Superconductor-proximity effect in hybrid structures: fractality versus chaos

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Complex Systems

Background:

• The proximity effect describes how a superconductor influences a neighboring normal material.
• Fractal spectra arise in systems with complex, self-similar structures or dynamics.
• Understanding hybrid superconductor-normal systems is crucial for novel electronic devices.

Purpose of the Study:

• To investigate the proximity effect in superconductor-normal systems with fractal energy spectra.
• To determine if a spectral gap emerges under these conditions, particularly for chaotic systems.
• To derive an analytical expression for the distribution of the smallest excitation eigenvalue.

Main Methods:

• Theoretical analysis of the superconductor-normal system with a fractal spectrum.
• Derivation of an analytical expression for the smallest excitation eigenvalue distribution.
• Numerical simulations to verify theoretical predictions across various models.

Main Results:

• Absence of a gap in the excitation spectrum, irrespective of the classical dynamics' chaotic nature.
• An analytical expression for the smallest excitation eigenvalue distribution, P(E1).
• Algebraic decay of P(E1) ~ E1(-D0) on small scales, where D0 is the fractal dimension.

Conclusions:

• The fractal nature of the normal system's spectrum prevents gap formation in the hybrid structure.
• The smallest eigenvalue distribution provides a characteristic signature of the fractal dimension.
• Theoretical findings are robustly supported by numerical evidence.