Weak-coupling analysis of quasiparticle excitations in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ along the $\mathrm{\Gamma }\text{−}M$ cut

We examine normal-state quasiparticle excitations along the $\mathrm{\Gamma }\text{−}M$ cut in momentum space for the putative $p$-wave superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ on the basis of fluctuation exchange approximation calculations. We take as input first-principles derived parameters for the band structure and spin-orbit and electron-electron interactions. The numerical results are in excellent agreement with data from photoemission experiments and provide insight into the underlying quasiparticle properties. We find that, despite the correlation-induced effective mass increase near the Fermi surface, the full $\beta$ and $\gamma$ bandwidths are, if anything, increased by correlations. Furthermore, for the $\gamma$ band we find anomalous lifetime broadening and a significant temperature of variation of unoccupied state quasiparticle energies for temperatures between 25 and 100 K, both of which are accounted for by the momentum dependence of the electron self-energy. In addition to aiding our understanding of experimental data, these results point to the challenge of assigning appropriate Fermi-liquid parameters or momentum-independent self-energies for schemes that require such approximations in order to model ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

Figure 1

Calculated momentum and energy-dependent photoemission spectral intensities, $A_{\nu }(\vec{k},E)$, for $\mathbf{k}=(k_x,k_y=0)$ at $T=25$ K for (a) $\beta$-band-dominant $\nu =d_{xz}$ orbitals and (b) $\gamma$-band-dominant $\nu =d_{xy}$ orbitals.

Figure 2

Quasiparticle dispersion as a function of (a) doping and (b) temperature. The doping dependence of the dispersion is largely accounted for by a shift in the Fermi level $E_F$. The energy of the Van Hove singularity and the Fermi surface effective mass have significant temperature dependence even though a similar dependence is not apparent for the states below $E_F$.

Figure 3

FLEX results for the energy dependence of the the $\beta$- and $\gamma$-band lifetimes at three different temperatures. Scattering is significantly larger for the $\gamma$ band which also displays a stronger temperature dependence near $E=0$.

Figure 4

Imaginary part of the orbital- and spin-diagonal parts of the self-energy, $\mathrm{Im}{\mathrm{\Sigma }}_{\nu \sigma ;\nu \sigma }(\mathbf{k},E)$, for the $\nu =d_{xy}$ and $d_{xz}$ orbitals and three different momentum values (momentum given in units of $\pi /a$). In panel (a) the energy range spans that bandwidth and in panel (b) we zoom in on energies near $E_F$. The $d_{xy}$ orbitals, which dominate the $\gamma$ band, have anomalous behavior for momentum values near the $M$ point, $\mathbf{k}=(\pi /a,\pi /a)$.