Superconducting subphase and substantial Knight shift in $Sr_2RuO_4$

TL;DR

This study investigates helical pairing in Sr2RuO4, revealing a superconducting subphase, first-order transitions, and a significant Knight shift reduction, aligning with recent experimental findings and challenging previous chiral pairing assumptions.

Contribution

The paper provides a detailed theoretical analysis of helical pairing effects in Sr2RuO4, explaining experimental observations of the superconducting subphase and Knight shift behavior.

Findings

Identification of a superconducting subphase with first-order transitions.

Agreement with experiments on the Knight shift reduction.

Prediction of a bicritical point in the phase diagram.

Abstract

Recent nuclear magnetic resonance experiments measuring the Knight shift in $Sr_2RuO_4$ have challenged the widely accepted picture of chiral pairing in this superconductor. Here we study the implications of helical pairing on the superconducting state while comparing our results with the available experimental data on the upper critical field and Knight shift. We solve the Bogoliubov-de-Gennes equation employing a realistic three-dimensional tight-binding model that captures the experimental Fermi surface very well. In agreement with experiments we find a Pauli limiting to the upper critical field and, at low temperatures and high fields, a second superconducting transition. These transitions which form a superconducting subphase in the H-T phase diagram are first-order in nature and merge into a single second-order transition at a bicritical point $(T^\ast,H^\ast$), for which we find (0.8~K, 2.4~T) with experiment reporting (0.8~K, $\sim$ 1.2~T) [\textit{Phys. Rev. B} \textbf{93}, 184513 (2016)]. Furthermore, we find a substantial drop in the Knight shift in agreement with recent experiments.