Quantum conductance-temperature phase diagram of granular superconductor K _x Fe_2-ySe₂

It is now well established that the microstructure of Fe-based chalcogenide K _x Fe_2-ySe₂ consists of, at least, a minor (~15 percent), nano-sized, superconducting K _s Fe₂Se₂ phase and a major (~85 percent) insulating antiferromagnetic K₂Fe₄Se₅ matrix. Other intercalated A_1-xFe_2-ySe₂ (A = Li, Na, Ba, Sr, Ca, Yb, Eu, ammonia, amide, pyridine, ethylenediamine etc.) manifest a similar microstructure. On subjecting each of these systems to a varying control parameter (e.g. heat treatment, concentration x,y, or pressure p), one obtains an exotic normal-state and superconducting phase diagram. With the objective of rationalizing the properties of such a diagram, we envisage a system consisting of nanosized superconducting granules which are embedded within an insulating continuum. Then, based on the standard granular superconductor model, an induced variation in size, distribution, separation and Fe-content of the superconducting granules can be expressed in terms of model parameters (e.g. tunneling conductance, g, Coulomb charging energy, E _c , superconducting gap of single granule, Δ, and Josephson energy J = πΔg/2). We show, with illustration from experiments, that this granular scenario explains satisfactorily the evolution of normal-state and superconducting properties (best visualized on a [Formula: see text] phase diagram) of A _x Fe_2-ySe₂ when any of x, y, p, or heat treatment is varied.