Is it possible for a metal to exist in a strictly two-dimensional system? This may seem trivial, but it is actually a longstanding problem. The electrical characteristics of an array of superconducting islands on a normal metal suggests that the answer could be 'yes'.
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Annett, J. Metals in flatland. Nature Phys 8, 8–9 (2012). https://doi.org/10.1038/nphys2192
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DOI: https://doi.org/10.1038/nphys2192