Non-Hermitian Skin Effect in a Non-Hermitian Electrical Circuit

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Non-Hermitian Systems

Background:

• The bulk-boundary correspondence traditionally links bulk topological invariants to edge states.
• This principle is challenged in non-Hermitian systems with broken reciprocity due to the non-Hermitian skin effect (NHSE).
• NHSE causes eigenstates to localize at boundaries, invalidating conventional methods.

Purpose of the Study:

• To experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity.
• To investigate the failure of the conventional bulk-boundary correspondence in such systems.
• To validate a new non-Bloch bulk-boundary condition for predicting topological edge states.

Main Methods:

• Fabrication of a 1D non-Hermitian topological circuit using voltage follower modules for unidirectional coupling.
• Experimental observation of topological edge states via impedance spectra measurements under open boundary conditions (OBC).
• Comparison of circuit Laplacians under periodic boundary conditions (PBC) and OBC to confirm the breakdown of conventional bulk-boundary correspondence.

Main Results:

• Successful experimental realization of a 1D non-Hermitian topological circuit with broken reciprocity.
• Observation of topological edge states at the open circuit boundary.
• Demonstration that the conventional bulk-boundary correspondence is inapplicable in this system.
• Validation of the non-Bloch bulk-boundary condition using a non-Bloch winding number for accurate prediction of edge states.

Conclusions:

• The conventional bulk-boundary correspondence fails in non-Hermitian systems with broken reciprocity and NHSE.
• A novel non-Bloch bulk-boundary condition accurately predicts topological edge states in these systems.
• Experimental validation of theoretical predictions in a practical circuit implementation.