Hard X-ray photoelectron spectroscopy of the charge-density wave system Ce$_{\mathrm{3}}$Co$_{\mathrm{4}}$Sn$_{\mathrm{13}}$

We study the electronic structure of the charge density wave (CDW ; T$_{\mathrm{CDW}}$ \textasciitilde 155 K) system Ce$_{\mathrm{3}}$Co$_{\mathrm{4}}$Sn$_{\mathrm{13}}$[1,2] using bulk-sensitive Hard X-ray photoelectron spectroscopy (HAXPES ; h$\nu $ \textasciitilde 6.480 keV). We measure the core-levels and valence band spectra of Ce$_{\mathrm{3}}$Co$_{\mathrm{4}}$Sn$_{\mathrm{13}}$ above and below the CDW transition, at T $=$ 170 K and T $=$ 20 K, respectively. While the Ce 3d core-levels show negligible changes, the Co 2p and Sn 3p core-levels show a small but finite increase in the peak-widths and binding energies in the CDW phase. The behavior of the Ce 3d and Co 2p core levels are consistent with a recent x-ray fluorescence study at the Ce L$_{\mathrm{3}}$-edge and Co K-edge[2]. Based on known atomic cross-sections, the HAXPES valence band spectra are not sensitive to Ce 4f partial density of states but show a feature at about 1.5 eV binding energy, which is attributed to Co 3d partial density of states. The valence band spectra show a clear Fermi edge even in the CDW phase, consistent with the metallic behavior observed by electrical resistivity[1]. The results indicate very weak charge-disproportionation in Ce$_{\mathrm{3}}$Co$_{\mathrm{4}}$Sn$_{\mathrm{13}}$ across the CDW transition. References : [1] C. S. Lue et al. Phys. Rev. B 85, 205120 (2012). [2] Y. Otomo et al. Phys . Rev. B 94, 075109 (2016).