Exceptional nexus with a hybrid topological invariant

Area of Science:

• Non-Hermitian physics
• Topological physics
• Acoustic metamaterials

Background:

• Exceptional points (EPs) are branch-point singularities in non-Hermitian systems.
• EPs possess nonzero topological charges.
• Understanding higher-order singularities is crucial for non-Hermitian topology.

Purpose of the Study:

• To theoretically and experimentally demonstrate a higher-order exceptional point, termed an exceptional nexus (EX).
• To investigate the topological properties of the EX, specifically its hybrid topological invariant (HTI).
• To characterize the HTI through experimental measurements of wave function critical behaviors.

Main Methods:

• Theoretical modeling of non-Hermitian systems to predict EX formation.
• Acoustic experiments to realize and observe the EX.
• Analysis of Berry phases and winding numbers to define the HTI.
• Experimental characterization of wave function critical behaviors.

Main Results:

• Demonstration of an exceptional nexus (EX) as a higher-order EP and cusp singularity.
• Identification of multiple exceptional arcs (EAs) segmenting the parameter space around the EX.
• Definition and experimental characterization of a hybrid topological invariant (HTI) for the EX.
• The HTI comprises distinct winding numbers from different complex planes.

Conclusions:

• The exceptional nexus represents a novel topological singularity in non-Hermitian systems.
• The hybrid topological invariant offers a new perspective on topological characterization.
• Findings advance the fundamental understanding of non-Hermitian topology and may enable new applications.