It was understood that Chern insulators cannot be realized in the presence of PT symmetry. In this paper, we reveal a new class of PT-symmetric Chern insulators, which has internal degrees of freedom forming real representations of a symmetry group with a complex endomorphism field. As a generalization to the conventional 2n-dimensional Chern insulators with integer n ≥ 1, these PT-symmetric Chern insulators have the n-th complex Chern number as their topological invariant, and have a ℤ classification given by the equivariant orthogonal K theory. Thus, in a fairly different sense, there exist ubiquitously Chern insulators with PT symmetry. By generalizing the Thouless charge pump argument, we find that, for a PT-symmetric Chern insulator with Chern number ν, there are equally many ν flavors of coexisting left- and right-handed chiral modes. Chiral modes with opposite chirality are complex conjugates to each other as complex representations of the internal symmetry group, but are not isomorphic. For the physical dimensionality d = 2, the PT-symmetric Chern insulators may be realized in artificial systems including photonic crystals and periodic mechanical systems.

中文翻译：

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等变PT对称实Chern绝缘子

可以理解，在存在PT对称性的情况下不能实现Chern绝缘子。在本文中，我们揭示了一种新型的PT对称Chern绝缘子，它具有内部自由度，形成具有复杂内同形场的对称群的真实表示。作为概括于常规2个Ñ与整数维陈绝缘体Ñ ≥1时，这些PT-对称陈绝缘体具有Ñ复数Chern数作为其拓扑不变性，并具有等变正交K理论给出的ℤ分类。因此，在完全不同的意义上，普遍存在具有PT对称性的Chern绝缘子。通过推广Thouless电荷泵论证，我们发现，对于具有Chern数ν的PT对称Chern绝缘子，左手和右手模式共存的ν风味相同。具有相反手性的手性模式是彼此复杂的共轭，作为内部对称基团的复杂表示，但不是同构的。对于物理维数d = 2，PT对称的Chern绝缘子可以在包括光子晶体和周期机械系统的人工系统中实现。