superconductor–metal transition. Phys. Rev. B 64, 132502 (2001). , &
- Vortices and quasiparticles near the superconductor–insulator transition in thin films. Phys. Rev. Lett. 95, 077002 (2005). , , &
- The rise of graphene. Nature Mater. 6, 183–191 (2007). &
- Magnetic penetration depth in layered compound NbSe2 measured by muon spin relaxation. Physica C 185, 2715–2716 (1991). et al.
- Electric and magnetic characterization of NbSe2 single crystals: Anisotropic superconducting fluctuations above Tc. Physica C 460, 789–790 (2007). et al.
- Electric field effect on superconductivity in atomically thin flakes of NbSe2. Phys. Rev. B 80, 184505 (2009). et al.
- Superconductivity in two-dimensional NbSe2 field effect transistors. Supercond. Sci. Technol. 26, 125020 (2013). et al.
- Structure and control of charge density waves in two-dimensional 1T-TaS2. Proc. Natl Acad. Sci. USA http://dx.doi.org/10.1073/pnas.1512092112 (in the press). et al.
- Quality heterostructures from two-dimensional crystals unstable in air by their assembly in inert atmosphere. Nano Lett. 15, 4914–4921 (2015). et al.
- One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013). et al.
- Multi-terminal transport measurements of MoS2 using a van der Waals heterostructure device platform. Nature Nanotech. 10, 534–540 (2015). et al.
- 1996). Introduction to Superconductivity 2nd edn (Dover,
- Intrinsic spin–orbit coupling in superconducting δ-doped SrTiO3 heterostructures. Phys. Rev. B 86, 085121 (2012). , , , &
- Resistive transition in superconducting films. J. Low Temp. Phys. 36, 599–616 (1979). &
- Approaching zero-temperature metallic states in mesoscopic superconductor–normal-superconductor arrays. Nature Phys. 8, 59–62 (2012). , , &
- Possibility of vortex–antivortex pair dissociation in two-dimensional superconductors. Phys. Rev. Lett. 42, 1165–1168 (1979). , &
- Pinning and creep in layered superconductors. Physica C 167, 177–187 (1990). , &
- True superconductivity in a two-dimensional superconducting–insulating system. Phys. Rev. B 64, 060504 (2001). &
- Transport phase diagram for superconducting thin films of tantalum with homogeneous disorder. Phys. Rev. B 81, 020505 (2010). , &
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