Fractal superconductivity near localization threshold

Understand

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$.

• We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.
• Our theoretical analysis is based on the analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations.
• Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.