Quantum Disorder and Quantum Chaos in Andreev Billiards

Abstract

We investigate the crossover from the semiclassical to the quantum description of electron energy states in a chaotic metal grain connected to a superconductor. We consider the influence of scattering off point impurities (quantum disorder) and of quantum diffraction (quantum chaos) on the electron density of states. We show that both the quantum disorder and the quantum chaos open a gap near the Fermi energy. The size of the gap is determined by the mean free time in disordered systems and by the Ehrenfest time in clean chaotic systems. Particularly, if both times become infinitely large, the density of states is gapless, and if either of these times becomes shorter than the electron escape time, the density of states is described by random matrix theory. Using the Usadel equation, we also study the density of states in a grain connected to a superconductor by a diffusive contact.

arXiv comment20 pages, 10 figures

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• Semiclassical gaps in the density of states of chaotic Andreev billiards
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• Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport
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• Subgap states in disordered superconductors
• The density of states of chaotic Andreev billiards
• Semiclassical theory of the Ehrenfest-time dependence of quantum transport
• The Ehrenfest Oscillations in The Level Statistics of Chaotic Quantum Dots
• Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot
• Induced Kramer-Pesch-Effect in a Two Gap Superconductor: Application to MgB2
• The spectral form factor near the Ehrenfest-time
• Exponential sensitivity to dephasing of electrical conduction through a quantum dot
• Classical limit of transport in quantum kicked maps
• Effective Random Matrix Theory description of chaotic Andreev billiards
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
• Ring--Shaped Andreev Billiards in Quantizing Magnetic Fields
• Effects of Andreev reflection on the conductance of quantum-chaotic dots
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• Universal parametric correlations in the classical limit of quantum transport
• Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time
• "Smile"-gap in the density of states of a cavity between superconductors
• Planckian superconductor
• Josephson currents in chaotic quantum dots
• Secondary "Smile"-gap in the density of states of a diffusive Josephson junction for a wide range of contact types
• Non-retracing orbits in Andreev billiards
• Microscopic theory of the Andreev gap
• Decreasing excitation gap in Andreev billiards by disorder scattering
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Chaos Beyond Linearized Stability Analysis: Folding of the Phase Space and Distribution of Lyapunov Exponents
• Breakdown of Universality in Quantum Chaotic Transport: the Two-Phase Dynamical Fluid Model