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

TL;DR

This paper presents a systematic method to construct flat band lattice models with broken time-reversal symmetry, enabling the study of localized states with flux-dependent circulatory currents.

Contribution

The authors develop a framework for creating all-bands-flat Hamiltonians with TRS breaking using flux threading and local transformations, expanding the design space of flat band systems.

Findings

Constructed ABF models in 1D, 2D, and 3D with flux threading.

Demonstrated flux-dependent circulatory currents in localized states.

Extended framework to models with coexisting flat and dispersive bands.

Abstract

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.