Paramagnetic Meissner, vortex, and onionlike ground states in a finite-size Fulde-Ferrell superconductor

Magnetic field induced global paramagnetic response in Fulde-Ferrell superconducting strip

“…Here we theoretically show, that magnetic response of SFN strip being in in-plane Fulde-Ferrell state is also diamagnetic at small and large fields, but there is finite range of fields where magnetic response is globally paramagnetic. It differs from global paramagnetic response predicted for small size unconventional superconducting disks [19] and thin disks/squares made of SFN trilayer [20], where it appears due to finite size effect and exists only at small fields. We argue that in case of SFN strip global paramagnetic response is connected with peculiar dependence of sheet superconducting current density on supervelocity in FF state and it appears in nonlinear regime (when dependence of superconducting current on vector potential is nonlinear).…”

“…To obtain full in-plane distribution of the superconducting order parameter and current density, one has to solve 3D Usadel equation which is complicated problem. Instead we use the Ginzburg-Landau like approach and describe SFN structure by the 2D (in y and z directions) equations with the effective superconducting order parameter Ψ averaged over the thickness of SFN trilayer [20]. The GL free energy functional describing 2D superconductor being in the FFLO phase was proposed in Ref.…”

“…The dimensionless free energy F and order parameter Ψ are introduced as: 7) is supplemented by the boundary conditions (∇ϕ + 2πA/Φ 0 )| n on the boundary of FF strip with vacuum [20].…”

Microscopic derivation of superconductor-insulator boundary conditions for Ginzburg-Landau theory revisited. Enhanced superconductivity at boundaries with and without magnetic field

“…( 41) are different from the phenomenological boundary conditions used in [20,21]. Whereas de Gennes boundary conditions, previously used for FFLO systems [42,43] correspond to setting γ = 0 in our boundary conditions Eq. ( 41).…”

“…( 23) were used before for these systems, see e.g. [42,43]. Note that these boundary conditions eliminate the PDW boundary states discussed in [20,21] and contradict the phenomenological GL boundary conditions used there.…”