Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence

By Elisabet Edvardsson, Flore K. Kunst, E. Bergholtz. Physical review B, 2018

186 citations recorded by the source corpus.

Non-Hermitian Hamiltonians, which describe a wide range of dissipative systems, and higher-order topological phases, which exhibit novel boundary states on corners and hinges, comprise two areas of intense current research. Here we investigate systems where these frontiers merge and formulate a generalized biorthogonal bulk-boundary correspondence, which dictates the appearance of boundary modes at parameter values that are, in general, radically different from those that mark phase transitions in periodic systems. By analyzing the interplay between corner/hinge, edge/surface, and bulk degrees of freedom we establish that the non-Hermitian extensions of higher-order topological phases exhibit an even richer phenomenology than their Hermitian counterparts and that this can be understood in a unifying way within our biorthogonal framework. Saliently this works in the presence of the non-Hermitian skin effect, and also naturally encompasses genuinely non-Hermitian phenomena in the absence thereof.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7d9ab6bb02d8024011e5680d97e120cbc87cc2ee

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Exceptional topology of non-Hermitian systems (2019, unknown): “Further generalizations to higher-order boundary states of NH models work analogously (Edvardsson, Kunst, and Bergholtz, 2019): In each case j r (cid:4) L r R j determines the existence of boundary states and accurately predicts the occurrence of phase transitions.”
Symmetry and Topology in Non-Hermitian Physics (2018, unknown): “[134] E.”
Perspective on topological states of non-Hermitian lattices (2019, background): “incompatible with the boundary condition. The quest for new phenomena shows now many promising possibilities, like the counterpart of higher-order topological states explored by Edvardsson and others [156, 157, 158], or the use of non-Hermiticity to model the ﬁnite lifetime introduced by electron-el”
A review on non-Hermitian skin effect (2022, methodology): “Some typical signatures include the localizations for an extensive number of bulk states, the breakdown of the conventional BBC and the defectiveness of the edge modes.”
Higher-order non-Hermitian skin effect (2020, background): “[60] E.”