1. National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China 2. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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 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 , there are equally many 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.
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