Phase transition beneath the superconducting dome in BaFe$_2$(As$_{1-x}$P$_x$)$_2$

TL;DR

This paper develops a theory explaining the suppression of superfluid density near a quantum critical point in BaFe$_2$(As$_{1-x}$P$_x$)$_2$, attributing it to disorder-induced micro-emulsions and frustrated Josephson couplings.

Contribution

It introduces a novel theory linking disorder, micro-emulsions, and frustrated Josephson couplings to superfluid density suppression near a quantum critical point.

Findings

Superfluid density is suppressed near the critical doping.

Disorder induces superconducting and antiferromagnetic puddles.

Frustrated Josephson couplings explain the low-frequency response anomalies.

Abstract

We present a theory for the large suppression of the superfluid-density, $\rho_s$, in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ 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 micro-emulsion. 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 non-trivial feature in the low frequency response in a narrow vicinity around $x_c$. We propose a number of experiments to test our theory.