The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*—at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram1. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range2 that includes p*. As a function of doping, we find that Cel/T is strongly peaked at p* (where Cel is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point3,4,5, as observed in heavy-fermion6 and iron-based7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.
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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 J. Chang, M. Horio, M.-H. Julien, S. Kivelson, R. Markiewicz, C. Proust, B. Ramshaw, S. Sachdev, A. Sacuto, J. Tallon, A.-M. Tremblay and C. Varma for discussions. C.M. and T.K. acknowledge support from the Laboratoire d’excellence LANEF (ANR-10-LABX-51-01) and the Laboratoire National des Champs Magnétiques Intenses (LNCMI) in Grenoble. J.K. was supported by the Slovak Research and Development Agency under grant number APVV-16-0372. L.T. acknowledges support from the Canadian Institute for Advanced Research (CIFAR) and funding from the Natural Sciences and Engineering Research Council of Canada (NSERC; PIN: 123817), the Fonds de recherche du Québec–Nature et Technologies (FRQNT), the Canada Foundation for Innovation (CFI), and a Canada Research Chair. This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund. Part of this work was funded by the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant GBMF5306 to L.T.). J.-S.Z. was supported by NSF MRSEC under Cooperative Agreement Number DMR-1720595 in the US. H.T. acknowledges MEXT Japan for a Grant-in-Aid for Scientific Research.