Superconductivity in Sr$_2$RuO$_4$ thin film under biaxial strain

TL;DR

This paper theoretically explores how biaxial strain influences electronic instabilities in Sr$_2$RuO$_4$ thin films, revealing strain-induced transitions between superconducting states and spin density waves, aligning with experimental observations.

Contribution

It provides a theoretical analysis of strain effects on superconductivity and magnetic order in Sr$_2$RuO$_4$, predicting phase transitions and electronic behavior under biaxial strain.

Findings

Positive strain induces p-wave superconductivity.

Further strain leads to spin density wave formation.

Negative strain causes transition from p-wave to s-wave superconductivity.

Abstract

Motivated by the success of experimental manipulation of the band structure through biaxial strain in Sr$_2$RuO$_4$ thin film grown on a mismatched substrate, we investigate theoretically the effects of biaxial strain on the electronic instabilities, such as superconductivity (SC) and spin density wave (SDW), by functional renormalization group. According to the experiment, the positive strain (from lattice expansion) causes charge transfer to the $\gamma$-band and consequently Lifshitz reconstruction of the Fermi surface. Our theoretical calculations show that within a limited range of positive strain a p-wave superconducting order is realized. However, as the strain is increased further the system develops into the SDW state well before the Lifshitz transition is reached. We also consider the effect of negative strains (from lattice constriction). As the strain increases, there is a transition from p-wave SC state to nodal s-wave SC state. The theoretical results are discussed in comparison to experiment and can be checked by further experiments.