Perspective on topological states of non-Hermitian lattices

TL;DR

This paper reviews recent developments in topological states of non-Hermitian lattices, connecting them to Floquet systems and discussing the role of Hamiltonian defectiveness in understanding their topological phases.

Contribution

It provides an overview of non-Hermitian topological states, linking them to Floquet systems and offering a scattering-based interpretation of Hamiltonian defectiveness.

Findings

Non-Hermitian topological states have become a prominent research area.

Hamiltonian defectiveness is crucial for understanding non-Hermitian topological phases.

A simple scattering picture helps interpret complex non-Hermitian concepts.

Abstract

The search of topological states in non-Hermitian systems has gained a strong momentum over the last two years climbing to the level of an emergent research front. In this Perspective we give an overview with a focus in connecting this topic to others like Floquet systems. Furthermore, using a simple scattering picture we discuss an interpretation of concepts like the Hamiltonian's defectiveness, i.e. the lack of a full basis of eigenstates, crucial in many discussions of topological phases of non-Hermitian Hamiltonians.