Kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, 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 ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, which not only reproduces the established inverse star of David (ISD) phase, but also predict a series of $D_{3h}\text{−}n$ 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 ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and drives the formation of noncollinear CDW patterns. Our work thus not only deepens the understanding of the CDW formation in ${\mathrm{AV}}_3{\mathrm{Sb}}_5$, but also demonstrates that the effective Hamiltonian is a suitable approach for investigating CDW mechanisms, which can be extended to various CDW systems.

• Received 16 February 2023
• Revised 22 October 2023
• Accepted 5 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.096101