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

TL;DR

This paper investigates how strain affects the anisotropic scattering rates in Sr$_2$RuO$_4$, revealing a transition from moderate to strong anisotropy near the Lifshitz point and explaining experimental observations through a superposition of scattering contributions.

Contribution

The study provides a detailed theoretical analysis of the anisotropic scattering rates near a Lifshitz transition in Sr$_2$RuO$_4$, explaining experimental data without invoking new universal laws.

Findings

Scattering rate becomes strongly anisotropic at the Lifshitz point.

Experimental $ au^{-1} o ext{omega}^{eta}$ behavior is explained by combined scattering contributions.

Predicted non-monotonic and strain-dependent scattering features can be tested experimentally.

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 $\gamma$-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 $\tau^{-1}\sim \omega $ at the Van Hove point and as $\tau^{-1}\sim \omega^{3/2}$ away from it. At higher energies, however, corrections of order $\omega^2$ become important in both regimes. We show that the experimentally observed behavior $\tau^{-1} \sim \omega^{\alpha}$ with $\alpha \approx 1.4(2)$ 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.