Mapping the unoccupied state dispersions in ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ with resonant inelastic x-ray scattering

The transition metal chalcogenide ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ undergoes a second-order phase transition at $T_c=328\text{K}$ involving a small lattice distortion. Below $T_c$, a band gap at the center of its Brillouin zone increases up to about 0.35 eV. In this work, we study the electronic structure of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ in its low-temperature semiconducting phase, using resonant inelastic x-ray scattering (RIXS) at the Ni $L_3$ edge. In addition to a weak fluorescence response, we observe a collection of intense Raman-like peaks that we attribute to electron-hole excitations. Using density functional theory calculations of its electronic band structure, we identify the main Raman-like peaks as interband transitions between valence and conduction bands. By performing angle-dependent RIXS measurements, we uncover the dispersion of these electron-hole excitations that allows us to extract the low-energy boundary of the electron-hole continuum. From the dispersion of the valence band measured by angle-resolved photoemission spectroscopy, we derive the effective mass of the lowest unoccupied conduction band.

Figure 1

(a) Schematic description of the experimental geometry generated with the VESTA software [15]. (b) XAS spectrum of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$, measured at the Ni $L_3$ edge by total fluorescence yield with $\sigma$-polarized incident light at 30 K and for specular geometry ($Q_{\parallel }=0$). The Brillouin zone of the low-temperature monoclinic phase of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ is shown in the inset.

Figure 2

(a) RIXS map as a function of incident photon energy, measured at the Ni $L_3$ edge with $\sigma$-polarized incident light at 30 K and in near-specular geometry ($Q_{\parallel }=0.06{\text{Å}}^{-1}$). The XAS spectrum of Fig. 1 is recalled on the vertical axis as a red curve. (b) RIXS spectra at selected incident photon energies, shown in the legend. The dashed lines indicate the main fluorescence and Raman-like structures.

Figure 3

(a) Calculated band structure of ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$ along the main high-symmetry directions [see the inset of Fig. 1 for a description of the high-symmetry points]. (b) RIXS spectrum in near-specular geometry ($Q_{\parallel }=0.06{\text{Å}}^{-1}$) for $\hslash {\omega }_{in}=853.3\text{eV}$ measured with $\sigma$-polarized incident light at 30 K. The colored arrows indicate fine structures in the RIXS spectrum that we attribute to specific interband transitions in the band structure of (a). The inset shows a possible extraction of the minimum gap by extrapolating the low-energy cutoff of the RIXS spectrum down to the baseline.

Figure 4

(a) RIXS spectra measured as a function of in-plane momentum $Q_{\parallel }$ along the $\mathrm{\Gamma }X$ direction. These spectra were obtained for $\hslash {\omega }_{in}=853.3\text{eV}$ and with $\sigma$-polarized incident light at 30 K. (b) RIXS map as a function of in-plane momentum $Q_{\parallel }$ along the $\mathrm{\Gamma }X$ direction [same parameters as in (a)]. (c) Example ($Q_{\parallel }=0.06{\text{Å}}^{-1}$) spectrum of (a) of our procedure for extracting the edge of the electron-hole continuum using the second derivative of (smoothed) RIXS spectra. (d) Dispersion of the electron-hole continuum extracted from the RIXS map in (b), together with a parabolic fit near its minimum.