The Determination of Length Scales Associated with Dynamic Inhomogeneity in Cuprate Superconductors

Abstract

We show that measurements of the quasiparticle (QP) relaxation time can be used to derive a characteristic phonon escape length l e, which is shown to be related to the characteristic length scale of charge inhomogeneities. The data on phonon escape length in La2− x Sr x CuO4 and other cuprates is found to agree quantitatively with the mean free path l m obtained from the temperature dependence of the normal state resistivity over a wide temperature range and also agrees well with the data on structural coherence lengths l s obtained from neutron scattering experiments. Remarkably, a common feature of different cuprates is that above T c (just above the critical fluctuation region) the length scale l e is approximately equal to the superconducting coherence length, ξs(0) and corresponds to a percolation threshold in 2D for Josephson tunnelling leading to the formation of a superconducting phase-coherent state by percolation.