Influence of $k_{\perp }$ broadening on ARPES spectra of the (110) and (001) surfaces of ${\mathbf{SrVO}}_{\mathbf{3}}$ films

To examine the effect of $k_{\perp }$ broadening on angle-resolved photoemission spectroscopy (ARPES) spectra, in situ ARPES using the variable polarization of synchrotron light has been performed for the (110) and (001) surfaces of ${\mathrm{SrVO}}_3$ films. Using the polarization dependence for the band structures of the V $3d{t}_{2g}$ states, we have separately observed the $d_{xy}$-derived states and the $d_{yz}/d_{zx}$ ones for the (110) surface. It is found that ARPES images for the $d_{yz}/d_{zx}$ states are considerably broader than those for the $d_{xy}$ states. Meanwhile, such a broadening is not observed in the identical $d_{yz}/d_{zx}$-derived band dispersion along the crystallographically equivalent direction on the (001) surface, indicating that the broadening of the ARPES image originates from the absence or presence of mirror symmetry in the respective states with respect to the ARPES-measurement planes. The observed spectroscopic behavior is well reproduced by the simulation where the $k_{\perp }$ broadening in the photoelectron emission process is taken into account. These results indicate that the consideration of the mirror symmetry of the band structures with respect to the ARPES-measurement plane is important for analyzing the ARPES-spectral line shape in the case that the $k_{\perp }$-broadening effect is dominant in ARPES spectra.

Figure 1

Schematic of the FSs of ${\mathrm{SrVO}}_3$ at (a) the (110) surface and (b) the (001) surface. Cylindrical FSs of the $d_{xy}$ (blue), $d_{yz}$ (green), and $d_{zx}$ (red) orbitals cross each other at the $\mathrm{\Gamma }$ point. The yellow plates in (a) and (b) represent the $\mathrm{\Gamma }MRX$ and $\mathrm{\Gamma }MX$ planes where the ARPES spectra are measured (ARPES-measured planes). The orange arrow indicates the crystallographically equivalent $\mathrm{\Gamma }-M$ direction. (c) LEED pattern obtained at the (110) surface of the ${\mathrm{SrVO}}_3$ films. The sharp $1\times 1$ spots with surface-reconstruction-derived $1\times 6$ spots are clearly observed. (d) LEED pattern obtained at the (001) surface. The sharp $1\times 1$ spots are also observed in addition to the surface-reconstruction-derived $c(2\times 2)$ spots.

Figure 2

Out-of-plane FSs of ${\mathrm{SrVO}}_3$ (110) films determined from the normal-emission ARPES measurements. (a) BZ of the SVO (110) surface. Normal-emission ARPES measurements were performed for the $\mathrm{\Gamma }MX$ emission plane (hatched by blue). (b) FSs calculated from the TB calculation for the ARPES emission (the $\mathrm{\Gamma }MX$) plane. The blue circle FS centered at the $\mathrm{\Gamma }$ point originates from the $d_{xy}$ states, while the parallel green and red lines originate from the $d_{yz}$ and $d_{zx}$ ones. (c) Out-of-plane FS mapping taken at the photon energies from 36 to 94 eV using LH light. The FS calculated for the $d_{xy}$ states is superimposed. The yellow thick line is the trajectory of the measured $\mathit{k}$ point of the ARPES measurement at 66 eV calculated using Eq. (2) with the inner potential of 20 eV. (d) Out-of-plane FS mapping using LV where the FSs calculated for the $d_{yz}$ and $d_{zx}$ states are superimposed. (e) FS mapping taken at the bulk-sensitive photon energies from 440 to 560 eV with LH light, together with the results of the TB calculation for the $d_{xy}$ states. It should be noted that ARPES intensities of $d_{xy}-(d_{yz}/d_{zx}-)$ derived bands become dominant in the LH (LV) mode, owing to the dipole selection rules for these light polarizations and measurement geometries used [38].

Figure 3

In-plane FSs and band structures of ${\mathrm{SrVO}}_3$ (110) films. (a) BZ of the SVO (110) surface where the ARPES measurements were performed for the $\mathrm{\Gamma }MRX$ plane (hatched by yellow). (b) FSs calculated from the TB calculation for the ARPES-measured (the $\mathrm{\Gamma }MRX$) plane. The blue parallel-line FS originates from the $d_{xy}$ states, while the two degenerated ellipses are centered at the $\mathrm{\Gamma }$ point from the $d_{yz}$ and $d_{zx}$ ones. (c), (d) In-plane FS mappings taken at the photon energy of 66 eV that corresponds to the $\mathrm{\Gamma }MRX$ plane using (c) LH and (d) LV light. The $d_{xy}$- and $d_{yz}/d_{zx}$-derived FSs obtained from the TB calculation are superimposed as solid blue lines and dotted green/red lines, respectively, for (c) and as dotted blue lines and solid green/red lines, respectively, for (d). The FS determined by ARPES is in good agreement with the result of the TB calculation. (e), (f) ARPES images along the $\mathrm{\Gamma }-M$ high-symmetry line taken at 66 eV with LH and LV light, respectively. Owing to the selection rule for the present experimental setup, the $d_{xy}$ band is dominant in (e), whereas the $d_{yz}$ and $d_{zx}$ bands are dominant in (f). (g), (h) Plots of peak positions determined from the ARPES data in (e) and (f) in comparison with the corresponding results of the TB calculation in the mass renormalization scheme for each $3d{t}_{2g}$ orbital. The best fit for the experimental results is obtained with the mass renormalization factor of 0.5.

Figure 4

ARPES images along the $\mathrm{\Gamma }-M$ line of ${\mathrm{SrVO}}_3$ (110) and (001) surfaces. (a) Comparison of ARPES images taken along the crystallographically equivalent $\mathrm{\Gamma }-M$ direction between the SVO (110) surface (upper panel) and the (001) surface (lower panel). The positional relationships between the ARPES-measurement direction and the surface orientation of the SVO film are illustrated in Figs. 1 and 1. Owing to the selection rule for the present experimental setup, only the $d_{yz}/d_{zx}$ bands are best observed in LV along the $\mathrm{\Gamma }-M$ direction at the (110) surface, whereas both the $d_{yz}/d_{zx}$ bands and the $d_{xy}$ band are observed along the $\mathrm{\Gamma }-M$ direction at the (001) surface. The observed ARPES images for the $d_{yz}/d_{zx}$ bands at the (110) surface are much broader than those at the (001) surface. (b) MDC at $E_{\mathrm{F}}$ along the $\mathrm{\Gamma }-M$ line at the (110) surface (upper panel) and the (001) surface (lower panel). The MDCs have been fitted to a linear combination of a Lorentzian function(s) [a hatched peak(s)] with a smooth background (dashed line).

Figure 5

Simulation results of ARPES spectra along the $\mathrm{\Gamma }-M$ line at (a) the (110) surface and (b) the (001) surface. (c) MDCs at $E_{\mathrm{F}}$ simulated for the (110) and (001) surfaces. The simulation successfully reproduces the key aspects of the ARPES results shown in Fig. 4.