Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
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DOI：
10.1103/physrevb.55.1142
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发表时间：
1997-01-01
影响因子：
3.7
通讯作者：
Zirnbauer, MR
中科院分区：
文献类型：
--
作者：
Altland, A;Zirnbauer, MR
与超导体接触的正常导电介观系统通过电子自旋的时间反转和旋转的对称操作来分类。四个对称类被确定，这对应于嘉当的对称空间的类型C，CI，D，和DIII。详细研究了Andreev反射引起的相移沿典型的半经典单电子轨道平均为沿着的系统。这样的系统特别有趣，因为它们没有真正的激发能隙，但支持接近化学势的准粒子态。无序或动态产生的混沌混合了状态，并产生了不同于维格纳-戴森的普遍水平统计形式。对于四种普适性类中的两种，通过映射到具有边界的一维自由费米气体上，计算了n能级关联函数。剩下的两类是拉盖尔正交和辛随机矩阵合奏。对于具有正常金属超导几何结构的量子点，计算了电导的弱局域化修正作为粘附概率和两个扰动破坏时间反演对称性和自旋旋转不变性的函数.从最大熵S-矩阵系综计算的普遍电导波动。它们比我们从正常导电系统的类比中天真地预期的要大2倍。这种增强是由慢模的数量增加了一倍来解释的：由于粒子和空穴在超导体附近的耦合，超前-滞后通道中的每一个库珀子和扩散模式都需要超前-超前（或滞后-滞后）通道中的相应模式。
Normal-conducting mesoscopic systems in contact with a superconductor are classified by the symmetry operations of time reversal and rotation of the electron's spin. Four symmetry classes are identified, which correspond to Cartan's symmetric spaces of type C, CI, D, and DIII. A detailed study is made of the systems where the phase shift due to Andreev reflection averages to zero along a typical semiclassical single-electron trajectory. Such systems are particularly interesting because they do not have a genuine excitation gap but support quasiparticle states close to the chemical potential. Disorder or dynamically generated chaos mixes the states and produces forms of universal level statistics different from Wigner-Dyson. For two of the four universality classes, the n-level correlation functions are calculated by the mapping on a free one-dimensional Fermi gas with a boundary. The remaining two classes are related to the Laguerre orthogonal and symplectic random-matrix ensembles. For a quantum dot with a normal-metal-superconducting geometry, the weak-localization correction to the conductance is calculated as a function of sticking probability and two perturbations breaking time-reversal symmetry and spin-rotation invariance. The universal conductance fluctuations are computed from a maximum-entropy S-matrix ensemble. They are larger by a factor of 2 than what is naively expected from the analogy with normal-conducting systems. This enhancement is explained by the doubling of the number of slow modes: owing to the coupling of particles and holes by the proximity to the superconductor, every cooperon and diffusion mode in the advanced-retarded channel entails a corresponding mode in the advanced-advanced (or retarded-retarded) channel.