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arXiv 1302.2866cond-mat.mes-hall
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电子Mach-Zehnder干涉仪的解析可解模型

Analytically solvable model of an electronic Mach-Zehnder interferometer

Stéphane Ngo Dinh, Dmitry A. Bagrets, Alexander D. Mirlin

摘要:

考虑了一类基于整数量子霍尔边态的非平衡电子马赫-曾德尔干涉仪模型。该模型的特点是电子-电子相互作用被限制在干涉仪的内部和量子量子点接触的传输系数,定义的干涉仪,它可以采取从零到一的任意值。我们用单粒子量--Fredholm积分算子的行列式和预解式建立了这些模型的精确解。在一般情况下,结果可以通过数值计算得到。在强荷电相互作用的情况下,算子获得块Toeplitz形式。通过分析相应的Riemann-Hilbert问题,我们将结果归结为某些奇异的单通道行列式(这是具有Fisher-Hartwig奇异性的Toeplitz行列式的推广),并得到了干扰电流(特别是Aharonov-Bohm振荡的可见性)的解析结果。我们的研究结果,这是在很好的协议与实验观察,显示了密切的联系所观察到的“瓣”结构的Aharonov-Bohm振荡的可见性和多个分支的渐近奇异积分行列式。

英文摘要:

We consider a class of models of non-equilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the interferometer and transmission coefficients of the quantum quantum point contacts, defining the interferometer, which may take arbitrary values from zero to one. We establish an exact solution of these models in terms of single-particle quantities --- determinants and resolvents of Fredholm integral operators. In the general situation, the results can be obtained numerically. In the case of strong charging interaction, the operators acquire the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem, we reduce the result to certain singular single-channel determinants (which are a generalization of Toeplitz determinants with Fisher-Hartwig singularities), and obtain an analytic result for the interference current (and, in particular, for the visibility of Aharonov-Bohm oscillations). Our results, which are in good agreement with experimental observations, show an intimate connection between the observed "lobe" structure in the visibility of Aharonov-Bohm oscillations and multiple branches in the asymptotics of singular integral determinants.

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