Quasiparticle Transport and Localization in High-TcSuperconductors

We present a theory of the effects of impurity scattering in $d_{x^2{-y}^2}$ superconductors and their quantum disordered counterparts, based on a nonlinear-sigma-model formulation. We show the existence, in a quasi-two-dimensional system, of a novel spin-metal phase with a nonzero spin diffusion constant at zero temperature. With decreasing interlayer coupling, the system undergoes a quantum phase transition (in a new universality class) to a localized spin insulator. Experimental implications for spin and thermal transport in the high-temperature superconductors are discussed.