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 15 K established that the CDW order in CsV3Sb5 comprises of a 2×2×4 structure: one layer of inverse-star-of-David and three consecutive layers of star-of-David pattern. We analyze the lattice distortions based on the 2×2×4 structure at 15 K, and find that the U1 lattice distortion is the primarylike (leading) order parameter while M1+ and L2- distortions are secondarylike order parameters for vanadium displacements. This conclusion is confirmed by the calculation of bare susceptibility χ0′(q) 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-metal atoms. The detailed temperature evolution of these modes' frequencies, half-width at half-maximums, and integrated intensities support a phase diagram with two successive structural phase transitions in CsV3Sb5: the first one with a primarylike order parameter appearing at TS=94K and the second isostructural one appearing at around T∗=70K. Furthermore, the T dependence of the integrated intensity for these modes shows two types of behavior below TS: the low-energy modes show a plateaulike behavior below T∗ while the high-energy modes monotonically increase below TS. These two behaviors are captured by the Landau free-energy model incorporating the interplay between the primarylike and the secondarylike order parameters via trilinear coupling. Especially, the sign of the trilinear term that couples order parameters with different wave vectors determines whether the primarylike and secondarylike order parameters cooperate or compete with each other, thus determining the shape of the T dependence of the intensities of Bragg peak in x-ray data and the amplitude modes in Raman data below TS. These results provide an accurate basis for studying the interplay between multiple CDW order parameters in kagome metal systems.
Bibliographical noteFunding Information:
The spectroscopic work conducted at Rutgers (S.-F.W. and G.B.) was supported by NSF Grants No. DMR-1709161 and No. DMR-2105001. The sample growth and characterization work conducted at UC Santa Barbara (B.R.O. and S.D.W.) was supported by the UC Santa Barbara NSF Quantum Foundry funded via the Q-AMASE-i program under Award No. DMR-1906325. B.R.O. also acknowledges support from the California NanoSystems Institute through the Elings fellowship program. The DFT phonon and bare susceptibility calculations work conducted at Weizmann Institute of Science (H.X.T. and B.H.Y.) was supported by the European Research Council (ERC Consolidator Grant “NonlinearTopo”, No. 815869), the ISF-Quantum Science and Technology (Grant No. 1251/19). The theoretical work conducted at the University of Minnesota (T.B.) was supported by the NSF CAREER Grant No. DMR-2046020. The work at NICPB was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme Grant Agreement No. 885413.
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