Interplay between effective mass anisotropy and Pauli paramagnetic effects in a multiband superconductor: Application toSr2RuO4

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 Sr2RuO4 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 (∼60) and the Hc2 anisotropy (∼20). Among the three bands; γ with the effective mass anisotropy ∼180, α with ∼120, and β with ∼60, the last one is found to be the major band, responsible for various magnetic responses while the minor γ 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 Sr2RuO4. The pairing symmetry of Sr2RuO4 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 β band has a full gap and the minor γ band has a d x 2 −y 2 like gap.

Anisotropy and multiband superconductivity in Sr2RuO4 determined by small-angle neutron scattering studies of the vortex lattice

“…Recently, Nakai and Machida proposed a model for Sr 2 RuO 4 based on a dominant β band. 75 While this seems to be in disagreement with a Γ ac > Γ β at high fields, the model describes the sharp h x (Ω) cut-off observed at low fields which is not possible using a single band. 50 A definitive understanding of how the superconductivity in Sr 2 RuO 4 correlates with the individual bands is thus still lacking.…”

“…36 However, numerical solutions to the Elienberger equations that include PPEs do provide a qualitatively accurate description of the measured Ω-dependence of the transverse VL form factor, and thereby further support for Pauli limiting in Sr 2 RuO 4 . 50,75 The numerical work also provides an estimate of the longitudinal form factor, which despite the PPE enhancement remains approximately two orders of magnitude smaller than h x . 50 From the rocking curves shown in Fig.…”

“…80 Theoretically, the role of the individual bands and their interplay has been studied extensively. [59][60][61][62][63]75,81 While there is broad consensus that all contribute to the superconductivity, different models vary regarding which bands are predicted to be dominant. However, in most cases the effects of an applied magnetic field have not been considered in detail.…”

“…One possible explanation is provided by the above mentioned model based on a dominant β band. 75 Alternatively, this may be due to a rotation of the vortex direction away from the applied field and towards the basal plane. To quantify such an effect we define ∆Ω for each data point in Fig.…”

Superconducting subphase in the layered perovskite ruthenateSr2RuO4in a parallel magnetic field

“…Here the clear evidence for the FFLO state has recently been reported in organic compounds [47][48][49] and a heavy fermion system CeCoIn 5 [50][51][52]. Theoretical calculations taking the paramagnetic effect into account have been proposed to explain experimental aspects such as field dependence of the specific heat, and H c2 suppression in Sr 2 RuO 4 [41,[53][54][55]. The consideration of the mixture of both singlet-and triplet-pairing would be promising for fully understanding of the novel superconductivity in Sr 2 RuO 4 .…”