Thermodynamic signatures of quantum criticality in cuprate superconductors

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 diagram 1 . 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 range 2 that includes p* . As a function of doping, we find that C el / T is strongly peaked at p* (where C el 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 point 3 – 5 , as observed in heavy-fermion 6 and iron-based 7 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. Measurements of the specific heat of two cuprate materials at low temperature in magnetic fields large enough to suppress superconductivity and over a wide doping range reveal that the pseudogap phase of cuprates ends at a quantum critical point.