Interplay between effective mass anisotropy and Pauli paramagnetic effects in a multiband superconductor--Application to Sr2RuO4--

TL;DR

This paper uses extended Eilenberger theory to analyze vortex lattice properties in Sr2RuO4, revealing how multiband anisotropy and Pauli effects influence magnetic responses and vortex formation.

Contribution

It provides a detailed multiband analysis of vortex properties in Sr2RuO4, explaining the disparity between vortex lattice and Hc2 anisotropies and identifying the roles of different bands.

Findings

The vortex lattice anisotropy exceeds the effective mass anisotropy.

The $eta$ band is the major contributor to magnetic responses.

The $eta$ band has a full gap, while the $ ext{γ}$ band has a $d_{x^2-y^2}$-like gap.

Abstract

We investigate the mixed state properties in a type II multiband superconductor with uniaxial anisotropy under the Pauli paramagnetic effects. Eilenberger theory extended to a multiband superconductor is utilized to describe the detailed vortex lattice properties, such as the flux line form factors, the vortex lattice anisotropy and magnetic torques. We apply this theory to Sr$_2$RuO$_4$ to analyze those physical quantities obtained experimentally, focusing on the interplay between the strong two-dimensional anisotropy and the Pauli paramagnetic effects. This study allows us to understand the origin of the disparity between the vortex lattice anisotropy ($\sim$60) and the $H_{\rm c2}$ anisotropy ($\sim$20). Among the three bands; $\gamma$ with the effective mass anisotropy $\sim$180, $\alpha$ with $\sim$120, and $\beta$ with $\sim$60, the last one is found to be the major band, responsible for various magnetic responses while the minor $\gamma$ band plays an important role in the vortex formation. Namely, in a field orientation slightly tilted away from the two dimensional basal plane those two bands cooperatively form the optimal vortex anisotropy which exceeds that given by the effective mass formula with infinite anisotropy. This is observed by small angle neutron scattering experiments on Sr$_2$RuO$_4$. The pairing symmetry of Sr$_2$RuO$_4$ realized is either spin singlet or spin triplet with the d-vector strongly locked in the basal plane. The gap structure is that the major $\beta$ band has a full gap and the minor $\gamma$ band has a $d_{x^2-y^2}$ like gap.