Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians

Details Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians

2011-07-06

arxiv.org/abs/1107.1064v1

Physics

Condensed Matter

Other Condensed Matter

5 pages, 1 figure

Scientific paper

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.

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