In this work we consider a generalization of the symmetry classification of topological insulators to non-Hermitian Hamiltonians which satisfy a combined PT-symmetry (parity and time-reversal). We show via examples, and explicit bulk and boundary state proofs that the typical paradigm of forming topological insulator states from Dirac Hamiltonians is not compatible with the construction of non-Hermitian PT-symmetric Hamiltonians. The topological insulator states are PT-breaking phases and have energy spectra which are complex (not real) and thus such non-Hermitian Hamiltonians are not consistent quantum theories.

http://arxiv.org/abs/1107.1064
Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)