Non-Hermitian Topological Systems

Abstract

T wo emerging fields-non-Hermitian systems and topological phases-have recently begun to merge together, but just how much they overlap remains an open question. On one side, "non-Hermitian" typically applies to systems that experience gain and loss. On the other side, a "topological phase" is a state of matter that is characterized by a property that remains invariant during continuous deformations of the system. At first blush, it is not at all obvious that a topological invariant could arise within a non-Hermitian (NH) system, which can be out of equilibrium and even unstable. Experiments have given evidence for topological phases in 1D and 2D NH systems, but researchers have yet to place these results in a broader context that might reveal other NH topological systems. Zongping Gong from the University of Tokyo and colleagues present a new general framework for classifying Figure 1: A non-Hermitian system is represented here in two dimensions with different regions experiencing gain (red) and loss (blue). New theoretical work addresses conditions under which the system supports topological phases. Such a phase can allow edge states (shown as a yellow arrow) that move in one direction around the material and are immune to defects and disorder.