High-Energy Anomaly in the Band Dispersion of the Ruthenate Superconductor

We reveal a “high-energy anomaly” (HEA) in the band dispersion of the unconventional ruthenate superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, by means of high-resolution angle-resolved photoemission spectroscopy (ARPES) with tunable energy and polarization of incident photons. This observation provides another class of correlated materials exhibiting this anomaly beyond high-$T_c$ cuprates. We demonstrate that two distinct types of band renormalization associated with and without the HEA occur as a natural consequence of the energetics in the bandwidth and the energy scale of the HEA. Our results are well reproduced by a simple analytical form of the self-energy based on the Fermi-liquid theory, indicating that the HEA exists at a characteristic energy scale of the multielectron excitations. We propose that the HEA universally emerges if the systems have such a characteristic energy scale inside of the bandwidth.

Figure 1

(a) Schematic polarization geometry used in the ARPES experiment, where the $p$-polarized light and $s$-polarized light are incident on the sample parallel and perpendicular with respect to the detection plane ($xz$ plane), respectively. (b),(c) Respective Fermi surfaces and electronic bands along the $\Gamma –M$ or $Z–M$ line of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ as determined from LDA calculations without hybridization between Ru $4d$ and O $2p$ states [26]. (d)–(g) ARPES images recorded along the $\Gamma –M$ or $Z–M$ line with different polarizations and incident photons.

Figure 2

(a),(b) ARPES images of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ along the $\Gamma –M$ or $Z–M$ line and their contour plots together with the energy-band dispersions (circles) recorded with 88-eV photons with $p$ and $s$ polarization, respectively; ARPES intensities are symmetrized with respect to the zone center ($\Gamma$ or $Z$). (c),(d) Comparison of the energy-band dispersion between ARPES results (circles) and LDA calculations (line) for $d_{zx}$ and $d_{xy}$ bands, respectively. The experimental dispersions were determined by fitting the momentum distribution curves, except for the flat dispersion around the bottom of the $d_{zx}$ band, which was determined by fitting the energy distribution curves. (e),(f) Real and imaginary parts of the self-energy ${\Sigma }^{\prime }(\omega )$ (open circles) and ${\Sigma }^{\prime \prime }(\omega )$ (closed circles) for $d_{zx}$ and $d_{xy}$ bands, respectively. These were obtained by ${\Sigma }^{\prime }(\omega )=\omega -{\epsilon }_k^{\mathrm{LDA}}$ and ${\Sigma }^{\prime \prime }(\omega )=-\frac{1}{2}{v}_0^{\mathrm{LDA}}\Delta k$, where ${\epsilon }_k^{\mathrm{LDA}}$, $v_0^{\mathrm{LDA}}$, and $\Delta k$ represent the LDA dispersion, and the velocity of the LDA dispersion, and the momentum distribution curve full width, respectively. For comparison, the ${\Sigma }^{\prime }(\omega )$ (black line) from previous theoretical calculations [29] is also shown. Solid and dashed lines in blue (red) represent the real and imaginary parts of the modeled self-energy [${\Sigma }_{\mathrm{model}}^{\prime }(\omega )$ and ${\Sigma }_{\mathrm{model}}^{\prime \prime }(\omega )$] obtained by fitting ${\Sigma }^{\prime }(\omega )$. (g),(h) Calculated spectral functions for $d_{zx}$ and $d_{xy}$ bands, respectively, where LDA dispersion is used as the bare dispersion and blue and red lines in (e) and (f) are used as the input self-energies.