2018/04/30 by Kohei Kawabata, Sho Higashikawa, Zongping Gong +2 · 2 citations
Physics and Astronomy · Mathematics · #quant-ph #cond-mat.mes-hall #cond-mat.quant-gas #math-ph #math.MP #physics.optics
paper · pdf · doi:10.1038/s41467-018-08254-y
published as Nat. Commun. 10, 297 (2019) · 6+11 pages, 5+10 figures
arxiv created 2019/01/17 · arxiv updated 2019/01/18
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.