Tobias Meng

Dresden University of Technology

Non-Hermitian topology driven to the edge

A global quantum system is often composed of several subsystems, for example electrons, phonons, and their environment. Typically, however, we are only interested in some of these subsystems, for example the electrons. Reducing the problem to these subsystems of interest often comes at the price of trading a complex global Hermitian Hamiltonian for an effective non-Hermitian subsystem Hamiltonian.

While this is not news per se, it has recently been understood that non-Hermitian Hamiltonians have their own flavor of topology, which is in fact much richer than the topology of Hermitian systems. Non-Hermitian topology leads to new phenomena, such as a non-Hermitian skin effect, and enables novel functionalities, such as non-Hermitian topological sensors.

In this talk, I will discuss how effective non-Hermitian Hamiltonians appear in the description of open quantum systems. For the example of an open Chern insulator, I will discuss „edge-selective extremal damping“ - in short, topology protects electrons at the edge from dissipation. Moving on to the example of a Hofstadter model, I will then discuss that Hermitian topology and non-Hermitian topology may even compete for localizing edge states at opposite ends of the sample. Overall, these phenomena illustrate the importance of non-Hermitian Hamiltonians, and the richness of their topology.