Anisotropic scattering rates in strain-tuned Sr$_2$RuO$_4$

TL;DR

The paper tackles how electron-electron scattering rates in Sr2RuO4 behave near a strain-tuned Lifshitz transition marked by a Van Hove singularity. Using a strained γ-band Hubbard model and second-order perturbation theory, it demonstrates universal low-energy scalings: $τ^{-1} \sim ω$ at the VHS and $τ^{-1} \sim ω^{3/2}$ away from the VHS, with logarithmic corrections at the VHS; higher-energy corrections of order $ω^2$ are also important. The authors show that the experimentally observed intermediate exponent $α \approx 1.4$ can be explained by a superposition of linear and quadratic contributions rather than a new universal law. They further predict a pronounced anisotropy, strain dependence, and a non-monotonic frequency dependence of the scattering rate at the Lifshitz transition, offering clear tests for spectroscopic and transport experiments and implications for the superconducting state in Sr2RuO4.

Abstract

Motivated by recent angle-resolved photoemission spectroscopy (ARPES) experiments, we analyze the temperature, frequency, and momentum dependence of the single-particle scattering rate in a model of the $γ$-band of Sr$_2$RuO$_4$ under strain, with particular emphasis on the behavior near the Lifshitz transition where the Fermi energy crosses a single Van Hove point. While the scattering rate is only moderately anisotropic at zero strain, we find that it becomes strongly anisotropic at the Lifshitz point. At the lowest energies, we recover the expected universal behavior: the scattering rate varies (ignoring logarithmic corrections) as $τ^{-1}\sim ω$ at the Van Hove point and as $τ^{-1}\sim ω^{3/2}$ away from it. At higher energies, however, corrections of order $ω^2$ become important in both regimes. We show that the experimentally observed behavior $τ^{-1} \sim ω^α$ with $α\approx 1.4(2)$ at the Van Hove point can be quantitatively explained by a superposition of linear and quadratic contributions to the scattering rate, which are comparable in magnitude at the intermediate energies probed by experiment, rather than in terms of a new universal power law. We further predict a distinctive anisotropy, strain dependence, and a non-monotonic frequency dependence of the scattering rate at a Lifshitz transition, all of which may be directly tested in experiments.

Figures (7)

• Figure 1: Fermi surfaces in the first Brillouin zone of Sr$_2$RuO$_4$ at $k_z=0$ for zero strain (left panel) and at the critical strain of the Lifshitz point (right panel). At the Lifshitz point the $\gamma$-sheet of the Fermi surface (shown in color) touches the Van Hove point at in-plane momentum $\boldsymbol{k}=\left(0,\pm\pi\right)$. The part of the Fermi surface near the Van Hove point marked in red refers to the hot regions, while cold parts of the Fermi surface, away from the Van Hove point, are shown in blue. The angle $\phi$ marks the azimuthal angle relative to $\left(0,\pi\right)$. Dashed lines indicate the $\alpha$- and $\beta$-sheets of the Fermi surface that are not analyzed in this paper.
• Figure 2: Anisotropy of the zero-frequency scattering rate $\Gamma_{\boldsymbol{k}_F}/U^2$ on the Fermi surface at $T = 9.9$ K for zero strain (light blue) and the critical strain of the Lifshitz transition (pink). The base area marks the first Brillouin zone boundary and $\Gamma_{\boldsymbol{k}_F}/U^2$ is measured in units of $10^{-2} \text{ eV}^{-1}$. While the scattering rate at zero strain is moderately anisotropic, a pronounced anisotropy with a sharp peak at the Van Hove point emerges at the Lifshitz transition.
• Figure 3: Temperature dependence of the imaginary part of the zero-frequency self-energy, $\Gamma_{\boldsymbol{k}}(0,T)$, for cold and hot momenta on the Fermi surface: $\phi = 0$ corresponds to the Van Hove point while $\phi = \pi/4$ is away from it. (a): Zero strain displaying low-$T$ quadratic Fermi liquid behavior with all states being cold. (b): Critical strain exhibiting $T$-linear behavior at $\phi = 0$ (hot) and $T^{3/2}$ behavior away from the Van Hove point with $\phi = \pi/4$ (cold).
• Figure 4: Log-log plot of the frequency dependence of the imaginary part of the self-energy at the critical strain.
• Figure 5: Scattering rate $\Gamma$ at the Lifshitz point and for the momentum at the Van Hove point as function of frequency for different temperatures. To facilitate the comparison of different $T$, $\Gamma$ has been scaled by the value at the local minimum and is plotted as function of $\omega/T$. The physical origin of the non-monotonic dependence of the scattering rate is further discussed in Appendix \ref{['app:AppendixA']}