Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 (A=K, Rb, Cs)

We investigate how the real and imaginary charge density waves interplay at the Van Hove singularity on the hexagonal lattices. A phenomenological analysis indicates the formation of 3Q complex orders at all three nesting momenta. Under a total phase condition, unequal phases at the three momenta break the rotation symmetry generally. The 3Q complex orders constitute a rich Haldane-model phase diagram. When effective time-reversal symmetries arise under 1-site translations, the Dirac semimetals are protected. The breakdown of these symmetries gaps the Dirac points and leads to the trivial and Chern insulator phases. These phases are deformations of purely real and imaginary orders, which exhibit trivial site and/or bond density and chiral flux orders, respectively. The exotic single-Dirac-point semimetals also appear along the gapless phase boundary. We further show that the theoretical model offers transparent interpretations of experimental observations in the kagome metals AV(3)Sb(5) with A = K, Rb, Cs. The topological charge density waves may be identified with the complex orders in the Chern insulator phase. Meanwhile, the lower-temperature symmetry-breaking phenomena may be interpreted as the secondary orders from the complex order ground states. Our work sheds light on the nature of the topological charge density waves in the kagome metals AV(3)Sb(5) and may offer useful indications to the experimentally observed charge orders in the future experiments.

Automated summary

The study investigates the interaction between real and imaginary charge density waves at the Van Hove singularity on hexagonal lattices. It reveals the formation of 3Q complex orders and the rich phase diagram they constitute. The theoretical model offers transparent interpretations of experimental observations in kagome metals and sheds light on the nature of topological charge density waves.