On the Fulde-Ferrell State in Spatially Isotropic Superconductors

Effects of superconducting fluctuations on the Fulde-Ferrell (FF) state are discussed in a spatially isotropic three-dimensional superconductor under a magnetic field. For this system, Shimahara recently showed that within the phenomenological Ginzburg-Landau theory, the long-range order of the FF state is suppressed by the phase fluctuation of the superconducting order parameter. [H. Shimahara: J. Phys. Soc. Jpn. {\bf 67} (1998) 1872, Physica B {\bf 259-261} (1999) 492] In this letter, we investigate this instability of the FF state against superconducting fluctuations from the microscopic viewpoint, employing the theory developed by Nozi\'eres and Schmitt-Rink in the BCS-BEC crossover field. Besides the absence of the second-order phase transition associated with the FF state, we show that even if the pairing interaction is weak, the shift of the chemical potential from the Fermi energy due to the fluctuations is crucial near the critical magnetic field of the FF state obtained within the mean-field theory.Comment: 11 pages, 1 figur

Enhancement of the upper critical field and a field-induced superconductivity in antiferromagnetic conductors

We propose a mechanism by which the paramagnetic pair-breaking effect is largely reduced in superconductors with coexisting antiferromagnetic long- range and short-range orders. The mechanism is an extension of the Jaccarino and Peter mechanism to antiferromagnetic conductors, but the resultant phase diagram is quite different. In order to illustrate the mechanism, we examine a model which consists of mobile electrons and antiferromagnetically correlated localized spins with Kondo coupling between them. It is found that for weak Kondo coupling, the superconductivity occurs over an extraordinarily wide region of the magnetic field including zero field. The critical field exceeds the Chandrasekhar and Clogston limit, but there is no lower limit in contrast to the Jaccarino and Peter mechanism. On the other hand, for strong Kondo coupling, both the low-field superconductivity and a field-induced superconductivity occur. Possibilities in hybrid ruthenate cuprate superconductors and some organic superconductors are discussed.Comment: 5 pages, 1 figure, revtex.sty, to be published in J.Phys.Soc.Jpn. Vol.71, No.3 (2002

Spin-Triplet Superconductivity Mediated by Phonons in Quasi-One-Dimensional Systems

We investigate the spin-triplet superconductivity mediated by phonons in quasi-one-dimensional (Q1D) systems with open Fermi surfaces. We obtain the ground state phase diagrams. It is found that spin-triplet superconductivity occurs for weak screening and strong on-site Coulomb interaction, even in the absence of any additional nonphonon pairing interactions. We find that the nodeless spin-triplet state is more favorable than the spin-triplet state with line nodes, for the parameter values of the Q1D superconductors (TMTSF)_2X. We also find that Q1D open Fermi surface, which is the specific feature of this system, plays an essential role in the pairing symmetry. We discuss the compatibility of the present results with the experimental results in these compounds.Comment: 8 pages, 15 figures, with jpsj2.cl

Coexistence of Singlet and Triplet Attractive Channels in the Pairing Interactions Mediated by Antiferromagnetic Fluctuations

We propose a phase diagram of quasi-low-dimensional type II superconductors in parallel magnetic fields, when antiferromagnetic fluctuations contribute to the pairing interactions. We point out that pairing interactions mediated by antiferromagnetic fluctuations necessarily include both singlet channels and triplet channels as attractive interactions. Usually, a singlet pairing is favored at zero field, but a triplet pairing occurs at high fields where the singlet pairing is suppressed by the Pauli paramagnetic pair-breaking effect. As a result, the critical field increases divergently at low temperatures. A possible relation to experimental phase diagrams of a quasi-one-dimensional organic superconductor is briefly discussed. We also discuss a possibility that a triplet superconductivity is observed even at zero field.Comment: 4 pages, 1 figure (Latex, revtex.sty, epsf.sty

Isotope effect in superconductors with coexisting interactions of phonon and nonphonon mechanisms

We examine the isotope effect of superconductivity in systems with coexisting interactions of phonon and nonphonon mechanisms in addition to the direct Coulomb interaction. The interaction mediated by the spin fluctuations is discussed as an example of the nonphonon interaction. Extended formulas for the transition temperature Tc and the isotope-effect coefficient alpha are derived for cases (a) omega_np omega_D, where omega_np is an effective cutoff frequency of the nonphonon interaction that corresponds to the Debye frequency omega_D in the phonon interaction. In case (a), it is found that the nonphonon interaction does not change the condition for the inverse isotope effect, i.e., mu^* > lambda_ph/2, but it modifies the magnitude of alpha markedly. In particular, it is found that a giant isotope shift occurs when the phonon and nonphonon interactions cancel each other largely. For instance, strong critical spin fluctuations may give rise to the giant isotope effect. In case (b), it is found that the inverse isotope effect occurs only when the nonphonon interaction and the repulsive Coulomb interaction, in total effect, work as repulsive interactions against the superconductivity. We discuss the relevance of the present result to some organic superconductors, such as kappa-(ET)2Cu(NCS)2 and Sr2RuO4 superconductors, in which inverse isotope effects have been observed, and briefly to high-Tc cuprates, in which giant isotope effects have been observed.Comment: 4 pages, 2 figures, (with jpsj2.cls, ver.1.2), v2:linguistic correction

Mechanism for the Singlet to Triplet Superconductivity Crossover in Quasi-One-Dimensional Organic Conductors

Superconductivity of quasi-one-dimensional organic conductors with a quarter-filled band is investigated using the two-loop renormalization group approach to the extended Hubbard model for which both the single electron hopping t_{\perp} and the repulsive interaction V_{\perp} perpendicular to the chains are included. For a four-patches Fermi surface with deviations to perfect nesting, we calculate the response functions for the dominant fluctuations and possible superconducting states. By increasing V_{\perp}, it is shown that a d-wave (singlet) to f-wave (triplet) superconducting state crossover occurs, and is followed by a vanishing spin gap. Furthermore, we study the influence of a magnetic field through the Zeeman coupling, from which a triplet superconducting state is found to emerge.Comment: 11 pages, 15 figures, published versio

Structure of the Fulde-Ferrell-Larkin-Ovchinnikov state in two-dimensional superconductors

Nonuniform superconducting state due to strong spin magnetism is studied in two-dimensional type-II superconductors near the second order phase transition line between the normal and the superconducting states. The optimum spatial structure of the orderparameter is examined in systems with cylindrical symmetric Fermi surfaces. It is found that states with two-dimensional structures have lower free energies than the traditional one-dimensional solutions, at low temperatures and high magnetic fields. For s-wave pairing, triangular, square, hexagonal states are favored depending on the temperature, while square states are favored at low temperatures for d-wave pairing. In these states, orderparameters have two-dimensional structures such as square and triangular lattices.Comment: 11 pages (LaTeX, revtex.sty), 3 figures; added reference

The Fulde-Ferrell-Larkin-Ovchinnikov State in the Organic Superconductor k-(BEDT-TTF)2Cu(NCS)2 as Observed in Magnetic Torque Experiments

We present magnetic-torque experiments on the organic superconductor k-(BEDT-TTF)2Cu(NCS)2 for magnetic fields applied parallel to the 2D superconducting layers. The experiments show a crossover from a second-order to a first-order transition when the upper critical field reaches 21 T. Beyond this field, which we interpret as the Pauli limit for superconductivity, the upper critical field line shows a pro-nounced upturn and a phase transition line separates the superconducting state into a low- and a high-field phase. We interpret the data in the framework of a Fulde-Ferrell-Larkin-Ovchinnikov state.Comment: 2 pages, 1 figur

A Two-dimensional Superconductor in a Tilted Magnetic Field - new states with finite Cooper-pair momentum

Varying the angle Theta between applied field and the conducting planes of a layered superconductor in a small interval close to the plane-parallel field direction, a large number of superconducting states with unusual properties may be produced. For these states, the pair breaking effect of the magnetic field affects both the orbital and the spin degree of freedom. This leads to pair wave functions with finite momentum, which are labeled by Landau quantum numbers 0<n<\infty. The stable order parameter structure and magnetic field distribution for these states is found by minimizing the quasiclassical free energy near H_{c2} including nonlinear terms. One finds states with coexisting line-like and point-like order parameter zeros and states with coexisting vortices and antivortices. The magnetic response may be diamagnetic or paramagnetic depending on the position within the unit cell. The structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states at Theta=0 is reconsidered. The transition n->\infty of the paramagnetic vortex states to the FFLO-limit is analyzed and the physical reason for the occupation of higher Landau levels is pointed out.Comment: 24 pages, 11 figure

Pairing competition in a quasi-one-dimensional model of organic superconductors (TMTSF)2X_{2}X in magnetic field

We microscopically study the effect of the magnetic field (Zeeman splitting) on the superconducting state in a model for quasi-one-dimensional organic superconductors (TMTSF)$_{2}X$. We investigate the competition between spin singlet and spin triplet pairings and the Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) state by random phase approximation. While we studied the competition by comparison with the eigenvalue of the gap equation at a fixed temperature in our previous study (Phys. Rev. Lett. \textbf{102} (2009) 016403), here we obtain both the $T_c$ for each pairing state and a phase diagram in the $T$(temperature)-$h_z$(field)-$V_y$(strength of the charge fluctuation) space. The phase diagram shows that consecutive transitions from singlet pairing to the FFLO state and further to $S_z=1$ triplet pairing can occur upon increasing the magnetic field when $2k_{F}$ charge fluctuations coexist with $2k_{F}$ spin fluctuations. In the FFLO state, the singlet d-wave and $S_{z}=0$ triplet $f$-wave components are strongly mixed especially when the charge fluctuations are strong.Comment: 11 pages, 9 figure