Equivariant PT-symmetric real Chern insulators

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 v.there are equally many v 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.

Equivariant PT-symmetric real Chern insulators

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 \mathbb{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 \upsilon, there are equally many \upsilon 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.