Magic angle of Sr$_2$RuO$_4$: Optimizing correlation-driven superconductivity

TL;DR

This paper investigates how structural distortions affect superconductivity in Sr$_2$RuO$_4$, predicting a specific octahedral rotation angle that maximizes $T_c$ and favors $d_{x^2-y^2}$ pairing, using advanced theoretical methods.

Contribution

It introduces a novel prediction of a 'magic' rotation angle in Sr$_2$RuO$_4$ that optimizes superconductivity, validated by FRG calculations and phase imaging proposals.

Findings

FRG reproduces key experimental results

Predicted a specific octahedral rotation angle for maximum $T_c$

Identified $d_{x^2-y^2}$ as the dominant pairing symmetry

Abstract

Understanding of unconventional superconductivity is crucial for engineering materials with specific order parameters or elevated superconducting transition temperatures. However, for many materials, the pairing mechanism and symmetry of the order parameter remain unclear: reliable and efficient methods of predicting the order parameter and its response to tuning parameters are lacking. Here, we investigate the response of superconductivity in Sr$_2$RuO$_4$ to structural distortions via the random phase approximation (RPA) and functional renormalization group (FRG), starting from realistic models of the electronic structure. Our results suggest that RPA misses the interplay of competing fluctuation channels. FRG reproduces key experimental findings. We predict a magic octahedral rotation angle, maximizing the superconducting $T_c$ and a dominant $d_{x^2-y^2}$ pairing symmetry. To enable experimental verification, we provide calculations of the phase-referenced Bogoliubov Quasiparticle Interference imaging. Our work demonstrates a designer approach to tuning unconventional superconductivity with relevance and applicability for a wide range of quantum materials.