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Charge density wave order in kagome metal AV$_3$Sb$_5$ (A= Cs, Rb, K)

We employ polarization-resolved electronic Raman spectroscopy and density functional theory to study the primary and secondary order parameters, as well as their interplay, in the charge density wave (CDW) state of the kagome metal AV3Sb5. Previous x-ray diffraction data at 15K established that the CDW order in CsV3Sb5 comprises of a 2x2x4 structure: one layer of inverse-star-of-David and three consecutive layers of star-of-David pattern. We analyze the lattice distortions based the 2x2x4 structure at 15K, and find that U lattice distortion is the primary order parameter while M and L distortions are secondary order parameters for Vanadium displacements. This conclusion is confirmed by the calculation of bare susceptibility that shows a broad peak at around qz=0.25 along the hexagonal Brillouin zone face central line (U-line). We also identify several phonon modes emerging in the CDW state, which are lattice vibration modes related to V and Sb atoms as well as alkali atoms. The detailed temperature evolution of these modes' frequencies, HWHM, and integrated intensities support a phase diagram with two successive structural phase transitions in CsV3Sb5: the first one with a primary order parameter appearing at TS=94K and the second isostructural one appearing at around 70K.