Symmetries of charge density wave states in AV₃Sb₅ Kagome compounds

Vanadium based Kagome metals AV₃Sb₅ undergo structural phase transitions driven by instabilities at the boundary of their hexagonal Brillouin zones. First principles calculations predict these instabilities to have wavevectors at the M and L points, as well as the U line connecting them. There is a large number of possible low symmetry crystal structures, and the ground state structure is still heavily debated. We perform an analysis of the crystal structure of AV₃Sb₅ compounds using a combination of group theory and density functional theory calculations. We determine the form of the crystal Hamiltonian, discuss the effects of the unique trilinear couplings, and sketch possible phase diagrams with multiple symmetry-broken phases.