The structure of kagome superconductors CsV${}_3$Sb${}_5$ in the charge density wave states

The structure of charge density wave states in AV${}_3$Sb${}_5$ (A = K, Rb, Cs) kagome superconductors remains elusive, with three possible $2a\times 2a\times 2c$ candidates: tri-hexagonal, star-of-David, and their mixture. In this study, we conducted a systematic first-principles investigation of the nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR) spectra for the $2a\times 2a\times 2c$ CsV${}_3$Sb${}_5$ structures. By comparing our simulations with experimental data, we have concluded that the NQR spectrum indicates the tri-hexagonal structure as the proper structure for CsV${}_3$Sb${}_5$ after its charge density wave phase transition. The NMR calculation results obtained from the tri-hexagonal structure are also consistent with the experimental data.