Dissipationless charge transport is one of the defining properties of superconductors, but the interplay between dimensionality and disorder in determining the onset of dissipation remains an open theoretical and experimental problem. Here, we present measurements of the dissipation phase diagrams of superconductors in the two-dimensional limit, layer by layer, down to a monolayer in the presence of temperature (T), magnetic field (B) and current (I) in 2H-NbSe2. Our results show that the phase diagram strongly depends on the thickness even in the two-dimensional limit. At four layers we can define a finite region in the I–B phase diagram where dissipationless transport exists at T = 0. At even smaller thicknesses, this region shrinks in area until in a monolayer it approaches a single point defined by T = B = I = 0. In applied field, we show that time-dependent Ginzburg–Landau simulations that describe dissipation by vortex motion qualitatively reproduce our experimental I–B phase diagram. Last, we show that by using non-local transport and time-dependent Ginzburg–Landau calculations that we can engineer charge flow and create phase boundaries between dissipative and dissipationless transport regions in a single sample, demonstrating control over non-equilibrium states of matter.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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We thank D. Rhodes and V. Vinokour for fruitful discussions and input. This research was primarily supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634), the Global Research Laboratory (GRL) Program (2016K1A1A2912707) funded by the Ministry of Science, ICT and Future Planning via the National Research Foundation of Korea (NRF), and Honda Research Institute USA Inc. We acknowledge computing resources from Columbia University’s Shared Research Computing Facility project, which is supported by NIH Research Facility Improvement Grant 1G20RR030893-01, and associated funds from the New York State Empire State Development, Division of Science Technology and Innovation (NYSTAR) Contract C090171, both awarded 15 April 2010. A.J.M. and D.M.K. were supported by the Basic Energy Sciences Division of the US Department of Energy under grant DE-SC0018218. D.M.K. additionally acknowledges support by the Deutsche Forschungsgemeinschaft through the Emmy Noether program (KA 3360/2-1). This research was also supported by The Israel Science Foundation (ISF grant no. 556/17), the Minerva Foundation, Federal German Ministry for Education and Research, grant no. 71294.
The authors declare no competing interests.
Peer review information: Nature Physics thanks Hadar Steinberg and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Supplementary Figs. 1–11 and Supplementary references 1–8.
Uniform flow, J / Jc = 0.22, B / Hc2 = 0.16.
Uniform flow, J / Jc = 0.43, B / Hc2 = 0.16.
Uniform flow, J / Jc = 0.65, B / Hc2 = 0.16.
Pinning, J / Jc = 0.022, B / Hc2 = 0.04.
Pinning, J / Jc = 0.09, B / Hc2 = 0.04.
Pinning, J / Jc = 0.17, B / Hc2 = 0.04.
Pinning, J / Jc = 0.43, B / Hc2 = 0.04.
Pinning, J / Jc = 0.02, B / Hc2 = 0.08.
Pinning, J / Jc = 0.09, B /Hc2 = 0.08.
Pinning, J / Jc = 0.17, B / Hc2 = 0.08.
Pinning, J / Jc = 0.43, B / Hc2 = 0.08.
Non-uniform flow, J / Jc = 0.43, B / Hc2 = 0.08.
Non-uniform flow, J / Jc = 0.87, B / Hc2 = 0.08.
Non-uniform flow, J / Jc = 1.7, B / Hc2 = 0.08.
Non-uniform flow, J / Jc = 2.6, B / Hc2 = 0.08.