Orbital-Dependent Band Narrowing Revealed in an Extremely Correlated Hund’s Metal Emerging on the Topmost Layer of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

We use a surface-selective angle-resolved photoemission spectroscopy and unveil the electronic nature on the topmost layer of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ crystal, consisting of slightly rotated ${\mathrm{RuO}}_6$ octahedrons. The $\gamma$ band derived from the $4d_{xy}$ orbital is found to be about three times narrower than that for the bulk. This strongly contrasts with a subtle variation seen in the $\alpha$ and $\beta$ bands derived from the one-dimensional $4d_{xz/yz}$. This anomaly is reproduced by the dynamical mean-field theory calculations, introducing not only the on-site Hubbard interaction but also the significant Hund’s coupling. We detect a coherence-to-incoherence crossover theoretically predicted for Hund’s metals, which has been recognized only recently. The crossover temperature in the surface is about half that of the bulk, indicating that the naturally generated monolayer of reconstructed ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ is extremely correlated and well isolated from the underlying crystal.

Figure 1

(a1),(a2) Fermi surface of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ obtained by DFT calculations without and with a ${\mathrm{RuO}}_6$ rotation by 8°, respectively. The $4d_{xy}$ and $4d_{xz/yz}$ bands are indicated by red and blue curves, respectively. (b) Fermi surface mapping by ARPES. (c) Spectral intensity for the bulk estimated from the MDC peaks in (f). We have normalized the MDCs for different photon energies to the background intensities around $k_x/\pi =0.8$. (d1),(d2) Magnified image around the zone edge [light blue rectangle in (b)]. Green ellipses mark the bulk FS. (e1),(e2) Dispersions across the zone edge [magenta arrows in (d1) and (d2)], measured at high and low photon energies, respectively. The color scale is maximized to the strongest intensity in each image. (f) MDCs at $E_F$ of (e1) and (e2). Blue arrows indicate Fermi crossings of the bulk band.

Figure 2

Band structure of the topmost layer, selectively observed by a 7-eV laser ARPES. Dispersions along (a) the (0, $\pi$)-($\pi$, $\pi$) cut and (b),(d) the (0,0)-($\pi$, 0) cut [dashed, colored arrows in (c)]. Panel (b) plots a narrow region of (d) with a different color scale. (e) Energy contour images around $\overline{\mathrm{\Gamma }}$ [orange arrows in (b) and yellow square in (c)]. (f) ARPES images and determined dispersions along typical momentum cuts [magenta and blue arrows in (c)]. (g),(h) The ${\gamma }^s$ and ${\beta }^s$ bands along (0,0)-($\pi$, 0), respectively, determined from spectral peaks in (d). The gray curves show the dispersions for the bulk ${\gamma }^b$ and ${\beta }^b$ [43]. The bulk bands narrowed by a factor of 2.7 and 1.3, respectively, are superimposed. (i) The off-diagonal ARPES images for ${\gamma }^s$ very close to $E_F$ [orange arrows in (c)]. The dispersions determined by ARPES (red circles) and the DFT results (solid curves) are compared.

Figure 3

(a) The $\mathrm{DFT}+\mathrm{DMFT}$ calculations in several conditions ($U$, $J$, and ${\mathrm{RuO}}_6$ rotation by 8°). The $4d_{xy}$ and $4d_{xz/yz}$ bands along (0,0)-($\pi$, 0) at $k_z=0$ are separately plotted in the top and bottom panels, respectively. The DFT dispersions are overlapped on each image. (b),(c) Energy distribution curves (EDCs) at (0,0) extracted for $4d_{xy}$ and $4d_{xz/yz}$, respectively. Magenta arrows in (a) and (b) indicate satellite peaks. (d1),(d2) Temperature dependence of the calculated mass enhancement ($m^{*}/m_{\mathrm{DFT}}$) without and with the rotation.

Figure 4

Coherence-incoherence crossover with temperature. (a1) Temperature evolution of the spectral peak intensity at a $k_F$ of the ${\beta }^s$ band (blue circle in the inset). A dotted green circle indicates the crossover temperature, above which the quasiparticle peak becomes negligible. (a2),(a3) EDCs and those divided by the Fermi function at measured temperatures. In the top and bottom panels, the data are displayed with and without an offset, respectively. (b1)–(b3) The data for the ${\gamma }^s$ band obtained in the same way as in (a1)–(a3).