Recent measurements of the doping dependence of the London penetration depth $\lambda (x)$ at low $T$ in clean samples of isovalent ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ at $T\ll T_c$ [Hashimoto et al., Science 336, 1554 (2012)] revealed a peak in $\lambda (x)$ near optimal doping $x=0.3$. The observation of the peak at $T\ll T_c$, 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 $\lambda (x)$ 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 $T=0$.

• Received 24 December 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.177003