Crossover and quantum critical phenomena in high-temperature superconductors

Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

Received: 8 April 1997
Accepted: 19 August 1997

Abstract

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 T_c 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 T_c. 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.