Novel Symmetry Classes in Mesoscopic Normalconducting-Superconducting Hybrid Structures

Novel Symmetry Classes in Mesoscopic Normalconducting-Superconducting Hybrid Structures

Mar 4, 1996 | Alexander Altland and Martin R. Zirnbauer
This paper introduces and analyzes four additional Gaussian random-matrix ensembles that describe the universality classes of mesoscopic normal-conducting (N) and superconducting (S) hybrid structures. These classes, denoted as D, C, DIII, and CI, are distinguished by their behavior under time-reversal symmetry and spin rotations. The study focuses on systems where the phase shift due to Andreev reflection averages to zero along typical semiclassical trajectories, leading to a gapless excitation spectrum near the chemical potential. The presence of disorder or dynamically generated chaos leads to novel universal level statistics. The paper calculates the level correlation functions for two of the classes by mapping them to a free 1D Fermi gas, while the other two classes are related to the Laguerre orthogonal and symplectic random-matrix ensembles. The weak localization correction to the conductance and universal conductance fluctuations are computed for a quantum dot with an NS-geometry, showing that the conductance fluctuations are larger than expected due to the doubling of slow modes caused by the coupling of particles and holes via the superconductor. The paper also discusses the implications of Coulomb effects on the symmetry classes and concludes that the symmetry remains intact and leads to observable consequences. The study provides a comprehensive framework for understanding the universal properties of mesoscopic NS-systems.This paper introduces and analyzes four additional Gaussian random-matrix ensembles that describe the universality classes of mesoscopic normal-conducting (N) and superconducting (S) hybrid structures. These classes, denoted as D, C, DIII, and CI, are distinguished by their behavior under time-reversal symmetry and spin rotations. The study focuses on systems where the phase shift due to Andreev reflection averages to zero along typical semiclassical trajectories, leading to a gapless excitation spectrum near the chemical potential. The presence of disorder or dynamically generated chaos leads to novel universal level statistics. The paper calculates the level correlation functions for two of the classes by mapping them to a free 1D Fermi gas, while the other two classes are related to the Laguerre orthogonal and symplectic random-matrix ensembles. The weak localization correction to the conductance and universal conductance fluctuations are computed for a quantum dot with an NS-geometry, showing that the conductance fluctuations are larger than expected due to the doubling of slow modes caused by the coupling of particles and holes via the superconductor. The paper also discusses the implications of Coulomb effects on the symmetry classes and concludes that the symmetry remains intact and leads to observable consequences. The study provides a comprehensive framework for understanding the universal properties of mesoscopic NS-systems.
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