Quasiclassical determination of the in-plane magnetic field phase diagram of superconductingSr2RuO4

Abstract

We have carried out a determination of the magnetic-field-temperature (H-T) phase diagram for realistic models of the high field superconducting state of tetragonal Sr2RuO4 with fields oriented in the basal plane. This is done by a variational solution of the Eilenberger equations. This has been carried for spin-triplet gap functions with a d-vector along the c-axis (the chiral p-wave state) and with a d-vector that can rotate easily in the basal plane. We find that, using gap functions that arise from a combination of nearest and next nearest neighbor interactions, the upper critical field can be approximately isotropic as the field is rotated in the basal plane. For the chiral dvector, we find that this theory generically predicts an additional phase transition in the vortex state. For a narrow range of parameters, the chiral d-vector gives rise to a tetracritical point in the H-T phase diagram. When this tetracritical point exists, the resulting phase diagram closely resembles the experimentally measured phase diagram for which two transitions are only observed in the high field regime. For the freely rotating in-plane d-vector, we also find that additional phase transition exists in the vortex phase. However, this phase transition disappears as the in-plane d-vector becomes weakly pinned along certain directions in the basal plane.

Magnetic field induced rotation of thed-vector in the spin-triplet superconductorSr2RuO4

“…Unfortunately, LDA estimates of λ are significantly larger than the values we have assumed in the calculations presented here [36]. A large value of spin-orbit coupling has previously been cited as evidence against the d-vector rotation picture [34,35,36]. Despite these objections, it is clear from our results that even for large values of λ the transition field B t for d-vector rotation, in Fig.…”

Evaluation of Spin-Triplet Superconductivity in Sr2RuO4

“…177) This additional transition can be easily suppressed by a slight misalignment of the field of only one degree. However, in this theoretical model, large in-plane anisotropy for such additional transition is expected, 177,178) which is incompatible with the experimental results. Another possibility is the crossover fromẑk x to the spin-polarized ðẑ À iŷÞk x state.…”

Vortex States for Nearly B||ab in a Chiral p-Wave Superconductor

“…However, the chiral-nonchiral transition has not been observed experimentally in Sr 2 RuO 4 [6,9,10], except for an experiment of the magnetization curve [11]. There were discussions in that the double transition [5,6,10] near H c2 corresponds to the chiral-nonchiral transition [8].…”

“…That is, we determine the spatial structure of g without using Pesch's approximation [8,20]. The normalized Fermi velocity isv = v/v F with v F = v 2 1/2 p .…”

“…This type of pairing is a candidate for the superconducting phase of Sr 2 RuO 4 [5,6]. As a typical phenomenon of chiral p-wave superconductors, theoretical studies suggest a chiral-nonchiral transition when a magnetic fieldB is applied in the orientationB ab [7,8]. At low fields, the chiral p ± -wave state is stable, because the free energy of the chiral p ± -wave state is lower than that of the nonchiral p x -or p y -wave states, because the latter nonchiral states have vertical line nodes.…”