Flat band fine-tuning and its photonic applications

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Flat bands in tight-binding lattices (networks) are characterized by macroscopic degeneracies and sensitivity to perturbations.
• These bands support compact localized eigenstates, protected by destructive interference, making them promising for exotic phases.

Purpose of the Study:

• To review systematic methods for constructing flat band networks using symmetries or fine-tuning.
• To explore the extension and adaptation of these construction methods in the presence of single-particle and many-body perturbations.

Main Methods:

• Systematic construction of flat band networks based on symmetries or fine-tuning.
• Analysis of the impact of single-particle and many-body perturbations on flat band properties.

Main Results:

• Discovery of non-perturbative metal-insulator transitions.
• Identification of fractal phases, nonlinear and quantum caging phenomena.
• Development of many-body nonergodic quantum models.

Conclusions:

• Flat band networks offer a powerful platform for exploring novel quantum phenomena.
• The construction strategies have significant implications for designing advanced nanophotonic systems like photonic crystals, nanocavities, and metasurfaces.