Finite temperature superfluid density in very underdoped cuprates

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The combination of a large superconducting gap, low transition temperature, and quasi two-dimensionality in strongly underdoped high temperature superconductors severely constrains the behavior of the ab-plane superfluid density ρwith temperature T. In particular, we argue that the contribution of nodal quasiparticles to ρ(T) is essential to account both for the amplitude of, and the recently observed deviations from, the Uemura scaling. A relation between Tc and ρ(0) which combines the effects of quasiparticle excitations at low temperatures and of vortex fluctuations near the critical temperature is proposed and discussed in light of recent experiments.