Spectral localizer for line-gapped non-hermitian systems

Abstract

Short-ranged and line-gapped non-hermitian Hamiltonians have strong topological invariants given by an index of an associated Fredholm operator. It is shown how these invariants can be accessed via the signature of a suitable spectral localizer. This numerical technique is implemented in an example with relevance to the design of topological photonic systems, such as topological lasers.

References in corpus (5)

• Local invariants identify topology in metals and gapless systems
• An operator-based approach to topological photonics
• Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory
• Invariants of disordered semimetals via the spectral localizer
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk

Cited by in corpus (9)

• Observation of non-Hermitian topology in a multi-terminal quantum Hall device
• Local markers for crystalline topology
• Classifying topology in photonic heterostructures with gapless environments
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Local and energy-resolved topological invariants for Floquet systems
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Topological photonic crystal fibre
• Dimensional crossover of class D real-space topological invariants