Exceptional non-Hermitian topology

Prof. Flore Kunst Max Planck Institute for the Science of Light
While topological phases of matter have predominantly been studied for isolated Hermitian systems, a recent shift has been made towards considering these phases in the context of non-Hermitian Hamiltonians. Non-Hermitian topological phenomena reveal an enrichment of the phenomenology of topological phases, and forms a rapidly growing new cross-disciplinary field. In particular, non-Hermiticity plays a central role in both classical and quantum systems. For example, in the classical realm, this comes about because of gain and loss processes in optics. In the quantum realm, non-Hermiticity describes the dynamics of open quantum systems as well as scattering, decay, broadening and resonances due to, for example, interactions and disorder. Non-Hermitian Hamiltonians may feature many exotic properties that are radically different from their Hermitian counterparts, such as the generic appearance of exotic exceptional structures, a breakdown of the famed bulk-boundary correspondence, and the piling up of bulk states at the boundaries known as the non-Hermitian skin effect. In this talk, I will provide an overview of the field focussing on fundamental aspects, experimental realizations and I will briefly touch upon applications.