Skin effect and winding number in disordered non-Hermitian systems

Unlike their Hermitian counterparts, non-Hermitian (NH) systems may display an exponential sensitivity to boundary conditions and an extensive number of edge-localized states in systems with open boundaries, a phenomena dubbed the “non-Hermitian skin effect." The NH skin effect has recently been connected to the winding number, a topological invariant unique to NH systems. In this talk, I’ll present a real-space generalization of the winding number that applies to disordered systems. This real-space winding number is topological, in the sense that it remains quantized for a localized system, and this quantized value still predicts the NH skin effect. We use our theory to demonstrate the NH Anderson skin effect, in which a skin effect is developed as disorder is added to a clean system, as well as explain recent results in optical funnels.