Proximity-induced sub-gaps in Andreev billiards

Abstract

We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cut-off in the path length distribution $P(s)$ will possess an energy gap on the scale of the Thouless energy. An exact quantum mechanical calculation for different Andreev billiards gives good agreement with the semi-classical predictions when the energy dependent phase shift for Andreev reflections is properly taken into account. Based on this new semi-classical Bohr-Sommerfeld approximation of the density of states, we derive a simple formula for the energy gap. We show that the energy gap, in units of Thouless energy, may exceed the value predicted earlier from random matrix theory for chaotic billiards.

4 pages, 6 figures

Cited by in corpus (15)

• Quantum Disorder and Quantum Chaos in Andreev Billiards
• Andreev billiards
• Ballistic quantum transport at high energies and high magnetic fields
• Geometrical enhancement of the proximity effect in quantum wires with extended superconducting tunnel contacts
• Adiabatic quantization of Andreev levels
• Multiple scattering theory for superconducting heterostructures
• The density of states of chaotic Andreev billiards
• Effective Random Matrix Theory description of chaotic Andreev billiards
• Bound states in Andreev billiards with soft walls
• A logarithmic contribution to the density of states of rectangular Andreev billiards
• Graphene Andreev Billiards
• Andreev bound states for cake shape superconducting-normal systems
• Superconductor-proximity effect in hybrid structures: Fractality versus Chaos
• Decreasing excitation gap in Andreev billiards by disorder scattering
• Application of the Trace Formula in Pseudointegrable Systems