A key role of correlation effects in the Lifshitz transition in Sr$_2$RuO$_4$

TL;DR

This paper investigates how electronic correlations influence the Lifshitz transition in Sr$_2$RuO$_4$, revealing that correlations lower the critical strain needed for the transition, aligning theoretical predictions with experimental observations.

Contribution

The study demonstrates that electronic correlations and orbital anisotropy significantly reduce the critical strain for the Lifshitz transition in Sr$_2$RuO$_4$, improving theoretical-experimental agreement.

Findings

Correlations lower the critical strain for the Lifshitz transition.

Experimental critical strain is smaller than density functional theory predictions.

Orbital anisotropy of Coulomb interactions is crucial for accurate modeling.

Abstract

Uniaxial pressure applied along an Ru-Ru bond direction induces an elliptical distortion of the largest Fermi surface of Sr$_2$RuO$_4$, eventually causing a Fermi surface topological transition, also known as a Lifshitz transition, into an open Fermi surface. There are various anomalies in low-temperature properties associated with this transition, including maxima in the superconducting critical temperature and in resistivity. In the present paper, we report new measurements, employing new uniaxial stress apparatus and new measurements of the low-temperature elastic moduli, of the strain at which this Lifshitz transition occurs: a longitudinal strain $\varepsilon_{xx}$ of $(-0.44\pm0.06)\cdot10^{-2}$, which corresponds to a B$_{1g}$ strain $\varepsilon_{xx} - \varepsilon_{yy}$ of $(-0.66\pm0.09)\cdot10^{-2}$. This is considerably smaller than the strain corresponding to a Lifshitz transition in density functional theory calculations, even if the spin-orbit coupling is taken into account. Using dynamical mean-field theory we show that electronic correlations reduce the critical strain. It turns out that the orbital anisotropy of the local Coulomb interaction on the Ru site is furthermore important to bring this critical strain close to the experimental number, and thus well into the experimentally accessible range of strains.