Spin-orbit and anisotropic strain effects on the electronic correlations of Sr$_2$RuO$_4$

TL;DR

This paper introduces a new implementation of the rotationally invariant slave boson method within DFT+DMFT to study electronic correlations in Sr$_2$RuO$_4$, highlighting the role of spin-orbit coupling and strain effects.

Contribution

The paper develops an explicit relation between local DMFT quantities and the Bloch basis, and applies it to analyze strain and spin-orbit effects in Sr$_2$RuO$_4$.

Findings

Spin-orbit coupling significantly influences mass enhancement differentiation.

Mass enhancement is weakly affected by uniaxial or biaxial strain.

Strain-induced Lifshitz transition has minimal impact on mass enhancement.

Abstract

We present an implementation of the rotationally invariant slave boson technique as an impurity solver for density functional theory plus dynamical mean field theory (DFT+DMFT). Our approach provides explicit relations between quantities in the local correlated subspace treated with DMFT and the Bloch basis used to solve the DFT equations. In particular, we present an expression for the mass enhancement of the quasiparticle states in reciprocal space. We apply the method to the study of the electronic correlations in Sr$_2$RuO$_4$ under anisotropic strain. We find that the spin-orbit coupling plays a crucial role in the mass enhancement differentiation between the quasi-one-dimensional $\alpha$ and $\beta$ bands, and on its momentum dependence over the Fermi surface. The mass enhancement, however, is only weakly affected by either uniaxial or biaxial strain, even across the Lifshitz transition induced by the strain.