Phenomenological aspects of phase fluctuation in high T_c superconductors: Cooper pair droplets

Abstract

We point out how fluctuation of the phase of the superconducting order parameter can play a key role in our understanding of high T_c superconductors. A simple universal criterion is given which illustrates why all oxide superconductors in contrast to classical superconductors ought to behave as a lattice of cooper pairs. T_c is to be thought of as the temperature of phase coherence or the temperature above which the lattice of Cooperpair "melts" into a phase of Cooper-pair droplets that starts forming at T ≈ T*. This is the pseudo-gap region. Quantum fluctuation of the phase predicts a superconductor to insulator phase transition for all underdoped materials.