Non-Hermitian Boundary Modes and Topology.

By Dan S. Borgnia, A. Kruchkov, Robert-Jan Slager. Physical Review Letters, 2019

637 citations recorded by the source corpus.

We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary codimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green's functions, we outline a generic perspective on the appearance of such modes and generate corresponding dispersion relations. In the process, we explain the skin effect in both topological and nontopological systems, exhaustively generalizing bulk-boundary correspondence to different types of non-Hermitian gap conditions, a prominent distinguishing feature of such systems. Indeed, we expose a direct relation between the presence of a point gap invariant and the appearance of skin modes when this gap is trivialized by an edge. This correspondence is established via a doubled Green's function, inspired by doubled Hamiltonian methods used to classify Floquet and, more recently, non-Hermitian topological phases. Our work constitutes a general tool, as well as a unifying perspective for this rapidly evolving field. Indeed, as a concrete application we find that our method can expose novel non-Hermitian topological regimes beyond the reach of previous methods.

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

View Paper: https://www.semanticscholar.org/paper/e27789484ba25acbff5917a439b3c769ba62ef6f

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In Atomic and Molecular Physics, and Optics

  1. Tian Zhang
  2. Xiujuan Zhang
  3. Yan-Feng Chen
  4. Ming-Hui Lu

In Statistical and Nonlinear Physics

  1. Tian Zhang
  2. Xiujuan Zhang
  3. Yan-Feng Chen
  4. Ming-Hui Lu

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