Phase transition beneath the superconducting dome in BaFe2(As1-xPx)2

We present a theory for the large suppression of the superfluid density rho(s) in BaFe2(As1-xPx)(2) in the vicinity of a putative spin-density wave quantum critical point at a P doping, x = x(c). We argue that the transition becomes weakly first order in the vicinity of x(c), and disorder induces puddles of superconducting and antiferromagnetic regions at short length scales; thus, the system becomes an electronic microemulsion. We propose that frustrated Josephson couplings between the superconducting grains suppress rho(s). In addition, the presence of "normal" quasiparticles at the interface of the frustrated Josephson junctions will give rise to a highly nontrivial feature in the low-frequency response in a narrow vicinity around x(c). We propose a number of experiments to test our theory.