The non-superconducting state of a high-temperature superconductor is in many ways more anomalous than the superconducting state. Unlike a standard metal, the 'normal' state shows possible signs that adding or removing one electron affects all the others.
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van der Marel, D. Electrons living apart together. Nature Phys 2, 585–586 (2006). https://doi.org/10.1038/nphys405
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DOI: https://doi.org/10.1038/nphys405