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Using weak measurements to extract the Z_2 index of a topological insulator

机译：使用弱测量值提取拓扑绝缘体的Z_2指数

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摘要

Recently, there has been an interest in applying the concept of weak values and weak measurements to condensed matter systems. Here a weak measurement protocol is proposed for obtaining the Z_2 index of a topological insulator. The setup consists of a topological insulator with a hole pierced by a time dependent Aharonov-Bohm flux. A certain weak value (A_(gs)) associated with the time-integrated magnetization in the hole has a universal response to a small ambient magnetic field (B), namely, A_(gs)B = 2h. This result is unaffected by disorder, interactions, and to a large extent, the speed of the flux threading. It hinges mainly on preventing the flux from leaking outside the hole, as well as being able to detect magnetization at a resolution of a few spins. A similar result may be obtained using only charge measurements, in a setup consisting of a double quantum dot weakly coupled to an LC circuit. Here one obtains <φ>_(weak)Q_0 = 2h, where <φ>_(weak) is a weak value associated with the flux on the inductor and Q_0 is the average capacitor charging. The universality of these results suggests that they may be used as a test bed for weak values in condensed matter physics.
机译：最近，人们对将弱值和弱测量的概念应用于凝聚态系统感兴趣。这里提出了一种弱测量协议，以获取拓扑绝缘体的Z_2指数。该装置包括一个拓扑绝缘体，该绝缘体的孔被时间相关的Aharonov-Bohm通量刺穿。与孔中的时间积分磁化强度相关的某个弱值（A_（gs））对小的环境磁场（B）具有普遍响应，即A_（gs）B = 2h。该结果不受无序，相互作用和焊剂穿线速度的影响。它的主要作用在于防止磁通量泄漏到孔的外部，以及能够以几转的分辨率检测磁化强度。在由弱耦合到LC电路的双量子点组成的设置中，仅使用电荷测量即可获得相似的结果。在这里，获得φ_（weak）Q_0 = 2h，其中<φ> _（weak）是与电感上的磁通量相关的弱值，而Q_0是电容器的平均充电量。这些结果的普遍性表明，它们可以用作凝聚态物理中微弱值的测试平台。

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