Quantized Decay Charges in Non-Hermitian Networks Characterized by Directed Graphs

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Topological physics

Background:

• Non-Hermitian physics explores systems with unique phenomena not found in Hermitian systems.
• The non-Hermitian skin effect (NHSE) localizes eigenstates at system boundaries due to non-reciprocal interactions.
• Traditional NHSE exhibits oscillatory wave patterns in localized eigenstates.

Purpose of the Study:

• Introduce a new class of non-Hermitian systems featuring pure decay modes.
• Characterize these pure decay modes and their topological properties.
• Explore versatile configurations and experimental validation of these modes.

Main Methods:

• Modeling non-Hermitian systems as directed graphs with nonreciprocal hopping.
• Defining and analyzing quantized decay charges as a topological invariant.
• Deriving universal conditions for the existence of pure decay modes.

Main Results:

• Identified pure decay modes with smooth exponential decay, unlike traditional NHSE.
• Introduced quantized decay charges as a novel topological invariant.
• Demonstrated versatile configurations including 1D rings, complex directed graphs, and higher-dimensional lattices.
• Experimental validation using microwave resonant circuits confirmed pure decay profiles.

Conclusions:

• Pure decay modes represent a new class of phenomena in non-Hermitian physics.
• Quantized decay charge serves as a robust topological invariant for these modes.
• The findings enable diverse physical realizations and suggest applications in photonics and signal processing.