Crossover from Vortex States to the Fulde-Ferrell- Larkin-Ovchinnikov State in Two-Dimensionals- andd-Wave Superconductors

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

“…1 (solid and continuing into dotted lines) cross at T * ≈ 0.06 T c , resulting in a kink in the upper transition line, in agreement with previous work. 32,36,41,42 On the other hand, the lower critical field, B c1 , for the stripe orientation along 110 (line with circles) is always lower than the critical field for the stripe orientation along 100 (short-dashed line). This indicates a first order transition between states with different orientation of stripes (long-dashed line).…”

“…This leads to coexistence of the FFLO with vortices; these states have been studied extensively and it is predicted that the resulting inhomogeneous state has a number of novel properties, including a change in the order of the transition as well as additional phase transitions within the nonuniform phase corresponding to transitions between states belonging to different Landau levels. 6,28,34,35,36,37,38,39,40 For d-wave superconductors the FFLO phases are modified by the intrinsic anisotropy of the order parameter. In the class of quasi-2D superconductors the upper critical transition line, B c2 (T ), has a kink at low temperatures corresponding to the discontinuous change in direction of the stripe modulation with respect to the nodes of the order parameter.…”

“…In the class of quasi-2D superconductors the upper critical transition line, B c2 (T ), has a kink at low temperatures corresponding to the discontinuous change in direction of the stripe modulation with respect to the nodes of the order parameter. 32,36,41,42 However, the reorientation transition, and the kink, are absent in 3D, 43 or if the shape of the Fermi surface is changed. 44 Recent calculations of the spatial modulation of the order parameter in 2D near B c2 predict that the energetically favored state at low temperature and high field forms a "square lattice" instead of stripe order.…”

“…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.…”