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Superconducting, insulating and anomalous metallic regimes in a gated two-dimensional semiconductor–superconductor array


The superconductor–insulator transition in two dimensions has been widely investigated as a paradigmatic quantum phase transition. The topic remains controversial because many experiments exhibit a metallic regime with saturating low-temperature resistance, which is at odds with conventional theory. Here, we explore this transition in a highly controllable system, a semiconductor heterostructure with epitaxial aluminium, patterned to form a regular array of superconducting islands connected by a gateable quantum well. Spanning nine orders of magnitude in resistance, the system exhibits regimes of superconducting, metallic and insulating behaviour, along with signatures of flux commensurability and vortex penetration. An in-plane magnetic field eliminates the metallic regime, restoring the direct superconductor–insulator transition; it also improves the scaling behaviour while strongly altering the scaling exponent.

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Fig. 1: Semiconductor/superconductor array.
Fig. 2: Voltage-controlled transitions.
Fig. 3: Experimental phase diagram.
Fig. 4: Temperature, magnetic field and nonlinear response.
Fig. 5: Flux effects in S, M* and I regimes.
Fig. 6: In-plane magnetic field effects.


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We thank A. Kapitulnik, S. Kivelson, K. Rasmussen, D. Shahar, B. Spivak, C. Strunk and V. Vinokur for useful discussion. Research was supported by Microsoft Station Q and the Danish National Research Foundation. C.M.M. acknowledges support from the Villum Foundation. F.N. acknowledges support from a Marie Curie Fellowship (no. 659653).

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Authors and Affiliations



C.B., C.M. and F.N. conceived the experiments. C.P. and J.S. grew the wafer. C.B. and F.N. fabricated the samples and performed measurements. C.B., C.M. and F.N. analysed the data and wrote the manuscript with input from M.K. and H.S.

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Correspondence to C. M. Marcus.

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Supplementary figures 1–8; Supplementary references 1–7

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Bøttcher, C.G.L., Nichele, F., Kjaergaard, M. et al. Superconducting, insulating and anomalous metallic regimes in a gated two-dimensional semiconductor–superconductor array. Nature Phys 14, 1138–1144 (2018).

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