High-temperature superconductivity as viewed from the maximum hardness principle

The Maximum Hardness Principle - and its reformulation by Chattaraj as the Minimum Polarizability Principle - is an immensely useful concept which works in support of a chemical intuition. As we show here, it may also be used to rationalize the scarcity of high-temperature superconductors, which stems - inter alia - from rarity of high-density of state metals in Nature. It is suggested that the high-temperature oxocuprate superconductors as well as their iron analogues - are energetically metastable at T ➔ 0 K and p ➔ 0 atm conditions, and their tendency for disproportionation is hindered only by the substantial rigidity of the crystal lattice, while the phase separation and/or superstructure formation is frequently observed in these systems. This hypothesis is corroborated by hybrid density functional theory theoretical calculations for Na- (thus: hole) or La- (thus: electron) doped CaCu(II)O₂ precursor. Non-equilibrium synthetic methods are suggested to be necessary for fabrication of high-temperature superconductors of any sort. Graphical abstract Doped oxocuprate superconductors are shown to be unstable with respect to phase separation (disproportionation) in accordance with the Maximum Hardness Principle; their metastability is mostly due to rigidity of [CuO₂] sheets and preparation using high-temperature conditions.