Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard

Abstract

A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit $\hslash \to 0$, which opens up a gap $E_{\mathrm{gap}}$ in the excitation spectrum. The time scale $\hslash /E_{\mathrm{gap}}\propto {\alpha }^{-1}\ln \hslash$ (with $\alpha$ the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.

4 pages, 2 figures, RevTeX; [2017: fixed broken eps figures]

References in corpus (3)

• Density of States below the Thouless Gap in a Mesoscopic SNS Junction
• Superconductors with Magnetic Impurities: Instantons and Sub-gap States
• A pseudointegrable Andreev billiard

Cited by in corpus (21)

• Spin relaxation dynamics of quasiclassical electrons in ballistic quantum dots with strong spin-orbit coupling
• Ehrenfest time dependent suppression of weak localization
• Moments of the transmission eigenvalues, proper delay times and random matrix theory I
• Quantum-to-classical correspondence in open chaotic systems
• Andreev billiards
• Quantum Andreev map: A paradigm of quantum chaos in superconductivity
• Moments of the transmission eigenvalues, proper delay times and random matrix theory II
• Semiclassical roots of universality in many-body quantum chaos
• Adiabatic quantization of Andreev levels
• Semiclassical gaps in the density of states of chaotic Andreev billiards
• Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots
• The density of states of chaotic Andreev billiards
• The classical and quantum dynamics of the inhomogeneous Dicke model and its Ehrenfest time
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
• Superconductivity-induced macroscopic resonant tunneling
• Effects of Andreev reflection on the conductance of quantum-chaotic dots
• Planckian superconductor
• Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time
• Microscopic theory of the Andreev gap
• Decreasing excitation gap in Andreev billiards by disorder scattering
• Macroscopic Resonant Tunneling through Andreev Interferometers