Enhancement of the london penetration depth in pnictides at the onset of spin-density-wave order under superconducting dome

Recent measurements of the doping dependence of the London penetration depth λ(x) at low T in clean samples of isovalent BaFe ₂(As_1-xP_x)₂ at T_c [Hashimoto et al., Science 336, 1554 (2012)SCIEAS0036-8075] revealed a peak in λ(x) near optimal doping x=0.3. The observation of the peak at T _c, points to the existence of a quantum critical point beneath the superconducting dome. We associate such a quantum critical point with the onset of a spin-density-wave order and show that the renormalization of λ(x) by critical magnetic fluctuations gives rise to the observed feature. We argue that the case of pnictides is conceptually different from a one-component Galilean invariant Fermi liquid, for which correlation effects do not cause the renormalization of the London penetration depth at T=0.