Probing momentum-dependent scattering in uniaxially stressed Sr$_2$RuO$_4$ through the Hall effect

TL;DR

This study reveals that uniaxial stress induces a Lifshitz transition in Sr$_2$RuO$_4$, significantly altering scattering processes and transport properties, with implications for understanding correlated electron behavior under strain.

Contribution

It demonstrates that scattering changes across the entire Brillouin zone are necessary to explain Hall effect anomalies during a Lifshitz transition in Sr$_2$RuO$_4$, highlighting orbital-dependent scattering effects.

Findings

Hall coefficient becomes more negative across the transition at electron-electron dominated temperatures.

Scattering rates on $xy$ orbital sections decrease dramatically during the transition.

Resistivity and Hall coefficient remain constant across the transition when defect scattering dominates.

Abstract

Under in-plane uniaxial stress, the largest Fermi surface sheet of the correlated metal Sr$_2$RuO$_4$ undergoes a Lifshitz transition from an electron-like to an open geometry. We investigate the effects of this transition on transport through measurement of the longitudinal resistivity $\rho_{xx}$ and the Hall coefficient $R_\text{H}$. At temperatures where scattering is dominated by electron-electron scattering, $R_\text{H}$ becomes more negative across the Lifshitz transition, opposite to expectations from the change in Fermi surface topology. We show that this change in $R_\text{H}$ is explainable only if scattering changes throughout the Brillouin zone, not just at the point in $k$-space where the Lifshitz transition occurs. In a model of orbital-dependent scattering, the electron-electron scattering rate on sections of Fermi surface with $xy$ orbital weight decreases dramatically. On the other hand, at temperatures where defect scattering dominates $\rho_{xx}$ and $R_\text{H}$ are essentially constant across the Lifshitz transition.