Exotic charge-density waves and superconductivity on the kagome lattice

Loop current order has long been pursued in various electronic systems, including cuprates and honeycomb lattice materials, but its realization remains elusive in both experiment and theory. Intriguingly, recent experimental evidence for AV[Formula: see text]Sb[Formula: see text] (A = K, Rb, Cs) and related kagome metals hints at the formation of orbital currents in the charge-density wave-ordered regime, providing a mechanism for spontaneous time-reversal symmetry breaking in the absence of local moments. However, concrete theoretical model realizations of the loop-current order in the kagome lattice have been very challenging and remain an outstanding, unresolved problem. In this work, we comprehensively explore the competitive charge instabilities of the spinless kagome lattice with inter-site Coulomb interactions at the pure-sublattice van Hove filling. From the analysis of the charge susceptibility, we find that, at the nesting vectors, while the onsite charge order is dramatically suppressed, the bond charge orders are substantially enhanced owing to the sublattice texture on the hexagonal Fermi surface. Furthermore, we demonstrate that nearest-neighbor and next-nearest-neighbor bonds are characterized by significant intrinsic real and imaginary bond fluctuations, respectively. The [Formula: see text] loop-current order is thus favored by the next-nearest-neighbor Coulomb repulsion. Interestingly, increasing interactions further leads to a nematic state with intra-cell sublattice density modulation that breaks the [Formula: see text] rotational symmetry. We further explore superconducting orders arising from onsite and bond charge fluctuations, and discuss our model's implications for the experimental status quo.