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Examples of non-hermitian quantum systems admitting topological insulatorphase are presented in one, two and three space dimensions. All of thesenon-hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity ismaintained with the introduction of appropriate inner-products in thecorresponding Hilbert spaces. The topological invariant characterizing aparticular phase is shown to be identical for a non-hermitian Hamiltonian andits hermitian counterpart, to which it is related through a non-unitarysimilarity transformation. A classification scheme for topological insulatorphases in pseudo-hermitian quantum systems is suggested.

A note on topological insulator phase in non-hermitian quantum systems