Thermal and Quantum critical Properties of overdoped La_{2-x}Sr_{x}CuO_{4}

Abstract

We analyze the extended superfluid density data of Božović \textit{ et al}. taken on homogenous thin films to explore the critical properties of the thermal (TSM) and quantum superconductor to metal (QSM) transitions in overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$. The temperature dependence reveals remarkable agreement with d-wave BCS behavior, where $σ\propto 1/λ^{2}$. No sign of the expected KTB transition is observable. We show that the critical amplitude $ρ_{s0}=ρ_{s}\left( T\right) /\left( 1-T/T_{c}\right) $ scales as $T_{c}\propto ρ_{s0}^{1/2}$ and with that as $T_{c}\propto ρ_{s}\left( 0\right) $, empirically verified by Božović \textit{et al}. Together with additional evidence for BCS behavior in overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ we show that the scaling relation $T_{c}\propto λ\left( 0\right) ^{-1}\propto Δ\left( 0\right) \propto ξ\left( 0\right) ^{-1}\propto H_{c2}\left( 0\right) ^{-1/2}\propto λ_{0}^{-1}\propto Δ_{0}\propto ξ_{0}^{-1}\propto H_{c20}^{-1/2}$ applies, by approaching the QSM and TSM transitions. This differs from the dirty limit behavior $λ\left( 0\right) \propto ξ\left( 0\right) ^{1/2}$, maintains the $T_{c}$ \ independence of the Ginzburg-Landau parameter $κ=λ_{o}/ξ_{0}$, and puts a stringent constraint on the effect at work. We notice that potential candidates appear to be the nonlocal effects on the penetration depth of clean d-wave superconductors explored by Kosztin and Legget.