Observation of anomalous amplitude modes in the kagome metal CsV3Sb5

Abstract

The kagome lattice provides a fertile platform to explore novel symmetry-breaking states. Charge-density wave (CDW) instabilities have been recently discovered in a new kagome metal family, commonly considered to arise from Fermi-surface instabilities. Here we report the observation of Raman-active CDW amplitude modes in CsV₃Sb₅, which are collective excitations typically thought to emerge out of frozen soft phonons, although phonon softening is elusive experimentally. The amplitude modes strongly hybridize with other superlattice modes, imparting them with clear temperature-dependent frequency shift and broadening, rarely seen in other known CDW materials. Both the mode mixing and the large amplitude mode frequencies suggest that the CDW exhibits the character of strong electron-phonon coupling, a regime in which phonon softening can cease to exist. Our work highlights the importance of the lattice degree of freedom in the CDW formation and points to the complex nature of the mechanism.

Fig. 1. Raman-active phonon modes in CsV₃Sb₅.

a Schematic illustration of the relation between the soft mode and amplitude mode in typical CDW materials, showing the latter emerges after the former freezes below T_CDW. ω_AM: amplitude mode frequency. ω_SM: soft mode frequency. b Crystal structure of CsV₃Sb₅. Sb sites with different Wyckoff positions are labeled as Sb1 and Sb2. The arrows illustrate the vibration patterns of the main lattice A_1g and E_2g modes. The E_2g mode is doubly degenerate, and only one form is shown. c, d Raman spectra measured on the ab-plane at 100 K and 4 K in the LL and LR polarization configurations. The dashed lines denote the main lattice phonons, and the dotted lines indicate the CDW-induced modes. e Comparison of the measured (Expt.) and the calculated Raman mode frequencies for the inverse Star of David (ISD) and Star of David (SD) lattice distortions. The thick lines denote the main lattice phonons. The dots indicate modes undetected in our experiment.

Fig. 2. Evolution of the Raman modes in CsV₃Sb₅ across the CDW transition.

a, b Temperature-dependent Raman intensity color plot for CsV₃Sb₅, measured in the LL and LR configurations. The normal phonon modes are labeled in black and the CDW-induced modes in white. The dashed lines mark T_CDW. c, d Temperature-dependent spectra for the A₂ and E₃ modes. e–g Frequency, linewidth, and amplitude for the E_2g and A_1g main lattice phonons. The frequency and amplitude are compared to the corresponding values at 200 K. h Temperature dependence of the Raman mode frequencies. i Temperature dependence of the linewidth of the A₂ and E₃ modes. Error bars are standard deviations obtained from the least-squares fits to the phonon peaks.

Fig. 3. Phonon band structures and mode mixing in the process of CDW distortion.

a Phonon band structures directly calculated by DFT. Here, 100% (0%) refers to the fully stable ISD (2 × 2 pristine) structure. 10% refers to the intermediate structure with 10% distortion from the pristine to ISD phases. After 2 × 2 × 1 band folding with no distortion, three imaginary modes ($M_1^{+}$) are folded to Γ. A weak ISD-type distortion lifts the degeneracy and leads to A_1g and E_2g modes. The ISD distortion gradually transforms imaginary modes to real. b Projections of the imaginary A_1g (E_2g) mode with 10% distortion to all the other phonon modes at Γ, as evolving into the stable ISD phase (100%). We highlight all A_1g and E_2g modes by orange and blue dots, respectively, at the Γ point. The dashed orange (blue) curve in (b) guides eyes to show the evolution of the imaginary A₂ (E₁) modes in the CDW distortion.

Fig. 4. Real space displacement patterns of the imaginary soft modes and the stable CDW-induced Raman modes in the 2 × 2 × 1 ISD phase.

a, b Soft modes with A_1g and E_2g symmetries, respectively. c, d CDW-induced A_1g and E_2g stable modes. The E_2g modes are pairs of chiral phonons and only one chiral mode is shown. The radius of the circles represents the amplitude of the vibration, and the arrow on the circles stands for the initial phase of the vibration. Cs atoms are omitted in the crystal structure for clarity, because they do not contribute to lattice vibrations.

Fig. 5. Evidence of strong-coupling CDW in CsV₃Sb₅.

Frequency of the amplitude mode ω_AM in the zero-temperature limit and the unscreened frequency of the soft mode ${\omega }_{\mathrm{SM}}^0$ far above T_CDW for a collection of CDW materials. Some of the materials feature two amplitude modes, hence two data points connected by a vertical line. Since no soft mode is observed in CsV₃Sb₅, ${\omega }_{\mathrm{SM}}^0$ is taken to be its acoustic phonon frequency at 300 K. Open (filled) symbols indicate the material is quasi-1D (quasi-2D). The dashed lines mark electron–phonon coupling constant λ = 1 and 3 according to mean-field theory. Source of data: ZrTe₃^,, TbTe₃^,, K_0.3MoO₃^,, 1T-TiSe₂^,, 2H-TaSe₂^,,, 2H-NbSe₂^–.