Fulde–Ferrell–Larkin–Ovchinnikov State in Perpendicular Magnetic Fields in Strongly Pauli-Limited Quasi-Two-Dimensional Superconductors

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We examine the Fermi-surface effect called the nesting effect for the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in strongly Pauli-limited quasi-two-dimensional superconductors, focusing on the effect of three-dimensional factors, such as interlayer electron transfer, interlayer pairing, and off-plane magnetic fields including those perpendicular to the most conductive layers (hereinafter called the perpendicular fields). We examine the systems with a large Maki parameter so that the orbital pair-breaking effect is negligible, except for the locking of the direction of the FFLO vector q in the magnetic-field direction. It is known that the nesting effect for the FFLO state can be strong in quasi-low-dimensional systems in which the orbital pair-breaking effect is suppressed by applying the magnetic field parallel to the layers. Hence, it has sometimes been suggested that the nesting effect may hardly enhance the stability of the FFLO state for perpendicular fields. We illustrate that, contrary to this view, the nesting effect can strongly stabilize the FFLO state for perpendicular fields as well as for parallel fields when tz is small so that the Fermi surfaces are open in the kz-direction, where tz denotes the interlayer transfer energy. In particular, the nesting effect in perpendicular fields can be strong in interlayer states. For example, in systems with cylindrical Fermi surfaces warped by tz ≠ 0, interlayer states with Δk ∝ sin kz exhibit μeHc ≈ 1.65Δα0 for perpendicular fields, which is much larger than typical values for parallel fields, such as μeHc = Δs0 of the s-wave state and μeHc ≈ 1.28Δd0 of the d-wave state in cylindrical systems with tz = 0. Here, μe and Hc are the electron magnetic moment and upper critical field of the FFLO state at T = 0, respectively, and Δα0≡2ωce−1/λα. We discuss the possible relevance of the nesting effect to the high-field superconducting phases in perpendicular fields observed in the compounds CeCoIn5 and FeSe, which are candidates for the FFLO state. The present result could potentially provide a physical reason for the fact that the areas in the phase diagrams occupied by the high-field phases for the perpendicular and parallel fields are of the same order.

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