Optical experimental evidence for a universal length scale for the dynamic charge inhomogeneity of cuprate superconductors

Time-resolved optical experiments can give unique information on the characteristic length scales of dynamic charge inhomogeneity on femtosecond time scales. From data on the effective quasiparticle relaxation time tau(r) in La(2-x)SrxCuO4 and Nd(2-x)Ce(x)CuO4, we derive the temperature and doping dependence of the intrinsic phonon escape length l(e), which can be a direct measure of charge inhomogeneity. Remarkably, a common feature of both p- and n-type cuprates is that, as T --> Tc, l(e) approaches the superconducting coherence length l(e) --> xi(s)0. In the normal state l(e) is found to be in excellent agreement with the mean free path l(m) obtained from the resistivity data and structural coherence lengths l(s) from neutron scattering experiments, implying the existence of complex intrinsic textures on different length scales which may have a profound effect on the functional properties of these materials.