Figure 1

The valence band of ${\mathrm{Ca}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{RuO}}_4$. (a) Plot of second derivative of ARPES intensity for the valence band of ${\mathrm{Ca}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{RuO}}_4$ taken along $\Gamma \mathrm{\text{−}}M\mathrm{\text{−}}X$ ($h\nu =75\mathrm{eV}$, $T=40\mathrm{K}$). (b) The corresponding EDCs along $\Gamma \mathrm{\text{−}}M\mathrm{\text{−}}X$. (c) Comparison of the EDCs for $x=0.2$, 0.5, 2, taken at the $\beta$ band crossing point along $\Gamma \mathrm{\text{−}}M$ ($h\nu =32\mathrm{eV}$, $T=40\mathrm{K}$).Reuse & Permissions

Figure 2

Band dispersion along high-symmetry directions in ${\mathrm{Ca}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{RuO}}_4$. (a) ARPES intensity plot along $X\mathrm{\text{−}}\Gamma \mathrm{\text{−}}X$. (b) The corresponding second derivative plot of (a). The white dashed lines are guides for eyes. (c) EDCs and (d) MDCs, within the red dashed box in (a), showing low-energy band dispersion, as indicated by blue dashed lines. (e) Second derivative plot of ARPES intensity along $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}M$. (f) Fermi crossings (black dots) indicated in (b) and (e), and Fermi surface sheets (red lines) calculated by LDA for ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ [21] in the first BZ.Reuse & Permissions

Figure 3

Fermi surface and electron occupancy of different orbitals. (a) Measured FS sheets of $\alpha$ (green contours centered at $X$), $\beta$ (red contour centered at $\Gamma$), and the folded $\alpha$ (blue dashed contour centered at $\Gamma$), along with the Fermi crossing points determined by ARPES (black solid dots) and symmetrized points according to the fourfold crystal symmetry (red open dots). The black dotted contour centered at $\Gamma$ is the derived $\gamma$ FS according to the Luttinger theorem. (b) Comparison of the EDCs at $M$ between ${\mathrm{Ca}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{RuO}}_4$ and ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, integrated over the $k$ region indicated by the shaded rectangle in (a). (c) The Sr content dependence of electron occupancy of $\gamma$ and $(\alpha +\beta )/2$, obtained by ARPES (red filled dots and lines), and LDA (black open dots and lines).Reuse & Permissions

Figure 4

Calculations that show OSMT in multiorbital systems. (a) QP weight for the 3-band Hubbard model with equal bandwidth $W$ as a function of charge transfer $\delta$ defined by $(n_{\alpha },n_{\beta },n_{\gamma })=(\frac{2}{3}-\frac{\delta }{2},\frac{2}{3}-\frac{\delta }{2},\frac{2}{3}+\delta )$. $U/W=4.0$; $J/W=1.0$. (b) Intraband and interband correlation functions, where ${\chi }_{\alpha \uparrow ,\alpha \downarrow }=⟨n_{\alpha \uparrow }{n}_{\alpha \downarrow }⟩-⟨n_{\alpha \uparrow }⟩⟨n_{\alpha \downarrow }⟩$, ${\chi }_{\gamma \uparrow ,\gamma \downarrow }=⟨n_{\gamma \uparrow }{n}_{\gamma \downarrow }⟩-⟨n_{\gamma \uparrow }⟩⟨n_{\gamma \downarrow }⟩$, and ${\chi }_{\alpha ,\gamma }=⟨(n_{\alpha \uparrow }+n_{\alpha \downarrow })(n_{\gamma \uparrow }+n_{\gamma \downarrow })⟩-⟨(n_{\alpha \uparrow }+n_{\alpha \downarrow })⟩⟨(n_{\gamma \uparrow }+n_{\gamma \downarrow })⟩$. (c) Same as in (a), except for the three bandwidths of $W$, $W$, $1.5W$. (d) Same as in (b), except for the three bandwidths of $W$, $W$, $1.5W$. Note that the $y$ axis is negative in (b) and (d). With increasing $\delta$, the intra-$\gamma$-band correlation becomes large and negative, while the interband correlation approaches zero.Reuse & Permissions