We present a theory for the large suppression of the superfluid density ${\rho }_s$ in ${\mathrm{BaFe}}_2\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right){}_2$ 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.

• Received 26 February 2015
• Revised 11 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.081113