Semiclassical theory of integrable and rough Andreev billiards

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• 作者：W. Ihra ; M. Leadbeater ; J.L. Vega and K. Richter
• 关键词：PACS. 05.45. ; a Nonlinear dynamics and nonlinear dynamical systems &#8211 ; 74.50.+r Proximity effects ; weak links ; tunneling phenomena ; and Josephson effects &#8211 ; 74.80.Fp Point contacts ; SN and SNS junctions
• 刊名：The European Physical Journal B - Condensed Matter
• 出版年：2001
• 出版时间：June 2001
• 年：2001
• 卷：21
• 期：3
• 页码：425-435
• 全文大小：292 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Condensed Matter
  Physics
  Complexity
  Fluids
  Solid State Physics and Spectroscopy
  Superconductivity, Superfluidity and Quantum Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1434-6036

文摘

We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding light onto the origin of the differences between the semiclassical theory and the corresponding result derived from random matrix models. Applications to a square billiard geometry and billiards with boundary roughness are discussed. The saturation of the quasiparticle excitation spectrum is related to the classical dynamics of the billiard. The influence of weak magnetic fields on the proximity effect in rough Andreev billiards is discussed and an analytical formula is derived. The semiclassical theory provides an interpretation for the suppression of the proximity effect in the presence of magnetic fields as a coherence effect of time reversed trajectories. It is shown to be in good agreement with quantum mechanical calculations.