Effects of Pauli paramagnetism on the superconducting vortex phase diagram in strong fields

Abstract

The Ginzburg-Landau (GL) functional and the resultant phase diagram of quasi two-dimensional superconductors in strong fields perpendicular to the layers, where the Pauli paramagnetic depairing is not negligible, are examined in details by assuming the weak coupling BCS model with a d x 2 −y 2 -like pairing. It is found that the temperature at which the mean field (MF) transition at Hc2 changes into a discontinuous one lies much above another temperature at which a line HFFLO(T ) of transition to a helical FFLO-like vortex solid may begin to appear. In addition to MF results, details of a real phase diagram near Hc2(T )-line are examined based on a theoretical argument and Monte Carlo simulations, and it is found that the MF discontinuous transition is changed due to the fluctuation into a crossover which is nearly discontinuous in systems with weak enough fluctuation. These results are consistent both with the MF discontinuous behavior and a suggestion of HFFLO(T ) in the heavy fermion superconductor CeCoIn5 with weak fluctuation and with their absence in cuprate and organic superconductors with strong fluctuation.

Phase diagram and spectroscopy of Fulde-Ferrell-Larkin-Ovchinnikov states of two-dimensionald-wave superconductors

“…32,45 The interplay between Pauli paramagnetism and the vortex phase of d-wave superconductors has also been studied in Refs. (36,46).…”

Fulde-Ferrell-Larkin-Ovchinnikov State in a Perpendicular Field of Quasi-Two-DimensionalCeCoIn5

“…In the FFLO state, pair-breaking due to the Pauli paramagnetic effect is reduced by the formation of a new pairing state (k↑, −k + q↓) with |q| ∼ 2µ B H/ v F (v F is the Fermi velocity) between the Zeeman split parts of the Fermi surface, instead of (k↑, −k↓)-pairing in ordinary BCS superconductors. A fascinating aspect of the FFLO state is that an inhomogeneous superconducting phase with a spatially oscillating order parameter ∆(r)= ∆ 0 cos(q·r) and spin polarization shows up in the vicinity of the upper critical field H c2 [1,2,3,4,5,6,7,8,9,10,11]. It has been shown that in the presence of a substantial orbital effect, 2D planar nodes appear periodically perpendicular to the Abrikosov vortex lattice.…”

“…It has been shown that in the presence of a substantial orbital effect, 2D planar nodes appear periodically perpendicular to the Abrikosov vortex lattice. [7,8,9,10,11] Despite the straightforward nature of the theoretical prediction, actual observations of the FFLO state have turned out to be extremely difficult. In fact, no solid evidence, which is universally accepted as proof of the FFLO state, has turned up in any superconductors thus far.…”

“…First, the superconducting-normal transition at H c2 is in the first order, indicating that superconductivity is limited by the Pauli paramagnetic effect [19,20,21]. Second, it has been pointed out that the FFLO state is readily destroyed by impurities [4,9,22], but this material is in the extremely clean regime [23]. Third, the superconducting symmetry is most likely to be the d-wave [19,24,25], which extends the stability of the FFLO state [4,6,26].…”

Quasiclassical analysis of vortex lattice states in Rashba noncentrosymmetric superconductors

“…Motivated by the recent revival of spatially modulated superconducting (SC) states induced by paramagnetic pair breaking (PPB) [1][2][3][4], noncentrosymmetric superconductors [5] in nonzero magnetic fields have been studied in recent years as a novel type of system with a peculiar modulated SC state. In noncentrosymmetric superconductors, the lack of spatial inversion symmetry results in a splitting of the original Fermi surface into two sheets and makes effects of PPB anisotropic.…”