Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics

Kohei Kawabata; Sho Higashikawa; Zongping Gong; Yuto Ashida; Masahito Ueda

doi:10.1038/s41467-018-08254-y

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arXiv · 1804.04676

Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics

Kohei Kawabata·Sho Higashikawa·Zongping Gong·Yuto Ashida·Masahito Ueda

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Abstract

Topological phases are enriched in non-equilibrium open systems effectively described by non-Hermitian Hamiltonians. While several properties unique to non-Hermitian topological systems were uncovered, the fundamental role of symmetry in non-Hermitian physics has yet to be fully understood, and it has remained unclear how symmetry protects non-Hermitian topological phases. Here we show that two fundamental anti-unitary symmetries, time-reversal and particle-hole symmetries, are topologically equivalent in the complex energy plane and hence unified in non-Hermitian physics. A striking consequence of this symmetry unification is the emergence of unique non-equilibrium topological phases that have no counterparts in Hermitian systems. We illustrate this by presenting a non-Hermitian counterpart of the Majorana chain in an insulator with time-reversal symmetry and that of the quantum spin Hall insulator in a superconductor with particle-hole symmetry. Our work establishes a fundamental symmetry principle in non-Hermitian physics and paves the way towards a unified framework for non-equilibrium topological phases.

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Kohei Kawabata, Sho Higashikawa, Zongping Gong, Yuto Ashida, Masahito Ueda. 2018-04-12. Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics. https://doi.org/10.1038/s41467-018-08254-y

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