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In a superconductor, the ratio of the carrier density, $n$, to theireffective mass, $m^*$, is a fundamental property directly reflecting the lengthscale of the superfluid flow, the London penetration depth, $\lambda_L$. In twodimensional systems, this ratio $n/m^*$ ($\sim 1/\lambda_L^2$) determines theeffective Fermi temperature, $T_F$. We report a sharp peak in the$x$-dependence of $\lambda_L$ at zero temperature in clean samples ofBaFe$_2$(As$_{1-x}$P$_x$)$_2$ at the optimum composition $x = 0.30$, where thesuperconducting transition temperature $T_c$ reaches a maximum of 30\,K. Thisstructure may arise from quantum fluctuations associated with a quantumcritical point (QCP). The ratio of $T_c/T_F$ at $x = 0.30$ is enhanced,implying a possible crossover towards the Bose-Einstein condensate limit drivenby quantum criticality.

A Sharp Peak of the Zero-Temperature Penetration Depth at Optimal Composition in BaFe2(As1-xPx)2