Identifying detrimental effects for multi-orbital superconductivity - Application to Sr$_2$RuO$_4$

TL;DR

This paper introduces the superconducting fitness concept to evaluate how various symmetry-breaking factors suppress superconductivity, especially in complex multi-orbital systems like Sr$_2$RuO$_4$, revealing a new inter-orbital suppression mechanism.

Contribution

It presents a novel framework called superconducting fitness to analyze suppression mechanisms in multi-orbital superconductors, applied to Sr$_2$RuO$_4$ to identify an inter-orbital effect.

Findings

Superconducting fitness quantifies suppression of critical temperature.

Identification of an inter-orbital suppression mechanism.

Application to Sr$_2$RuO$_4$ explains its critical field behavior.

Abstract

We propose a general scheme to probe the compatibility of arbitrary pairing states with a given normal state Hamiltonian by the introduction of a concept called superconducting fitness. This new quantity gives a direct measure of the suppression of the superconducting critical temperature in presence of key symmetry breaking fields. A merit of the superconducting fitness is that it can be used as a tool to identify non-trivial mechanisms to suppress superconductivity under various external influences, in particular, magnetic fields or distortions, even in complex multi-orbital systems. In the light of this new concept we analyse the multi-band superconductor Sr$_2$RuO$_4$ and propose a new mechanism for the suppression of superconductivity in multi-orbital systems, which we call inter-orbital effect, as a possible explanation for the unusual limiting feature observed in the upper critical field of this material.