Quantum Phase Fluctuation in High T C Superconductors

If phase coherence determines the superconducting transition temperature T c in the cuprate oxides, it is of great interest to understand the role that dynamics of the phase fluctuation plays in bringing about depletion of the superconducting condensate. We will show that a phase correlation function can be calculated that allows us to describe depletion of superconducting condensate as a result of the quantum fluctuation. In two dimension, dynamic phase fluctuation or pair fluctuation gives rise to a condensate depletion linear with temperature as T→ O in superconductors with nodes at the fermi surface. Superconducting order parameter has an amplitude and a phase. In the ground state the phase has to be blocked in all space. It has been suggested [1] that the superconducting transition temperature T c in the oxide materials is related to the loss of long range phase coherence. Beyond T c the system lives, in this model, unlike classical superconductors in an ill understood mixture of Cooper pairs that have a nonzero amplitude and a highly fluctuating phase. The dynamics of the phase fluctuation and depletion of superfluid density of the superconducting state is the object of this study. We write the superconducting order parameter as ψ (t) .where ψ (t) = |ψ| exp (iθ (x,t)) (1) where |ψ| is the amplitude assumed constant in space and θ (x, t) is the phase assumed fluctuating in space and time..The phase dynamics is contained in 1