  Kagome metals AV3Sb5 (A=K,Rb,or Cs) exhibit intriguing charge density wave
(CDW) instabilities, which interplay with superconductivity and band topology.
However, despite firm observations, the atomistic origins of the CDW phases, as
well as hidden instabilities, remain elusive. Here, we adopt our newly
developed symmetry-adapted cluster expansion method to construct a
first-principles-based effective Hamiltonian of CsV3Sb5, which not only
reproduces the established inverse star of David (ISD) phase, but also predict
a series of D3h-n states under mild tensile strains. With such atomistic
Hamiltonians, the microscopic origins of different CDW states are revealed as
the competition of the second-nearest neighbor V-V pairs versus the
first-nearest neighbor V-V and V-Sb couplings. Interestingly, the effective
Hamiltonians also reveal the existence of ionic Dzyaloshinskii-Moriya
interaction in the high-symmetry phase of CsV3Sb5 and drives the formation of
non-collinear CDW patterns. Our work thus not only deepens the understanding of
the CDW formation in AV3Sb5,but also demonstrates that the effective
Hamiltonian is a suitable approach for investigating CDW mechanisms, which can
be extended to various CDW systems.
