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Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

机译：拓扑绝缘体和超导体中的电磁和重力响应及异常

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One of the defining properties of the conventional three-dimensional ("Z_2" or "spin-orbit") topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analog of such a magnetoelectric effect in the thermal (or gravitational) and magnetic dipole responses in all symmetry classes that admit topologically nontrivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry, which lack SU(2) spin rotation symmetry (e.g., due to spin-orbit interactions), such as the B phase of ~3He, the thermal response is the only probe that can detect the nontrivial topological character through transport. We show that, for such topological superconductors, applying a temperature gradient produces a thermal-(or mass-) surface current perpendicular to the thermal gradient. Such charge, thermal, or magnetic dipole responses provide a definition of topological insulators and superconductors beyond the single-particle picture. Moreover, we find, for a significant part of the "tenfold" list of topological insulators found in previous work in the absence of interactions, that in general dimensions, the effective field theory describing the space-time responses is governed by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting, this shows that the classification of these topological insulators is robust to adiabatic deformations by interparticle interactions in general dimensionality. In particular, this applies to symmetry classes DⅢ, CI, and AⅢ in three spatial dimensions, and to symmetry classes D and C in two spatial dimensions.
机译：常规三维（“ Z_2”或“自旋轨道”）拓扑绝缘子的定义特性之一是其特有的磁电效应，如轴电动力学所描述。在本文中，我们讨论了在所有对称类别中允许拓扑非平凡绝缘子或超导体存在三个维度的热（或引力）和磁偶极子响应中此类磁电效应的类似物。特别是，对于具有时间反转对称性的拓扑超导体（或超流体），其缺乏SU（2）自旋旋转对称性（例如，由于自旋轨道相互作用），例如〜3He的B相，其热响应为只能通过传输检测非平凡拓扑特征的探针。我们表明，对于此类拓扑超导体，施加温度梯度会产生垂直于热梯度的热（或质量）表面电流。这种电荷，热或磁偶极子响应提供了单粒子图片以外的拓扑绝缘体和超导体的定义。此外，我们发现，在先前工作中没有相互作用的情况下发现的拓扑绝缘子的“十倍”列表的很大一部分中，在一般维度上，描述时空响应的有效场论受场论异常支配。 。由于已知异常对下面的费米子是否相互作用不敏感，因此表明这些拓扑绝缘子的分类对于通过大尺度上的粒子间相互作用对绝热变形具有鲁棒性。特别是，这在三个空间维度上适用于对称类别DⅢ，CI和AⅢ，在两个空间维度上适用于对称类别D和C。

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