Crossover and quantum critical phenomena in high-temperature superconductors

We apply the scaling theory of quantum phase transitions to the experimental phase diagram of high-temperature superconductors in the temperature-doping plane. We find that the relation between transition temperature Tc and zero-temperature penetration depth, and the sheet resistance become universal in the underdoped limit where the materials are essentially 2D and the insulator-to-superconductor transition occurs. The predominance of phase fluctuations in this doping regime manifests itself as a suppression of the fermionic density of states around the chemical potential, that is, in terms of a pseudogap. This provides a natural explanation of a variety of measurements, which show a pseudogap opening above Tc. We also discuss the implications of the disappearance of the pseudogap in the overdoped regime in terms of mean-field superconductor-to-normal state transitions