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

In a superconductor, the ratio of the carrier density, $n$, to their effective mass, $m^*$, is a fundamental property directly reflecting the length scale of the superfluid flow, the London penetration depth, $\lambda_L$. In two dimensional systems, this ratio $n/m^*$ ($\sim 1/\lambda_L^2$) determines the effective Fermi temperature, $T_F$. We report a sharp peak in the $x$-dependence of $\lambda_L$ at zero temperature in clean samples of BaFe$_2$(As$_{1-x}$P$_x$)$_2$ at the optimum composition $x = 0.30$, where the superconducting transition temperature $T_c$ reaches a maximum of 30\,K. This structure may arise from quantum fluctuations associated with a quantum critical 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 driven by quantum criticality.