Anomalous Edge State in a Non-Hermitian Lattice

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Photonics

Background:

• Topological insulators exhibit a bulk-boundary correspondence, linking bulk topological invariants to edge states.
• Non-Hermiticity, often arising from gain and loss, can fundamentally alter quantum system properties.

Purpose of the Study:

• To investigate how non-Hermiticity modifies the bulk-boundary correspondence in topological insulators.
• To explore the properties of edge states in a non-Hermitian 1D system.

Main Methods:

• A one-dimensional tight-binding model with non-Hermitian terms (gain/loss) and long-range hopping was analyzed.
• The system's Hamiltonian was studied, focusing on exceptional points in momentum space and winding numbers.
• Chiral symmetry was used to analyze the stability of edge states.

Main Results:

• The bulk-boundary correspondence was shown to be modified by non-Hermiticity.
• A fractional winding number of 1/2 was found, associated with an exceptional point.
• A single, dynamically stable, zero-energy edge state was identified.
• This edge state demonstrated robustness against disorder due to chiral symmetry protection.

Conclusions:

• Non-Hermiticity leads to a fractional winding number and a unique edge state in topological insulators.
• The identified edge state is dynamically stable and robust to disorder, protected by chiral symmetry.
• Experimental realization using coupled resonator optical waveguides is proposed.