March 27, 2024 | Carlo Danieli, Alexei Andreanov, Daniel Leykam, Sergej Flach
This review discusses the fine-tuning of flat bands in tight-binding networks and their photonic applications. Flat bands, characterized by macroscopic degeneracies and sensitivity to perturbations, are intriguing for their potential to induce exotic phases and unconventional orders. The challenge lies in constructing such networks, which often rely on symmetries and fine-tuning. The review covers systematic methods for constructing flat band networks based on symmetries or fine-tuning, and explores how these constructions can be extended and adapted in the presence of perturbations, both single-particle and many-body. This has led to the discovery of non-perturbative metal-insulator transitions, fractal phases, nonlinear and quantum caging, and many-body nonergodic quantum models. The implications of these findings for the design of fine-tuned nanophotonic systems, including photonic crystals, nanocavities, and metasurfaces, are discussed. The review also delves into the types of flat bands, their tuning and detuning properties, and their applications in photonics, highlighting the role of disorder, driving, and interactions in these systems.This review discusses the fine-tuning of flat bands in tight-binding networks and their photonic applications. Flat bands, characterized by macroscopic degeneracies and sensitivity to perturbations, are intriguing for their potential to induce exotic phases and unconventional orders. The challenge lies in constructing such networks, which often rely on symmetries and fine-tuning. The review covers systematic methods for constructing flat band networks based on symmetries or fine-tuning, and explores how these constructions can be extended and adapted in the presence of perturbations, both single-particle and many-body. This has led to the discovery of non-perturbative metal-insulator transitions, fractal phases, nonlinear and quantum caging, and many-body nonergodic quantum models. The implications of these findings for the design of fine-tuned nanophotonic systems, including photonic crystals, nanocavities, and metasurfaces, are discussed. The review also delves into the types of flat bands, their tuning and detuning properties, and their applications in photonics, highlighting the role of disorder, driving, and interactions in these systems.