Quasiparticle Interference on Cubic Perovskite Oxide Surfaces

We report the observation of coherent surface states on cubic perovskite oxide ${\mathrm{SrVO}}_3(001)$ thin films through spectroscopic-imaging scanning tunneling microscopy. A direct link between the observed quasiparticle interference patterns and the formation of a $d_{xy}$-derived surface state is supported by first-principles calculations. We show that the apical oxygens on the topmost ${\mathrm{VO}}_2$ plane play a critical role in controlling the coherent surface state via modulating orbital state.

Figure 1

Typical topographic images of ${\mathrm{SrVO}}_3(001)$ surface and metallic tunneling spectra (110-nm-thick film). (a),(b) Topographic images with sample bias voltage $V_s=-100\mathrm{mV}$ (a); the enlarged image in (b) shows the $(\surd 2\times \surd 2)\text{−}R45°$ structure. (c) The model used to generate the topographic image with a $(\surd 2\times \surd 2)\text{−}R45°$ structure. (d) Spatially averaged tunneling spectra ($dI/dV$) obtained from the surface.

Figure 2

Observation of quasiparticle interference pattern on the surface of ${\mathrm{SrVO}}_3(001)$. (a),(b) Simultaneously acquired topographic (a) and conductance (b) images at $V_s=-150\mathrm{mV}$. The inset in (b) shows the enlarged image in which we can see a wavelike pattern with approximately 1 nm periodicity. (c), (d) FTs of (a) and (b), respectively. Bragg peaks representing the $\surd 2a\times \surd 2a$ apical oxygen structure are highlighted by green circles in (c), and the wave vector ${\mathit{q}}^{*}$ is highlighted by green-dashed ellipses in (d). The $\overline{\mathrm{\Gamma }}-\overline{X}$ direction corresponds to the direction of the nearest-neighbor V atoms. The data shown in (a)–(d) are taken from a 110-nm-thick film. (e) Energy-dependent intensity profiles of the FTs along $\overline{\mathrm{\Gamma }}-\overline{X}$ (intensity averaged over three samples with thickness 20, 40, and 110 nm), along with the values of $q^{*}$ obtained from the three films. QPI patterns were independent of film thickness (Fig. S2), which is consistent with fully relaxed films.

Figure 3

Simulation of the electronic states on the surface of ${\mathrm{SrVO}}_3(001)$. (a) Cross-sectional view of the calculated relaxed near-surface structure. ${\mathrm{V}}_{\mathrm{O}}$ and ${\mathrm{V}}_b$ denote the V-atom sites with and without apical oxygen, respectively. (b) Calculated density of states averaged over ${\mathrm{V}}_{\mathrm{O}}$ and ${\mathrm{V}}_b$ sites. (c) Schematic drawing of the surface Brillouin zone (BZ). Green lines mark the BZ of the $(\surd 2\times \surd 2)\text{−}R45°$ structure. (d)–(g) Spectral weights of the $d_{xy}$ and $d_{xz}/d_{yz}$ orbitals for ${\mathrm{V}}_{\mathrm{O}}$ (${\mathrm{V}}_b$) are shown in (d) and (e) [(f) and (g)], respectively. The top axis of (b) and right axes of (d)–(g) represent the renormalized energy scale $E_{\mathrm{re}}$ using a renormalization factor of 0.4 (i.e., $E_{\mathrm{re}}=0.4E$). (h)–(j) Simulated total spectral weight at $E_{\mathrm{re}}=-250\mathrm{meV}$ (h) and the associated scattering probability (i). The experimental Fourier transform image of conductance mapping at $V_s=-250\mathrm{mV}$ is shown in (j) for comparison with (i). (k) The orbital and site dependence of onsite energies relative to the degenerate bulk $t_{2g}$ states; see Table S2 in the Supplemental Material [30] for details. The onsite energy differences within our model mainly reflect local crystal field effects; these are not related to onsite Coulomb repulsion $U$. See Ref. [30] for details of our calculations.

Figure 4

Schematic illustration of interorbital and intraorbital spectral weight transfer mechanisms and the related appearance or disappearance of QPI patterns. (a) Spectral weight transfer from $d_{xy}$ orbitals (red) to $d_{xz}/d_{yz}$ orbitals (blue) at the ${\mathrm{V}}_b$ site. (b) Spectral weight transfer from $d_{xy}$ orbitals (red) at the ${\mathrm{V}}_b$ site (left) to $d_{xy}$ orbitals (red) at the ${\mathrm{V}}_{\mathrm{O}}$ site (right). (a) and (b) only highlight the lower energy band branch near the $\overline{X}$ point. (c), (d) Distribution of the $d_{xy}$- and $d_{xz}/d_{yz}$- derived spectral weight in real space for high (c) and low (d) energy regions.