The European Physical Journal B - Condensed Matter and Complex Systems

, Volume 21, Issue 3, pp 425-435

Semiclassical theory of integrable and rough Andreev billiards

  • W. IhraAffiliated withMax-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
  • , M. LeadbeaterAffiliated withMax-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
  • , J.L. VegaAffiliated withMax-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
  • , K. RichterAffiliated withMax-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany

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Abstract:

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.

PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 74.50.+r Proximity effects, weak links, tunneling phenomena, and Josephson effects – 74.80.Fp Point contacts; SN and SNS junctions