T-breaking density wave order in topological kagome metals

Kagome lattice metals $AV_ 3 Sb_ 5$ (A = Cs, K, Rb) host charge order derived from partially filled topologically non-trivial bands. In addition, recent muon spin resonance (muSR) measurements in $CsV_ 3 Sb_ 5$ detect an unambiguous signature of broken time reversal (T-) symmetry in the charge order phase. In this talk, I will address the question: what is the character of emergent correlated phases derived from partially filled Chern bands? I will advance a framework which enables a low energy tight-binding description of such a system using exponentially localized Wannier orbitals. The key conclusion is the existence of a density wave ground state that spontaneously breaks T - symmetry. I will argue that such a T-breaking property of the density wave is a fingerprint of the underlying band topology and is absent in other topologically trivial systems (arXiv:2105.15204).