Exceptional nexus with a hybrid topological invariant

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Science  27 Nov 2020:
Vol. 370, Issue 6520, pp. 1077-1080
DOI: 10.1126/science.abd8872

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When all routes are exceptional

The exploration of non-Hermitian physics and parity-time symmetry have provided a route to develop a wealth of exotic physical effects. In such dissipative systems, the balance of gain and loss of the system lead to what are called exceptional points, or “sweet spots,” which relate to optimal device operation or material properties. The ability to tune the gain and loss over a range of system properties leads to exceptional arcs. Tang et al. show that systems can be designed in which the tuning of multiple parameters leads to a crossroads, or nexus, of exceptional arcs. Illustrating the effect in an acoustic system, the same properties should be attainable over various types of dissipative systems and thus provide a versatile route to fine-tune optimal performance of materials and devices.

Science, this issue p. 1077


Branch-point singularities known as exceptional points (EPs), which carry a nonzero topological charge, can emerge in non-Hermitian systems. We demonstrate with both theory and acoustic experiments an “exceptional nexus” (EX), which is not only a higher-order EP but also the cusp singularity of multiple exceptional arcs (EAs). Because the parameter space is segmented by the EAs, the EX possesses a hybrid topological invariant (HTI), which consists of distinct winding numbers associated with Berry phases accumulated by cyclic paths on different complex planes. The HTI is experimentally characterized by measuring the critical behaviors of the wave functions. Our findings constitute a major advance in the fundamental understanding of non-Hermitian systems and their topology, possibly opening new avenues for applications.

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