Quantum interference and the formation of the proximity effect in chaotic normal-metal/superconducting structures

Abstract

We discuss a number of basic physical mechanisms relevant to the formation of the proximity effect in superconductor/normal metal (SN) systems. Specifically, we review why the proximity effect sharply discriminates between systems with integrable and chaotic dynamics, respectively, and how this feature can be incorporated into theories of SN systems. Turning to less well investigated terrain, we discuss the impact of quantum diffractive scattering on the structure of the density of states in the normal region. We consider ballistic systems weakly disordered by pointlike impurities as a test case and demonstrate that diffractive processes akin to normal metal weak localization lead to the formation of a hard spectral gap -- a hallmark of SN systems with chaotic dynamics. Turning to the more difficult case of clean systems with chaotic boundary scattering, we argue that semiclassical approaches, based on classifications in terms of classical trajectories, cannot explain the gap phenomenon. Employing an alternative formalism based on elements of quasiclassics and the ballistic $\sigma$-model, we demonstrate that the inverse of the so-called Ehrenfest time is the relevant energy scale in this context. We discuss some fundamental difficulties related to the formulation of low energy theories of mesoscopic chaotic systems in general and how they prevent us from analysing the gap structure in a rigorous manner. Given these difficulties, we argue that the proximity effect represents a basic and challenging test phenomenon for theories of quantum chaotic systems.

21 pages (two-column), 6 figures; references added

References in corpus (5)

• Universal gap fluctuations in the superconductor proximity effect
• Excitation spectrum of Andreev billiards with a mixed phase space
• Effects of electron-electron interaction on the conductance of open quantum dots
• Andreev Conductance of Chaotic and Integrable Quantum Dots
• Spectral Features of the Proximity Effect

Cited by in corpus (33)

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• Quantum-to-classical correspondence in open chaotic systems
• Quantum Disorder and Quantum Chaos in Andreev Billiards
• Andreev billiards
• Quantum Andreev map: A paradigm of quantum chaos in superconductivity
• Oscillations of Induced Magnetization in Superconductor-Ferromagnet Heterostructures
• Adiabatic quantization of Andreev levels
• Semiclassical gaps in the density of states of chaotic Andreev billiards
• Superconductivity near a magnetic domain wall
• Subgap states in disordered superconductors
• The density of states of chaotic Andreev billiards
• Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard
• Quasiclassical expressions for the free energy of superconducting systems
• Spectral characteristics of a fully-superconducting SQUIPT
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Universal spectral statistics of Andreev billiards: semiclassical approach
• Magnetic-field dependence of transport in normal and Andreev billiards: a classical interpretation to the averaged quantum behavior
• Quasiparticle entropy in superconductor/normal metal/superconductor proximity junctions in the diffusive limit
• Vortex core near planar defects in a clean layered superconductor
• Quantum decay of the supercurrent and intrinsic capacitance of Josephson junctions beyond the tunnel limit
• "Smile"-gap in the density of states of a cavity between superconductors
• Density of proper delay times in chaotic and integrable quantum billiards
• Non-retracing orbits in Andreev billiards
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Decreasing excitation gap in Andreev billiards by disorder scattering
• Transition from coherent mesoscopic single particle transport to proximity Josephson-current
• Superconducting proximity effect in quantum wires without time-reversal symmetry
• Non-linear sigma-model for odd triplet superconductivity in superconductor/ferromagnet structures
• Breakdown of Universality in Quantum Chaotic Transport: the Two-Phase Dynamical Fluid Model
• Geometry effects in the magnetoconductance of normal and Andreev Sinai billiards