Materials with a kagome lattice, a two-dimensional network of corner-sharing triangles, exhibit a rich array of phenomena, including quantum magnetism, Dirac fermions, nontrivial topology, density waves, and superconductivity. The recently discovered kagome metals AV₃Sb₅ (A = K, Rb, or Cs) represent a particularly exciting new platform to study the interplay of these phenomena. These compounds possess Fermi levels near Dirac points or van Hove singularities, creating a landscape ripe for various intriguing ground states. Indeed, the coexistence of charge density waves (CDWs) and superconductivity has been observed, with strong evidence suggesting that both orders are unconventional. For example, the CDW transition is possibly accompanied by a large anomalous Hall effect, and the superconductivity features a pair-density wave state. The nature of the CDW state and its formation mechanism in AV₃Sb₅ have been the subject of intense investigation. This study focuses on CsV₃Sb₅, which undergoes a CDW transition at *T*_CDW ≈ 94 K. Hard X-ray and neutron scattering experiments have failed to detect soft phonons, phonon modes whose frequencies soften as the temperature approaches the transition temperature, a hallmark of many known CDW systems. While density functional theory (DFT) calculations predict phonon instabilities, the absence of experimental evidence for soft modes in CsV₃Sb₅ challenges the conventional understanding of CDW formation, where a soft phonon condenses at zero frequency, triggering the lattice distortion that characterizes the CDW state. This discrepancy raises fundamental questions about the interplay between Fermi surface nesting, electron-phonon coupling, and the lattice degree of freedom in the formation of the CDW in these kagome materials. The lack of consensus on the in-plane structure and *c*-axis periodicity further complicates the picture. The 2 × 2 modulation of the crystal lattice observed in CsV₃Sb₅ has led to suggestions that Fermi surface nesting at the van Hove singularity plays a central role in driving the CDW transition. However, the calculated electronic susceptibility doesn’t display the expected divergence, and the influence of electron-phonon coupling cannot be ignored. Because the CDW involves lattice distortions, probing the lattice degrees of freedom is crucial to understanding the underlying mechanism. Raman scattering spectroscopy, which is sensitive to changes in lattice vibrations, provides a powerful tool to investigate this aspect. In well-understood CDW systems, such as transition metal dichalcogenides, the appearance of amplitude modes, collective excitations that emerge from the condensation of a soft phonon, serves as direct evidence of CDW order and a key probe of the CDW order parameter. The temperature dependence of these amplitude modes, along with zone-folded modes (phonon modes that become Raman active due to the CDW-induced superlattice), offers valuable insight into the CDW transition. This study uses Raman scattering to investigate the CDW state in CsV₃Sb₅, aiming to elucidate the roles of lattice distortions and electron-phonon coupling in the CDW formation.

Extensive research has explored charge density waves (CDWs) in various materials, establishing a framework based on soft phonon condensation as the primary driving force. The classic example is found in transition metal dichalcogenides (TMDs) where phonon softening precedes the CDW transition, and the subsequent appearance of amplitude modes provides direct spectroscopic evidence for CDW order. This established paradigm posits that a divergence in electronic susceptibility, often attributed to Fermi surface nesting, leads to a Kohn anomaly—a dip in the phonon dispersion relation—that ultimately culminates in the soft phonon's condensation. The amplitude mode frequency is directly linked to the strength of the electron-phonon coupling and the CDW order parameter, providing valuable insights into the CDW's nature. However, recent discoveries challenge this established framework, particularly in unconventional CDWs exhibiting unique properties such as the coexistence of CDW and superconductivity. The kagome metal family AV₃Sb₅ exemplifies this trend, showing a CDW transition without clear evidence of phonon softening. Theoretical investigations have explored competing mechanisms such as Fermi surface nesting, electron-phonon interaction, and interplay between electronic and lattice degrees of freedom. Studies have used various experimental techniques, including hard X-ray diffraction, neutron scattering, and angle-resolved photoemission spectroscopy (ARPES), to probe the electronic structure and lattice dynamics of these materials. DFT calculations have also attempted to explain the observed CDW states, focusing on various possible lattice distortions and their correlation with electronic properties. Despite these efforts, a unified and consistent understanding of CDW formation in these materials is yet to be achieved, emphasizing the need for further investigations.

Single crystals of CsV₃Sb₅ were synthesized using the flux method, and Raman scattering spectroscopy was employed to study the lattice dynamics. Measurements were performed using home-built confocal microscopy setups in a back-scattering geometry with 532 nm laser excitation. The scattered light was analyzed using a grating spectrograph and a liquid-nitrogen-cooled charge-coupled device. The samples were mounted in a vacuum chamber to maintain a controlled environment, and temperature control was achieved using a Montana Instrument Cryostation, allowing for investigation across a range of temperatures. Polarization-resolved Raman measurements were conducted using various polarization configurations (XX, XY, LL, LR) to determine the symmetry of the observed vibrational modes. The acquired spectra were fitted with Lorentzian functions to extract the frequency, linewidth, and integrated intensity of the Raman peaks. The temperature dependence of these parameters was then carefully analyzed to identify CDW-induced modes and distinguish between amplitude modes and zone-folded modes. Density functional theory (DFT) calculations were performed using the Vienna ab-initio Simulation Package (VASP) to obtain phonon dispersion relations. The Perdew-Burke-Ernzerhof (PBE)-type generalized gradient approximation (GGA) method was employed, along with projected augmented wave (PAW) potentials and the DFT-D3 correction to account for van der Waals interactions. The calculations considered different possible lattice distortions, including Star of David (SD) and inverse Star of David (ISD) structures, allowing for a comparison with the experimentally observed Raman modes. The analysis involved computing the vibrational patterns and symmetries of the modes, facilitating the identification of amplitude modes arising from soft phonon modes, even without the direct observation of phonon softening. Finally, mode mixing was investigated by calculating the overlap between the predicted soft modes and the real modes of the stable ISD phase using eigenvector projections to quantify the degree of hybridization between amplitude modes and zone-folded modes.

This study reports the observation of Raman-active CDW amplitude modes in CsV₃Sb₅. Multiple CDW-induced modes were observed below the CDW transition temperature (*T*_CDW ≈ 94 K), and their symmetries and frequencies were found to be consistent with DFT calculations for a single-layer CsV₃Sb₅ with an inverse Star of David (ISD) lattice distortion. The temperature dependence of these modes revealed two distinct behaviors. One set of modes, labeled A₂, exhibited significant softening and broadening as the temperature approached *T*_CDW, characteristics consistent with CDW amplitude modes. Another set of modes, labeled E₃, showed minimal frequency shift and broadening, consistent with zone-folded modes. However, a crucial finding is that the amplitude modes and the zone-folded modes are strongly hybridized, a phenomenon rarely observed in other CDW materials. This hybridization leads to a redistribution of spectral weight, imparting amplitude-mode-like properties to the zone-folded modes. DFT calculations revealed that the CDW formation in CsV₃Sb₅ is similar to that in other CDW systems, involving the condensation of a soft phonon mode at the CDW wavevector. Although experimental soft phonon modes were not directly detected, DFT predicted soft modes at the M points of the Brillouin zone that transform as the irreducible representation M(A_g). Upon CDW distortion, these imaginary soft modes become real modes with positive frequencies, corresponding to the observed amplitude modes. These amplitude modes, however, strongly hybridize with zone-folded modes, making their experimental detection challenging. The real space displacement patterns of the soft modes and the CDW-induced Raman modes were calculated and compared to clarify their relationship and the extent of their hybridization. The strength of hybridization is quantified by calculating the projection of the imaginary soft mode onto other phonon modes in the stable ISD phase. The large amplitude mode frequencies and the anomalous hybridization suggest a strong-coupling CDW regime in CsV₃Sb₅, which could explain the absence of experimentally observable soft phonons. Several criteria support this strong coupling scenario: a large CDW-induced gap, substantial lattice distortion, the formation of V atom clusters, the commensurate nature of the CDW structure, and a double-minimum elastic potential for the ions. A comparison of the amplitude mode frequencies of CsV₃Sb₅ with other CDW materials further supports the strong-coupling picture.

The observation of Raman-active CDW amplitude modes in CsV₃Sb₅, despite the absence of experimentally observed soft phonons, highlights the complexity of CDW formation in this kagome metal. The strong hybridization between amplitude modes and zone-folded modes is unusual, suggesting indirect coupling through the electronic system. This suggests that the conventional weak-coupling picture, where soft phonon condensation drives the CDW transition, may not fully capture the physics of CsV₃Sb₅. Instead, the findings strongly support a strong-coupling scenario, where the electron-phonon interaction plays a dominant role. The strong coupling could suppress phonon softening, while the hybridization between different modes might obscure the signature of the soft mode in Raman scattering experiments. The results reconcile previously conflicting observations: the absence of experimental soft phonons and the evidence for an electronically driven CDW. The strong electron-phonon coupling, manifested in the large amplitude mode frequencies and the significant mode mixing, is a key factor determining the CDW characteristics. This work adds to the growing body of evidence challenging the traditional understanding of CDW formation and encourages further investigation into the interplay between electron-phonon coupling, Fermi surface instabilities, and lattice distortions in determining the ground state of kagome metals.

This study reveals the existence of Raman-active CDW amplitude modes in CsV₃Sb₅, a kagome metal that lacks experimentally observable soft phonons. The strong hybridization between amplitude modes and zone-folded modes strongly suggests a strong-coupling CDW regime. The findings provide crucial insights into the complex interplay between electron-phonon coupling and lattice distortions in driving the CDW transition, challenging the conventional weak-coupling paradigm. Future research should explore the interplay between CDW amplitude modes and superconducting Higgs modes in these materials, and investigate the potential for controlling these symmetry-breaking states using ultrafast optical techniques.

The study primarily focuses on bulk crystals of CsV₃Sb₅, and the Raman scattering technique probes the bulk properties of the material. Surface effects, which may influence the CDW order, are not directly addressed. While DFT calculations provide valuable insights into the lattice dynamics, approximations inherent in the computational methods might affect the accuracy of the results. The strong hybridization between amplitude modes and zone-folded modes makes it difficult to definitively isolate and characterize individual modes. This limitation necessitates a combined experimental and theoretical approach, using different experimental techniques to corroborate the conclusions. Future studies could explore the use of other experimental probes sensitive to surface properties and the effects of reduced dimensionality, enhancing our understanding of the CDW mechanism.