Recent measurements of the doping dependence of the London penetration depth L(x) at low T in clean samples of isovalent BaFe2(As1-xPx)2 at T<<Tc [Hashimoto et al., Science 336 1554 (2012)] revealed a peak in L(x) near optimal doping x=0.3. The observation of the peak at T<<Tc, 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 L(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. I will also discuss other manifestations of quantum criticality as seen in the experiments on the specific heat jump near the end point of the coexistence phase (tetra-critical point) and on the quantum transport.
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