Non-universal suppression of the excitation gap in chaotic Andreev billiards: Superconducting terminals as sensitive probes for scarred states

Abstract

When a quantum-chaotic normal conductor is coupled to a superconductor, random-matrix theory predicts that a gap opens up in the excitation spectrum which is of universal size $E_g^{\mathrm{RMT}}\approx 0.3\hslash /t_D$, where $t_D$ is the mean scattering time between Andreev reflections. We show that a scarred state of long lifetime $t_S\gg t_D$ suppresses the excitation gap over a window $\Delta E\approx 2E_g^{\mathrm{RMT}}$ which can be much larger than the narrow resonance width ${\Gamma }_S=\hslash /t_S$ of the scar in the normal system. The minimal value of the excitation gap within this window is given by ${\Gamma }_S/2\ll E_g^{\mathrm{RMT}}$. Hence the scarred state can be detected over a much larger energy range than it is the case when the superconducting terminal is replaced by a normal one.

4 pages, 4 figures

References in corpus (8)

• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical Theory of Chaotic Conductors
• Quantum-to-classical correspondence in open chaotic systems
• Andreev billiards
• Quantum Andreev map: A paradigm of quantum chaos in superconductivity
• Ehrenfest-time dependence of weak localization in open quantum dots
• Effective Random Matrix Theory description of chaotic Andreev billiards
• Quantum-classical correspondence in the wavefunctions of Andreev billiards

Cited by in corpus (1)

• Effects of Andreev reflection on the conductance of quantum-chaotic dots