Infrared probe of the charge density wave gap in $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$

The V-based kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$ = K, Rb, Cs) exhibit a cascade of exotic quantum phenomena including charge density wave (CDW) order and superconductivity. Considerable effort has been made to understand the nature of the CDW phase of $A{\mathrm{V}}_3{\mathrm{Sb}}_5$, but the origin remains elusive. A new family of the V-based kagome metals $R{\mathrm{V}}_6{\mathrm{Sn}}_6$ ($R$ = Y, Sc, or rare-earth ions) has attracted recent interest. Among $R{\mathrm{V}}_6{\mathrm{Sn}}_6$, only $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ shows a CDW order. Thus, $R{\mathrm{V}}_6{\mathrm{Sn}}_6$ can be a new platform for investigating the nature of the CDW phase of the V-based kagome metals. Here, combining infrared spectroscopy with density-functional theory (DFT) calculations, we investigate the electronic response of $R{\mathrm{V}}_6{\mathrm{Sn}}_6$ ($R$ = Y, Sc). While the optical conductivity ${\sigma }_1\left(\omega \right)$ spectra of $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ show no anomaly from 10 to 300 K, those of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ exhibit drastic changes below the CDW transition temperature $T_{\mathrm{CDW}}\approx 92\mathrm{K}$: the suppression of the Drude responses and the appearance of the absorption peaks at about 34 and 270 meV. A distinct multipeak structure in the energy region between 270 and 800 meV due to the interband transitions associated with the van Hove singularities (vHSs) at the $M$ point is hardly affected by the CDW transition, implying the robustness of the vHSs at the $M$ point against the CDW transition. Our DFT calculations demonstrate that the vHSs at the $M$ point remain intact in the CDW phase of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and the CDW gaps corresponding to the absorption peak at 270 meV open most clearly on the $k_{\mathrm{z}}=1/3$ and 1/2 planes. The calculated phonon dispersions of the pristine phase of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ reveal that the structural instability with the imaginary phonon frequencies on the A-H-L plane ($k_{\mathrm{z}}=1/2$) and along the $\overline{\mathrm{M}}\text{−}\overline{\mathrm{K}}$ line ($k_{\mathrm{z}}=1/3$) induces the out-of-plane charge modulation, indicating that the CDW transition of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ is associated with its structural phase transition.

Figure 1

Temperature-dependent reflectivity spectra $R$(ω) of (a) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (b) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$. Insets of (a) and (b) display $R$(ω) of $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ below 75 meV, respectively. Temperature-dependent optical conductivity ${\sigma }_1\left(\omega \right)$ below 200 meV of (c) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (d) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$. Temperature-dependent optical conductivity ${\sigma }_1\left(\omega \right)$ below 900 meV of (e) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (f) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$.

Figure 2

Drude-Lorentz oscillator model analyses on ${\sigma }_1\left(\omega \right)$ of (a), (b) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (c), (d) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ at 10 and 300 K, respectively. Solid lines centered at zero energy represent two Drude peaks, D1 and D2. Seven Lorentz oscillators are used to reproduce optical excitations at higher energies, i.e., peaks α, a, $b, A, B, C$, and D. Insets show fitting results below 200 meV. Temperature-dependent SWs and widths of the peaks D1, D2, and Α for $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ (e), (f), (g) and $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ (h), (i), (g). Insets of (h) and (i) show sum of the SWs of peaks D1 and α and SWs of peaks D2 and $A$, respectively. Dashed lines in (h), (i), and (j) denote the CDW transition temperature $T_{\mathrm{CDW}}$ of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$.

Figure 3

Difference ${\sigma }_1\left(\omega \right)$ spectra ${\sigma }_1\left(T\right)-{\sigma }_1\left(300\mathrm{K}\right)$ of (a) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (b) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$. Optical spectral weights (SWs) of (c) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (d) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$. (e) Difference ${\sigma }_1\left(\omega \right)$ spectra ${\sigma }_1\left(T\right)-{\sigma }_1\left(100\mathrm{K}\right)$ of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$. Red and orange arrows indicate zero crossing and maximum of ${\sigma }_1\left(T\right)-{\sigma }_1\left(100\mathrm{K}\right)$ spectra, respectively. (f) Temperature dependence of CDW gap $\left(2{\mathrm{\Delta }}_{\mathrm{CDW}}\right)$ obtained from zero crossing (red circles) and maximum of transferred peak (orange triangles).

Figure 4

 ${\sigma }_1\left(\omega \right)$ of (a) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (b) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ in energy region between 200 and 900 meV. Data are shifted vertically for clarity. Temperature dependences of resonance energies of peaks $A, B, C$, and $D$ are highlighted by arrows. Electronic band structures of (c) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (d) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ for pristine phase. Interband transitions corresponding to peaks $A, B, C$, and $D$ are denoted by vertical arrows. (e) Calculated interband optical conductivity of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ for pristine and CDW phases. (f) Experimental interband optical conductivity of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ at 100 K (pristine phase) and 10 K (CDW phase).

Figure 5

Calculated phonon dispersions of (a) $\mathrm{Y}{\mathrm{V}}_6{\mathrm{Sn}}_6$ and (b) $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ for the pristine phase along the Γ−Μ−Κ ($k_{\mathrm{z}}=0$), A-H-L ($k_{\mathrm{z}}=1/2$) (left panel), and $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{M}}\text{−}\overline{\mathrm{K}}$ paths ($k_{\mathrm{z}}=1/3$) (right panel). Unfolded electronic band structures of $\mathrm{Sc}{\mathrm{V}}_6{\mathrm{Sn}}_6$ in pristine and $\sqrt{3}\times \sqrt{3}\times 3$ CDW phases for (c) $k_{\mathrm{z}}=0$, (d) $k_{\mathrm{z}}=1/3$, and (e) $k_{\mathrm{z}}=1/2$. Band shift on $k_{\mathrm{z}}=0$ plane and CDW gap openings on $k_{\mathrm{z}}=1/3$ and $k_{\mathrm{z}}=1/2$ planes are indicated by red arrows in (c), (d), and (e), respectively.