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, λL. In two dimensional systems, this ratio n/m * (∼ 1/λ 2 L ) determines the effective Fermi temperature, TF . We report a sharp peak in the x-dependence of λL at zero temperature in clean samples of BaFe2(As1−xPx)2 at the optimum composition x = 0.30, where the superconducting transition temperature Tc reaches a maximum of 30 K. This structure may arise from quantum fluctuations associated with a quantum critical point (QCP). The ratio of Tc/TF at x = 0.30 is enhanced, implying a possible crossover towards the Bose-Einstein condensate limit driven by quantum criticality.In two families of high temperature superconductors, cuprates and iron-pnictides, superconductivity emerges in close proximity to an antiferromagnetically ordered state, and the critical temperature T c has a dome shaped dependence on doping or pressure [1][2][3]. What happens inside this superconducting dome is still a matter of debate [3][4][5]. In particular, elucidating whether a quantum critical point (QCP) is hidden inside it (Figs. 1A and B) may be key to understanding high-T c superconductivity [4,5]. A QCP marks the position of a quantum phase transition (QPT), a zero temperature phase transition driven by quantum fluctuations [7].The London penetration depth λ L is a property that may be measured at low temperature in the superconducting state to probe the electronic structure of the material, and look for signatures of a QCP. The absolute value of λ L in the zero-temperature limit immediately gives the superfluid density λ −2which is a direct probe of the superconducting state; here m * i and n i are the effective mass and concentration of the superconducting carriers in band i, respectively [8]. Measurements on high-quality crystals are necessary because impurities and inhomogeneity may otherwise wipe out the signatures of the QPT. Another advantage of this approach is that it does not require the application of a strong magnetic field, which may induce a different QCP or shift the zero-field QCP [9].BaFe 2 (As 1−x P x ) 2 is a particularly suitable system for penetration depth measurements as, in contrast to most other Fe-based superconductors, very clean [10] and homogeneous crystals of the whole composition series can be grown [11]. In this system, the isovalent substitution of P for As in the parent compound BaFe 2 As 2 offers an elegant way to suppress magnetism and induce superconductivity [11]. Non-Fermi liquid properties are apparent in the normal state above the superconducting dome ( Fig. 2A) [11,12] and de Haas-van Alphen (dHvA) oscillations [10] have been observed over a wide x range including the superconducting compositions, giving detailed information on the electronic structure. Because P and As are isoelectric, the system remains compensated for all values of x (i.e., volumes of the electron and hole Fermi surfaces...
