Compact localized currents in flat bands with broken time-reversal symmetry

We develop a systematic framework for constructing all-bands-flat (ABF) lattice Hamiltonians that explicitly break time-reversal symmetry (TRS). By threading magnetic flux through disconnected polygonal plaquettes and applying local entangling unitary transformations, we map plaquettes onto families of ABF models in one, two, and three dimensions. This procedure preserves the flux configuration while converting semi-detangled geometries into ABF lattices with nontrivial hopping structure. The resulting flat bands admit compact localized states (CLSs) whose support includes both the flux-threaded plaquettes and auxiliary sites introduced by the unitary transformations. In these TRS-broken constructions, the CLSs host localized circulatory currents whose magnitude depends on the applied flux. We further extend the framework to lattices with coexisting flat and dispersive bands, illustrating cases with both orthogonal and non-orthogonal CLSs. Our results provide a controlled route for generating dispersionless lattices supporting flux-induced local currents.