The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is examined in quasi-one-dimensional s-wave and d-wave superconductors with particular attention paid to the effect of the Fermi-surface anisotropy. The upper critical field H c2 (T ) is found to exhibit a qualitatively different behavior depending on the ratio of the hopping energies t b /t a and the direction of the FFLO modulation vector q, where t a and t b are the intra-and interchain hopping energies, respectively. In particular, when t b /t a < ∼ 0.1 and q a, we find a novel dimensional crossover of H c2 (T ) from one dimension to two dimensions, where a is the lattice vector of the most conductive chain. Just below the tricritical temperature T * , the upper critical field H c2 (T ) increases steeply as in one-dimensional systems, but when the temperature decreases, the rate of increase in H c2 (T ) diminishes and a shoulder appears. Near T = 0, H c2 (T ) shows a behavior typical of the FFLO state in two-dimensional systems, i.e., an upturn with a finite field at T = 0. When the angle between q and a is large, the upper critical field curve is convex upward at low temperatures, as in three-dimensional systems, but the magnitude is much larger than that of a three-dimensional isotropic system. For t b /t a > ∼ 0.15, the upper critical fields exhibit a two-dimensional behavior, except for a slight shoulder in the range of 0.2 > ∼ t b /t a > ∼ 0.15. The upper critical field is maximum for q a both for s-wave and d-wave pairings, while it is only slightly larger than the Pauli paramagnetic limit for q ⊥ a. The relevance of the present results to the organic superconductor (TMTSF) 2 ClO 4 is discussed.

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We propose a mechanism that helps stabilize a superconducting state with broken time-reversal symmetry, which was predicted to realize in a d-wave superconducting film [A. B. Vorontsov, Phys. Rev. Lett. 102, 177001 (2009)]. In this superconducting phase, the time-reversal symmetry breaking is accompanied by spontaneous breaking of the translation symmetry along the film surface.We examine how the normal-superconducting phase boundary in the thickness-temperature phase diagram of the film is modified depending on the Fermi surface shape. In particular, the nonuniform superconducting phase is found to substantially extend to a smaller thickness region in the phase diagram when the Fermi surface satisfies a nesting condition. We demonstrate this Fermi surface effect using a square-lattice tight-binding model.

We report a theoretical study on the phase transition between superconducting states with and without spontaneous surface current. The phase transition takes place due to the formation of surface Andreev bound states in unconventional superconductors. Based on the quasiclassical theory of superconductivity, we examine the influence of atomic-scale surface roughness on the surface phase transition temperature Ts. To describe the surface effect, the boundary condition for the quasiclassical Green's function is parameterized in terms of specularity (the specular reflection probability in the normal state at the Fermi level). This boundary condition allows systematic study of the surface effect ranging from the specular limit to the diffuse limit. We show that diffuse quasiparticle scattering at a rough surface causes substantial reduction of Ts in the d-wave pairing state of high-Tc cuprate superconductors. We also consider a p-wave pairing state in which Andreev bound states similar to those in the d-wave state are generated. In contrast to the d-wave case, Ts in the p-wave state is insensitive to the specularity. This is because the Andreev bound states in the p-wave superconductor are robust against diffuse scattering, as implied from symmetry consideration for odd-frequency Cooper pairs induced at the surface; the p-wave state has odd-frequency pairs with s-wave symmetry, while the d-wave state does not.

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