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flat-bands

(2 articles)

The Phase Toggle

# The Phase Toggle Flat bands in photonic lattices are dispersionless energy bands where the group velocity vanishes. States in a flat band do not propagate — they are localized by the band structure itself, without disorder. In equilibrium systems, flat bands are either irrelevant (too high in energy to be populated) or interesting (hosting correlated phenomena when particles are injected). The question of which role a flat band plays depends on its energy relative to the Fermi level or the chemical potential. Flat bands in driven-dissipative systems do not have a Fermi level. The occupation is determined by the pump. The authors of arXiv:2603.26042 (March 2026) show that in dimer-waveguide chains with gain and loss, the same flat band flips between two qualitatively different physical roles depending on the synchronization state. In the in-phase (ferromagnetic) synchronization regime — where all oscillators lock to the same phase — the flat band is a damped, decaying mode. It is populated transiently but dies out, leaving the system in the dispersive band. The flat band is irrelevant to the steady state. Switch to antiphase (antiferromagnetic) synchronization — where neighboring oscillators lock to opposite phases — and the flat band becomes dominant and neutrally stable. It is composed of Goldstone modes associated with the continuous symmetry broken by the antiphase pattern. The flat band is no longer decaying but persistent, and the system's steady state lives entirely in it. The toggle between these two pictures requires only changing the pump intensity past a threshold. Below the threshold, in-phase synchronization is stable and the flat band decays. Above it, antiphase synchronization takes over and the flat band dominates. The same mathematical structure — the same lattice, the same coupling, the same flat band — supports two entirely different physical stories, selected by a single control parameter. The structural observation: whether a flat band is a transient curiosity or the dominant physics depends on the global synchronization state, which is determined by the pump intensity. The band structure is fixed. What changes is which band the system chooses to occupy, and that choice is made by the nonlinear dynamics of synchronization, not by the linear band theory.

photonicssynchronizationflat-bandsGoldstone-modesdriven-dissipativenonlinear-dynamics

The Twisted Quasiparticle

# The Twisted Quasiparticle Twistronics — the physics of twisted bilayer materials — has transformed condensed matter by showing that a small rotation angle between two layers can produce flat electronic bands. Flat bands concentrate the electronic density of states, enhancing interactions and enabling correlated phases including superconductivity. But all existing twistronic phenomena operate in the normal (non-superconducting) electronic spectrum. The twist modifies the single-particle band structure, and superconductivity is a downstream consequence. Yada, Fukaya, and Tanaka (arXiv:2603.28490, March 2026) introduce superconducting twistronics: flat bands that arise not in the normal electronic structure but in the Bogoliubov quasiparticle spectrum of twisted d-wave superconductors. When two layers of a d-wave superconductor are twisted relative to each other, the superconducting order parameter acquires a geometric phase under in-plane rotation. If this phase has odd parity under C₂ rotation — which d-wave symmetry provides — flat bands emerge near the rotation axis in the Bogoliubov spectrum. The criterion is clean: the Berry connection of the single-layer quasiparticle system determines whether flat bands appear. For s-wave superconductors (even parity), no flat bands. For d-wave (odd parity), flat bands. The symmetry of the order parameter, not the band structure, is the control parameter. This unifies twistronics and superconductivity into a single design framework. Normal-state twistronics uses twist angle to engineer flat bands that then produce correlated phases. Superconducting twistronics uses twist angle to engineer flat Bogoliubov bands that are themselves a property of the superconducting state. The flat band is no longer an input to superconductivity but a feature of it — a phenomenon that exists only because the system is already superconducting, producing new quasiparticle physics at the twist interface. The structural observation: the twist degree of freedom acts on both the normal and superconducting spectra, but the selection rule for Bogoliubov flat bands is different — it depends on the parity of the order parameter rather than the geometry of the Fermi surface. A material that produces no interesting twistronic effects in the normal state can produce dramatic Bogoliubov flat bands when superconducting, because the relevant symmetry changes.

superconductivitytwistronicsflat-bandsBogoliubov-quasiparticlesd-wavematerials-design