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arXiv 1012.0932cond-mat.mes-hall
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拓扑超导体Andreev反射的随机矩阵理论

Random-matrix theory of Andreev reflection from a topological superconductor

C. W. J. Beenakker, J. P. Dahlhaus, M. Wimmer, A. R. Akhmerov

摘要:

本文用随机矩阵理论的圆形系综计算了费米能级上Andreev反射本征值R_n的概率分布。在没有自旋旋转对称性的情况下,电导G的统计依赖于超导体的拓扑量子数Q。通过证明当p<N/d(d=2或d=1,存在或不存在时间反演对称性)时G的p阶累积量与Q无关,我们证明了这种依赖性在散射通道数N中是非微扰的。因此,弱局域化等大N效应无法探测拓扑量子数。对于小的N,我们计算的电导的全分布P(G),并找到定性的差异,在拓扑平凡和非平凡的阶段。

英文摘要:

We calculate the probability distribution of the Andreev reflection eigenvalues R_n at the Fermi level in the circular ensemble of random-matrix theory. Without spin-rotation symmetry, the statistics of the electrical conductance G depends on the topological quantum number Q of the superconductor. We show that this dependence is nonperturbative in the number N of scattering channels, by proving that the p-th cumulant of G is independent of Q for p<N/d (with d=2 or d=1 in the presence or in the absence of time-reversal symmetry). A large-N effect such as weak localization cannot, therefore, probe the topological quantum number. For small N we calculate the full distribution P(G) of the conductance and find qualitative differences in the topologically trivial and nontrivial phases.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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