# Nature of the quantum metal in a two-dimensional crystalline superconductor

## Abstract

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.

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## Acknowledgements

We acknowledge helpful discussions with Z. Han, J.-D. Pillet, E. Shimsoni, O. Vafek, A. Kapitulnik, D. Xiao and D. Gopalan. We thank J. Shi, F. Zhao, D. Wang and S. Chen for assistance with device fabrication. This material is based on work supported by the NSF MRSEC Program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). Salary support is provided by the NSF under grants NEB- 1124894 (A.W.T.) and DMR-1056527 (A.N.P.). Some measurements were performed at the National High Magnetic Field Laboratory, which is supported by the NSF Cooperative Agreement (DMR-0654118), the State of Florida and the Department of Energy. S.J. is supported by the National Basic Research Program of China (grants 2013CB921901 and 2014CB239302). R.J.C. is supported by the Department of Energy, Division of Basic Energy Sciences (grant DOE FG02-98ER45706). P.K. acknowledges support from the Army Research Office (grant W911NF-14-1-0638).

## Author information

A.W.T., B.H., C.R.D. and A.N.P. conceived and designed the experiment; Z.J.Y. and S.J. synthesized the NbSe2 crystals; A.W.T. fabricated the devices with assistance from Y.D.K.; A.W.T. and B.H. performed the transport measurements; A.W.T., B.H., C.R.D. and A.N.P. analysed the data and wrote the paper. R.J.C., J.H., P.K., C.R.D. and A.N.P. advised.

Correspondence to C. R. Dean or A. N. Pasupathy.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 407 kb)

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Tsen, A., Hunt, B., Kim, Y. et al. Nature of the quantum metal in a two-dimensional crystalline superconductor. Nature Phys 12, 208–212 (2016) doi:10.1038/nphys3579

• #### DOI

https://doi.org/10.1038/nphys3579

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