Superconductivity of fractal aggregates

Abstract

Using McMillan's formula relating the superconducting transition temperature T_c with the electron-phonon coupling strength and the phonon cut-off frequency, we show that T_c is considerably enhanced for a finite-size fractal aggregate (like diffusion-limited aggregate), compared to that for a compact crystalline system with identical constituents. We compare the result with the available results for T_c enhancement in conventional metallic alloy superconductors due to amorphous structures, where such fractal models have been employed recently to study classical transport and other thermodynamic properties. We also investigate the magnetic response of an infinite random mixture of such superconducting fractal grains in an insulating host matrix. Implications of this analysis on the new high-T_c superconductors are discussed.