Ring--Shaped Andreev Billiards in Quantizing Magnetic Fields
J. Cserti (1), P. Polin\'ak (1), G. Palla (1), U. Z\"ulicke (2), C. J., Lambert (3) ((1) E\"otv\"os University, (2) Universit\"at Karlsruhe,, Karlsruhe, Germany, (3) Lancaster University, Lancaster, UK)
TL;DR
This paper provides a semiclassical analysis of ring-shaped Andreev billiards in magnetic fields, deriving an exact secular equation within the BdG formalism, and compares classical orbit classifications with numerical solutions.
Contribution
It introduces a new semiclassical approach and an exact secular equation for analyzing mesoscopic hybrid systems in magnetic fields, enhancing understanding of their thermodynamic properties.
Findings
Excellent agreement between semiclassical and numerical results
New insights into electron and hole orbit classifications
Potential for improved thermodynamic property calculations
Abstract
We present a detailed semiclassical study of a clean disk--shaped insulator--normal-metal--superconductor hybrid system in a magnetic field. It is based on an exact secular equation that we derived within the microscopic Bogoliubov--de Gennes (BdG) formalism. Results obtained from a classification of electron and hole orbits are in excellent agreement with those from an exact numerical diagonalization of the BdG equation. Our analysis opens up new possibilities for determining thermodynamic properties of mesoscopic hybrid systems.
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