High-Tc Superconductivity: Strong Indication of Filamentary-Chaotic Conductance and Possible Routes to Superconductivity Above Room Temperature

TL;DR

This paper explores fractal and filamentary structures in high-T_c superconductors, proposing routes to achieve room-temperature superconductivity through specific composite materials and nano-structured domain configurations.

Contribution

It introduces a fractal theory-based relation for T_c, links optimal doping to universal constants, and suggests new material structures for room-temperature superconductivity.

Findings

T_c relates to fractal domain structures and Fibonacci numbers.

Composite materials like tenorite-CuI may enable high-temperature superconductivity.

Nano-channels in fractal structures could facilitate fast charge transport.

Abstract

The empirical relation of T_co(K)=2740/<q>_c^4 between the transition temperature of optimum doped superconductors T_co and the mean cationic charge <q>_c, a physical paradox, can be recast to strongly support fractal theories of high-T_c superconductors, thereby applying the finding that the optimum hole concentration of h^+ = 0.229 can be linked with the universal fractal constant delta_1 = 8.72109... of the renormalized Henon map. The transition temperature obviously increases steeply with a domain structure of ever narrower size, characterized by Fibonacci numbers. With this backing superconductivity above room temperature can be conceived for synthetic sandwich structures of <q>_c less than 2+. For instance, composites of tenorite and cuprite respectively tenorite and CuI (CuBr, CuCl) onto AuCu alloys are proposed. This specification is suggested by previously described filamentary superconductivity of 'bulk' CuO_1-x samples. In addition, cesium substitution in the Tl-1223 compound is an option. A low mean cationic charge allows the development of a frustrated nano-sized fractal structure of possible ferroelastic nature delivering nano-channels for the very fast charge transport, in common for both high-T_c superconductors and organic inorganic halide perovskite solar materials.