Theory of the Resistive Transition in Overdoped Tl₂Ba₂CuO₆₊ₓ: Implications for the angular dependence of the quasiparticle scattering rate in High-Tc superconductors

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We show that recent measurements of the magnetic field dependence of the magnetization, specific heat and resistivity of overdoped Tc 17K Tl₂Ba₂CuO₆₊δ in the vicinity of the superconducting Hc₂ imply that the vortex viscosity is anomalously small and that the material studied is inhomogeneous with small, a few hundred Å, regions in which the local Tc is much higher than the bulk Tc. 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.