Novel electronic orders on the kagome lattice near van Hove singularities

The kagome lattice is unique in that Dirac bands, van Hove singularities, and flat band are all present in the band structure. In particular, the Bloch states near the upper van Hove points are sublattice polarized, while they are pair-wise mixed in sublattice contents near the lower van Hove points. These features, combined with correlation effects, may lead to novel electronic orders. We briefly review our theoretical investigations on the kagome lattice near the van Hove fillings by the singular-mode functional renormalization group, quantum Monte Carlo, and effective mean field theory. We establish rich phases of the model under extended Hubbard interactions or Su-Schrieffer-Heeger-like electron-phonon coupling. Among these phases, three types of 2×2 orders are of particular interest. Near the upper van Hove filling, we predicted the 2 × 2 charge bond order in 2013, which is highly relevant in AV₃Sb₅ (A=K,Rb,Cs) kagome materials. In the superconducting channel, we constructed a self-consistent theory for the 2×2 pair density wave, which is made possible by the sublattice polarization and attractive pairing interaction on the nearest neighbor bonds, predicting anisotropic energy gap in momentum space and quantized thermal Hall conductance in the chiral case of the pair density wave, which are consistent with recent photoemission and transport experiments. Near the lower van Hove filling, we further predicted a topological 2 × 2 non-collinear antiferromagnetic state with spins on neighboring sites orthogonal as Cartesian axes in three dimensions, which is a Chern insulator supporting quantized thermal Hall conductance.