Theory of the resistive transition in overdoped Tl₂Ba₂CuO_6+δimplications for the vortex viscosity and the quasiparticle scattering rate in high-T_csuperconductors

We show that recent measurements of the magnetic field dependence of the magnetization, specific heat and resistivity of overdoped T_c∼17KTl₂Ba₂CuO_6+δin the vicinity of the superconducting H_c2imply that the vortex viscosity is anomalously small and that the material studied is inhomogeneous with small (a few hundred angstroms), regions in which the local T_cis much higher than the bulk T_c.The anomalously small vortex viscosity can be derived from a microscopic model in which the quasiparticle lifetime varies dramatically around the Fermi surface, being small everywhere except along the zone diagonal (“cold spot”). We propose experimental tests of our results.