Nonlinearity enabled higher-dimensional exceptional topology

TL;DR

This paper demonstrates how nonlinearity fundamentally influences the formation of higher-dimensional exceptional topologies in non-Hermitian systems, combining theory and circuit experiments to reveal new topological phenomena.

Contribution

It introduces the concept of nonlinearity enabling higher-order exceptional points with hybrid topological invariants in simple coupled resonators, advancing understanding of nonlinear non-Hermitian topologies.

Findings

Experimental verification of exceptional nexus in nonlinear systems

Identification of anisotropic critical behavior of eigenspectra

Confirmation of hybrid topological invariant via phase rigidities

Abstract

The role of nonlinearity on topology has been investigated extensively in Hermitian systems, while nonlinearity has only been used as a tuning knob in a PT symmetric non-Hermitian system. Here, in our work, we show that nonlinearity plays a crucial role in forming topological singularities of non-Hermitian systems. We provide a simple and intuitive example by demonstrating with both theory and circuit experiments an exceptional nexus (EX), a higher-order exceptional point with a hybrid topological invariant (HTI), within only two coupled resonators with the aid of nonlinear gain. Phase rigidities are constructed to confirm the HTI in our nonlinear system, and the anisotropic critical behavior of the eigenspectra is verified with experiments. Our findings lead to advances in the fundamental understanding of the peculiar topology of nonlinear non-Hermitian systems, possibly opening new avenues for applications.