Interaction-driven Chern insulating phases in the [Formula: see text] lattice with Rashba spin-orbit coupling

The magnetic interaction is a necessary ingredient to break the time-reversal symmetry in realizing quantum anomalous Hall, or Chern insulating phases. Here, we study topological phases in the [Formula: see text] model, a minimal theoretical model supporting the flat band, taking account of Rashba spin-orbit coupling and flat-band-induced spontaneous ferromagnetism. By analyzing the interaction-driven phase diagrams, band structures, topological edge states, and topological invariants, we demonstrate that this system offers a platform for realizing a wide range of phases, including normal insulators, semimetals, and Chern insulators. Uniquely, there exist both high-Chern-number insulators and valley-polarized Chern insulators. In the latter phase, edge channels exist in the single valley, leading to nearly [Formula: see text] valley polarization. These findings demonstrate the potential of interaction-driven systems in realizing exotic phases and their promising role in future applications in topology electronics and valleytronics.