Beyond-adiabatic flat Chern bands from a double-helix skyrmion crystal

Abstract

A central challenge in flat-band engineering is suppressing kinetic energy without sacrificing Berry curvature. We show that a double-helix skyrmion crystal (DHSKX)--two sublattice-resolved skyrmion textures locked at opposite helicities, obtained here as the classical ground state of a frustrated honeycomb spin model--provides such a route under double exchange. The key mechanism is a single real-space organization, phase clustering: the $\pi$-locked helicities expel the wave function's phase winding from the skyrmion cores, and the magnetic $C_3$ symmetry pins it into three phase-locked clusters whose distributed destructive interference cancels net transport while preserving the Berry curvature. Ordinary skyrmion crystals, even with the same symmetry, do not develop this organization. Phase clustering yields isolated flat $|C| = 1$ Chern bands over broad coupling windows, one of which surpasses the adiabatic reference in quantum geometry at intermediate coupling. In this beyond-adiabatic window, band-projected exact diagonalization gives finite-size evidence consistent with $\nu = 1/3$ Laughlin-type fractional-Chern-insulator physics; the same texture also hosts a higher-Chern ($C = -2$) flat band. Built from site-resolved complex hoppings alone, the DHSKX architecture is directly programmable in topolectric, acoustic, and photonic platforms.