Universal Critical Quantum Properties of Cuprate Superconductors}

Using the scaling theory of quantum critical phenomena we explore the occurrence of universal critical behavior at the insulator-to-superconductor and superconductor-to-normal state transitions at zero temperature. Experimentally, theses phase transitions are driven by doping and correspond to critical endpoints of the phase transition line in the temperature-hole concentration plane. Provided that the order parameter is a complex scalar in two dimensions, and that the London relation between superfluid number density and magnetic penetration depth holds, the scaling theory predicts universal behavior close to the insulator-to-superconductor transition. In particular, transition temperature and zero temperature penetration depth are universally related and the sheet resistance adopts a universal value. These predictions agree remarkably well with available experimental data and provide useful constraints for a microscopic theory.