Quantum critical behaviour in a high-T-c superconductor

Quantum criticality is associated with a system composed of a nearly infinite number of interacting quantum degrees of freedom at zero temperature, and it implies that the system looks on average the same regardless of the time- and length scale on which it is observed. Electrons on the atomic scale do not exhibit such symmetry, which can only be generated as a collective phenomenon through the interactions between a large number of electrons. In materials with strong electron correlations a quantum phase transition at zero temperature can occur, and a quantum critical state has been predicted(1,2), which manifests itself through universal power-law behaviours of the response functions. Candidates have been found both in heavy-fermion systems(3) and in the high-transition temperature (high-Tc) copper oxide superconductors(4), but the reality and the physical nature of such a phase transition are still debated(5-7). Here we report a universal behaviour that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a quantum phase transition of an unconventional kind in the high-Tc superconductors.