Superconductor-proximity effect in hybrid structures: Fractality versus Chaos

Abstract

We study the proximity effect of a superconductor to a normal system with fractal spectrum. We find that there is no gap in the excitation spectrum, even in the case where the underlying classical dynamics of the normal system is chaotic. An analytical expression for the distribution of the smallest excitation eigenvalue $E_g$ of the hybrid structure is obtained.On small scales it decays algebraically as $\mathcal{P}(E_g)\sim E_g^{-D_0}$, where $D_0$ is the fractal dimension of the spectrum of the normal system. Our theoretical predictions are verified by numerical calculations performed for various models.

arXiv comment4 pages, 4 figures

References in corpus (14)

• Induced superconductivity distinguishes chaotic from integrable billiards
• Universal gap fluctuations in the superconductor proximity effect
• Density of States below the Thouless Gap in a Mesoscopic SNS Junction
• Critical quantum chaos and the one dimensional Harper model
• Superconductor-proximity effect in chaotic and integrable billiards
• Quantum Andreev map: A paradigm of quantum chaos in superconductivity
• Effect of the coupling to a superconductor on the level statistics of a metal grain in a magnetic field
• Excitation spectrum of Andreev billiards with a mixed phase space
• Commensurability effects in Andreev antidot billiards
• Proximity-induced sub-gaps in Andreev billiards
• Reflection of light from a disordered medium backed by a phase-conjugating mirror
• Quantum mechanical relaxation of open quasiperiodic systems
• Density of States in a Mesoscopic SNS Junction
• Brightness of a phase-conjugating mirror behind a random medium

Cited by in corpus (2)

• Andreev billiards
• Tail States below the Thouless Gap in SNS junctions: Classical Fluctuations