Anatomy of skin modes and topology in non-Hermitian systems

By Ching Hua Lee, R. Thomale. Physical review B, 2018

667 citations recorded by the source corpus.

A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to the imposed boundary conditions, which is beyond any known phenomenon from Hermitian systems. In addition to topologically protected boundary modes, macroscopically many ``skin'' boundary modes may appear under open boundary conditions. We rigorously derive universal results for characterizing all avenues of boundary modes in non-Hermitian systems for arbitrary hopping range. For skin modes, we introduce how exact energies and decay lengths can be obtained by threading an imaginary flux. Furthermore, for 1D topological boundary modes, we derive a new generic criterion for their existence in non-Hermitian systems which, in contrast to previous formulations, does not require specific tailoring to the system at hand. Our approach is intimately based on the complex analytical properties of in-gap exceptional points, and gives a lower bound for the winding number related to the vorticity of the energy Riemann surface. It also reveals that the topologically nontrivial phase is partitioned into subregimes where the boundary mode's decay length depends differently on complex momenta roots.

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

View Paper: https://www.semanticscholar.org/paper/9eedd2472eef4216191e10eefb9e3a5d06c2eaa6

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Citations in the corpus

Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices (2019, background): “Especially, the non-Hermitian topology is attracting special attention for the violation of the conventional bulk-boundary correspondence of Hermitian topological systems, and new ways of topological characterization are needed [39–62].”
Probing non-Hermitian skin effect and non-Bloch phase transitions (2019, methodology): “[21].”
Perspective on topological states of non-Hermitian lattices (2019, background): “ally in Ref. [47] for a non-Hermitian SSH model with asymmetric Perspective on topological states of non-Hermitian lattices 10 hoppings and dubbed non-Hermitian skin effect. Recently, Lee and Thomale [64] presented a characterization of these peculiar boundary modes and provided conditions for their”
Reciprocal skin effect and its realization in a topolectrical circuit (2019, background): “The skin effect constitutes a breakdown of bulk-boundary correspondence, which is not found in closed systems [17–20].”
Non-Hermitian systems and topology: A transfer-matrix perspective (2018, methodology): “Indeed, bulk invariants computed taking this into account for certain specific models [50, 57, 72] have been shown to correctly predict the existence of the topological boundary modes.”
Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class (2020, methodology): “To elucidate such a non-Bloch feature of non-Hermitian systems, recent works have developed a non-Bloch band theory that works even under arbitrary boundary conditions [25, 27, 30, 34, 40, 53, 54].”
A review on non-Hermitian skin effect (2022, methodology): “4 [31-35], interpreting NHSE from different points of view [36-48], developing new theories, methods and material designs to describe the NHSE-related topological properties and the”