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

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Adagideli, Inanc ; Beenakker, C.
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Date of publication of this fulltext: 05 Aug 2009 13:33


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 $\\hbar\\to 0$, which opens up a gap $E_{\\rm gap}$ in the excitation spectrum. The time scale $\\hbar/E_{\\rm gap}\\propto\\alpha^{-1}\\ln\\hbar$ (with $\\alpha$ the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.

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