Non-Hermitian Boundary Modes and Topology

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Topological Materials

Background:

• Non-Hermitian systems exhibit unique phenomena like the skin effect.
• Bulk-boundary correspondence is a key concept in topological phases.
• Understanding boundary modes is crucial for designing novel quantum systems.

Purpose of the Study:

• To develop a universal framework for boundary mode existence in non-Hermitian systems.
• To generalize the bulk-boundary correspondence to non-Hermitian systems with various gap conditions.
• To identify novel non-Hermitian topological regimes.

Main Methods:

• Formulation of boundary mode formation criteria using local Green's functions.
• Analysis of skin effect in topological and nontopological non-Hermitian systems.
• Application of doubled Green's function, inspired by doubled Hamiltonian methods.

Main Results:

• A generic perspective on boundary mode appearance and their dispersion relations.
• Generalization of bulk-boundary correspondence to non-Hermitian systems.
• Direct relation established between point gap invariants and skin modes.
• Identification of novel non-Hermitian topological regimes.

Conclusions:

• The developed method provides a unifying perspective for non-Hermitian systems.
• It serves as a general tool for exploring topological phenomena.
• The approach reveals new possibilities for non-Hermitian topological physics.