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Related Experiment Videos

Proximity-induced subgaps in andreev billiards.

J Cserti1, A Kormányos, Z Kaufmann

  • 1Department of Physics of Complex Systems, Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/A, Hungary.

Physical Review Letters
|July 30, 2002
PubMed
Summary

Any billiard with a limited path length distribution exhibits an energy gap related to Thouless energy. This study provides a new formula for this gap, potentially exceeding random matrix theory predictions for chaotic billiards.

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Area of Science:

  • Condensed matter physics
  • Quantum chaos
  • Mesoscopic physics

Background:

  • Andreev billiards are mesoscopic systems exhibiting quantum interference effects.
  • The density of states in such systems is crucial for understanding their electronic properties.
  • Previous studies often relied on random matrix theory, which may not fully capture all physical aspects.

Purpose of the Study:

  • To investigate the density of states in Andreev billiards.
  • To identify the conditions leading to an energy gap.
  • To develop a new semiclassical approximation for the density of states and energy gap.

Main Methods:

  • Exact quantum mechanical calculations for Andreev billiards.
  • Semiclassical analysis incorporating energy-dependent phase shifts for Andreev reflections.

Related Experiment Videos

  • Derivation of a new semiclassical Bohr-Sommerfeld approximation.

    • Main Results:

    • A finite upper cutoff in the path length distribution P(s) leads to an energy gap on the scale of the Thouless energy.
    • Exact quantum calculations show good agreement with semiclassical predictions when phase shifts are included.
    • A simple formula for the energy gap was derived from the new approximation.
    • The calculated energy gap, in units of Thouless energy, can exceed predictions from random matrix theory for chaotic billiards.

    Conclusions:

    • The presence of an energy gap in Andreev billiards is linked to path length distribution cutoffs.
    • The developed semiclassical Bohr-Sommerfeld approximation offers accurate predictions for the density of states and energy gap.
    • This work provides new insights into quantum transport phenomena in mesoscopic systems and challenges existing theoretical predictions.