Competing orders in kagome metals AV₃Sb₅

A family of vanadium-based compounds AV3Sb5 (A = K, Rb, Cs) has recently emerged as a paradigmatic material to study diverse exotic states, including quantum spin liquids, time-reversal symmetry broken charge orderings, and chiral superconductivity. Despite prior exhaustive discoveries, a kagome lattice in genuine two dimensions is elusive, as all the known kagome materials are a three-dimensional approximant in a layered structure. In this work, we theoretically demonstrate that the AV₃Sb₅ monolayer can be stable and a host of strong electronic correlations from enriched van Hove singularities by using first-principles and mean-field calculations. Most importantly, the symmetry of two-dimensional monolayer is lowered enforced by stoichiometry which gives rise to the type-II van Hove singularities.We found that enrichment of the van Hove singularities leads to a variety of instabilities such as 2x2 charge density waves (CDW), s- and d-wave superconductivity orders, and the competing physics can be tuned via electron-filling or interaction strength. In connection with future experiments, we calculate the anomalous Hall conductivity that can probe the correlated orders. Lastly, we discuss plausible scenarios of nematicity in bulk system reported by recent experiments by unveiling the role of interlayer coupling based on the Ginzburg-Landau theory.