Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions

Abstract

The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be further affected in non-Hermitian systems, experiencing loss and/or gain? In this work, we take the first step in this direction, by studying a bulk-Hermitian continuous system with non-Hermitian boundary conditions. We find in this case that edge modes emerge at the roots of the scattering matrix, as opposed to the Hermitian case, where they emerge at its poles (or, more accurately, coalescence of roots and poles). This entails a nontrivial modification to the relative Levinson's theorem. We then show that the topological structure remains the same as in the Hermitian case, and the generalized BEC holds, provided one employs appropriately modified contours in the wave-vector plane so that the scattering matrix phase winding counts the edge modes correctly. We exemplify all this using a paradigmatic model of waves in a shallow ocean or active systems in the presence of odd viscosity, as well as 2D electron gas with Hall viscosity. We use this opportunity to examine the case of large odd viscosity, where the scattering matrix becomes $2\times 2$, which has not been discussed in previous works on the Hermitian generalized BEC.

21 pages, 8 figures; v2: New appendix B and references added; v3: Published version

References in corpus (10)

• Topological Photonics
• Making Sense of Non-Hermitian Hamiltonians
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological active matter
• Non-Bloch band theory and bulk-edge correspondence in non-Hermitian systems
• Dissipative and Hall viscosity of a disordered 2D electron gas
• Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
• Topology in shallow-water waves: A spectral flow perspective
• Bulk-edge correspondence and trapping at a non-Hermitian topological interface

Cited by in corpus (4)

• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Hybrid-Order Topological Phase And Transition in 1H Transition Metal Compounds
• Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity
• Non-Hermitian topological wall modes in rotating Rayleigh-Benard convection