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arXiv · 1902.07217

Non-Hermitian Boundary Modes

Dan S. Borgnia·Alex Jura Kruchkov·Robert-Jan Slager
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Abstract

We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green 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 non-topological systems, exhaustively generalizing bulk-boundary correspondence in the presence of non-Hermiticity. This is accomplished 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.

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Dan S. Borgnia, Alex Jura Kruchkov, Robert-Jan Slager. 2019-04-18. Non-Hermitian Boundary Modes. https://doi.org/10.1103/physrevlett.124.056802

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