The electronic properties of cuprate high-temperature superconductors in their normal state are highly two-dimensional: transport along the crystal planes is perfectly metallic, but is insulating along the perpendicular ‘c-axis’ direction. The ratio of the in-plane to the perpendicular resistance can exceed 104 (refs 1,2,3,4). This anisotropy was identified as one of the mysteries of the cuprates early on5,6, and although widely different proposals exist for its microscopic origin7,8,9, there is little empirical information on the microscopic scale. Here, we elucidate the properties of the insulating layers with a newly developed scanning noise spectroscopy technique that can spatially map the current and its time-resolved fluctuations. We discover atomic-scale noise centres that exhibit megahertz current fluctuations 40 times the expectation from Poissonian noise, more than what has been observed in mesoscopic systems10. Such behaviour can happen only in highly polarizable insulators and represents strong evidence for trapping of charge in the charge reservoir layers. Our measurements suggest a picture of metallic layers separated by polarizable insulators within a three-dimensional superconducting state.
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We thank C. Beenakker, A. Ben Hamida, Y. Blanter, D. Chatzopoulos, V. Cheianov, T. Klapwijk, M. Leeuwenhoek and J. van Ruitenbeek for help and valuable discussions. This project was financially supported by the European Research Council (ERC StG SpinMelt) and by the Netherlands Organisation for Scientific Research (NWO/OCW), as part of the Frontiers of Nanoscience programme, as well as through a Vidi grant (680-47-536).
Supplementary Figures 1–9; Supplementary References 1–7