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

By Yibin Hu, T. Hughes. 2011

201 citations recorded by the source corpus.

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 proofs from separate bulk and gapless boundary-state perspectives 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 that are complex (not real) and, thus, are not consistent quantum theories.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c287fbb470911c7c00f1e3733938cbf5e6c92366

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Non-Hermitian Chern Bands. (2018, unknown): “This Hamiltonian is “η-pseudo-Hermitian” [94,95] (not PT-symmetric [38,58]), namely, it satisfies η−1H†η 1⁄4 H, where η is the direct product of spatial inversion and σz:”
Topological photonics (2018, background): “That said, it was shown (Esaki et al., 2011; Hu and Hughes, 2011) that a large class of systems that are PT symmetric in the bulk must have edge states that “break” PT ; namely, they have complex eigenvalues.”
Topological insulator laser: Theory (2018, background): “Introducing nonhermiticity to topological systems raises fundamental questions concerningwhether non-Hermitian topological systems can exist at all (23), and if they do, how to define the topological phases and their stability (24).”
Anomalous helical edge states in a non-Hermitian Chern insulator (2018, unknown): “Recent studies have also revealed that nonHermiticity alters the nature of the bulk-boundary correspondence in topological systems [43, 46, 47, 49, 51, 59, 60, 67].”
Exceptional topology of non-Hermitian systems (2019, unknown): “It can be intuitively understood why these symmetries prevent the existence of skin states: For example, PT symmetry maps one boundary to the opposite boundary, such that any state localized at only one of the boundaries automatically breaks PT (Hu and Hughes, 2011).”
Symmetry and Topology in Non-Hermitian Physics (2018, unknown): “[101] Y.”
Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices (2019, background): “[40] Yi Chen Hu and Taylor L.”
Edge states and topological phases in non-Hermitian systems (2011, background): “After the completion of this work, we noticed Ref.[37] in which the SU(1, 1) and SO(3, 2) models are discussed in the context of topological insulators.”