Non-Hermitian Topological Systems

Two 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 topological phases of non-Hermitian systems [1]. They create a “periodic table” of NH topological phases based on the symmetries of the system and the number of dimensions. Under their classification, 2D non-Hermitian systems should not have topological phases, which would seem to conflict with recent experimental and theoretical work [2, 3]. However, the apparent discrepancy is a result of different definitions for what constitutes a NH topological phase, which means the book on non-Hermitian topological systems isn’t yet closed.