Low-energy optical properties of the nonmagnetic kagome metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$

Temperature-dependent reflectivity measurements on the kagome metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ in a broad frequency range of $50-20000{\mathrm{cm}}^{-1}$ down to $T$=10 K are reported. The charge-density wave (CDW) formed below $T_{\mathrm{CDW}}$ = 94 K manifests itself in a prominent spectral-weight transfer from low to higher energy regions. The CDW gap of 60–75 meV is observed at the lowest temperature and shows significant deviations from an isotropic BCS-type mean-field behavior. Absorption peaks appear at frequencies as low as 200 ${\mathrm{cm}}^{-1}$ and can be identified with interband transitions according to density-functional calculations. The change in the interband absorption compared to ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ reflects the inversion of band saddle points between the K and Cs compounds. Additionally, a broader and strongly temperature-dependent absorption feature is observed below 1000 ${\mathrm{cm}}^{-1}$ and assigned to a displaced Drude peak. It reflects localization effects on charge carriers.

Figure 1

(a) Temperature-dependent reflectivity in the $ab$ plane. (b) Calculated optical conductivity in a broad frequency and temperature range. Inset: dc-resistivity measured on the same crystal as used in the optical measurements, overlaid with the values obtained from the Hagen-Rubens fit of the reflectivity. First derivative of the dc-resistivity curve marks the CDW transition at 94 K. (c) Temperature- and frequency-dependent dielectric permittivity. Zero crossing, the screened plasma frequency, is marked in the inset and shows a clear blueshift below $T_{\mathrm{CDW}}$. Temperature dependence of the plasma frequency is also shown, demonstrating the clear increase across the CDW transition.

Figure 2

(a) Difference optical-conductivity $[\mathrm{\Delta }{\sigma }_1={\sigma }_1\left(T\right)-{\sigma }_1\left(100\text{K}\right)]$ spectra in the CDW region. The 100 K data measured right above the transition are chosen as the base curve. The zero crossing in the difference curves marks the CDW gap (note that the optical measurements detect the transitions across the Fermi energy and hence the observed value corresponds to $2\mathrm{\Delta }$). (b) Optical conductivity at the absorption edge. The extrapolation of the steepest part to the frequency axis is taken as the $2\mathrm{\Delta }$ (c) Temperature dependence of the gap obtained from the zero crossing and the extrapolation of the absorption edge clearly deviates from the BCS-type mean-field behavior (solid lines) above 50 K.

Figure 3

Low-energy optical conductivity for selected temperatures. The thin-solid lines are Drude-Lorentz fits to the optical conductivity as described in the text. Please note that for 10 K spectrum, the localization peak cannot be observed but is estimated based on the linear shift with respect to the peaks observed at higher temperatures. The solid circles are the dc conductivity values. Orange arrows show the low-energy absorption bands, while the green arrow demonstrates the spectral weight transfer to a peak below $T_{\mathrm{CDW}}$.

Figure 4

(a) A sample decomposition of the optical conductivity at room temperature consists of a Drude peak (green), a localization peak (blue), and multiple peaks due to interband transitions (orange). (b) The temperature dependence of the localization peak obtained by subtracting the Drude and interband contributions from the experimental optical conductivity. The fits to the localization peak are also shown as a guide to the eye. Inset: Temperature evolution of the peak position.

Figure 5

(a) Temperature-dependent total spectral weight. The overall SW is conserved within the measured energy range. (b) Temperature dependence of the localization peak SW obtained by the integration of the Lorentzian fits to the experimental curves shown in Fig. 4. An abrupt decrease in the SW across $T_{\mathrm{CDW}}$ is visible.

Figure 6

(a) Band structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. (b) Band-resolved optical conductivity. (c) Experimental interband transitions at 100 K (normal state) and at 10 K (CDW state). Orange and green arrows mark, respectively, the peak positions of the interband transitions and the spectral weight transfer toward higher energies below $T_{\mathrm{CDW}}$. (d) Calculated optical conductivity in the normal and CDW states given for two types of distortions (star-of-David and tri-hexagonal). Right panel shows the undistorted (normal state) and distorted (CDW) structures.

Figure 7

(a) Normal-state interband transitions in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and ${\mathrm{KV}}_3{\mathrm{Sb}}_5$, as seen experimentally (symbols) and calculated with DFT (lines). Experimental data are taken at 100 K for ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and 90 K for ${\mathrm{KV}}_3{\mathrm{Sb}}_5$, right above $T_{\mathrm{CDW}}$. (b) A comparison of the ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ band structures in the $k_z=0$ plane. Note the difference around $M$ in the vicinity of the saddle points.