Superconducting state of the organic conductor (TMTSF)2ClO4

Modern History of Organic Conductors: An Overview

This short review article provides the reader with a summary of the history of organic conductors. To retain a neutral and objective point of view regarding the history, background, novelty, and details of each research subject within this field, a thousand references have been cited with full titles and arranged in chronological order. Among the research conducted over ~70 years, topics from the last two decades are discussed in more detail than the rest. Unlike other papers in this issue, this review will help readers to understand the origin of each topic within the field of organic conductors and how they have evolved. Due to the advancements achieved over these 70 years, the field is nearing new horizons. As history is often a reflection of the future, this review is expected to show the future directions of this research field.

Triplet superconductivity in coupled odd-gon rings

Shedding light on the nature of spin-triplet superconductivity has been a long-standing quest in condensed matter physics since the discovery of superfluidity in liquid ³He. Nevertheless, the mechanism of spin-triplet pairing is much less understood than that of spin-singlet pairing explained by the Bardeen-Cooper-Schrieffer theory or even observed in high-temperature superconductors. Here we propose a versatile mechanism for spin-triplet superconductivity which emerges through a melting of macroscopic spin polarization stabilized in weakly coupled odd-gon (e.g., triangle, pentagon, etc) systems. We demonstrate the feasibility of sustaining spin-triplet superconductivity with this mechanism by considering a new class of quasi-one-dimensional superconductors A₂Cr₃As₃ (A = K, Rb, and Cs). Furthermore, we suggest a simple effective model to easily illustrate the adaptability of the mechanism to general systems consisting of odd-gon units. This mechanism provides a rare example of superconductivity from on-site Coulomb repulsion.

Nematic Superconductivity in Doped Bi2Se3 Topological Superconductors

Nematic superconductivity is a novel class of superconductivity characterized by spontaneous rotational-symmetry breaking in the superconducting gap amplitude and/or Cooper-pair spins with respect to the underlying lattice symmetry. Doped Bi 2 Se 3 superconductors, such as Cu x Bi 2 Se 3 , Sr x Bi 2 Se 3 , and Nb x Bi 2 Se 3 , are considered as candidates for nematic superconductors, in addition to the anticipated topological superconductivity. Recently, various bulk probes, such as nuclear magnetic resonance, specific heat, magnetotransport, magnetic torque, and magnetization, have consistently revealed two-fold symmetric behavior in their in-plane magnetic-field-direction dependence, although the underlying crystal lattice possesses three-fold rotational symmetry. More recently, nematic superconductivity was directly visualized using scanning tunneling microscopy and spectroscopy. In this short review, we summarize the current research on the nematic behavior in superconducting doped Bi 2 Se 3 systems and discuss issues and perspectives.

Fulde-Ferrell state in superconducting core/shell nanowires: role of the orbital effect

The orbital effect on the Fulde-Ferrell (FF) phase is investigated in superconducting core/shell nanowires subjected to the axial magnetic field. Confinement in the radial direction results in quantization of the electron motion with energies determined by the radial j and orbital m quantum numbers. In the external magnetic field, the twofold degeneracy with respect to the orbital magnetic quantum number m is lifted which leads to the Fermi wave vector mismatch between the paired electrons, [Formula: see text]. This mismatch is transferred to the nonzero total momentum of the Cooper pairs, which results in a formation of the FF phase occurring sequentially with increasing magnetic field. By changing the nanowire radius R and the superconducting shell thickness d, we discuss the role of the orbital effect in the FF phase formation in both the nanowire-like ([Formula: see text]) and nanofilm-like ([Formula: see text]) regime. We have found that the irregular pattern of the FF phase which appears for the case of the nanowire-like regime, for the nanofilm-like geometry evolves towards the regular distribution in which the FF phase stability regions emerge periodically between the BCS states. The transition between these two different phase diagrams is explained as resulting from the orbital effect and the multigap character of superconductivity in the core/shell nanowires.

Exotic magnetic states in Pauli-limited superconductors

Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.

Microscopic Study of the Fulde-Ferrell-Larkin-Ovchinnikov State in an All-Organic Superconductor

Quasi-two-dimensional superconductors with a sufficiently weak interlayer coupling allow magnetic flux to penetrate in the form of Josephson vortices for in-plane applied magnetic fields. A consequence is the dominance of the Zeeman interaction over orbital effects. In the clean limit, the normal state is favored over superconductivity for fields greater than the paramagnetic limiting field, unless an intermediate, inhomogeneous state is stabilized. Presented here are nuclear magnetic resonance (NMR) studies of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state for β''-(ET)2SF5CH2CF2SO3. The uniform superconductivity-FFLO transition is identified at an applied field value of 9.3(0.1) T at low temperature (T=130  mK), and evidence for a possible second transition between inhomogeneous states at ∼11  T is presented. The spin polarization distribution inferred from the NMR absorption spectrum compares favorably to a single-Q modulation of the superconducting order parameter.

The Fulde-Ferrell-Larkin-Ovchinnikov state in layered d-wave superconductors: in-plane anisotropy and resonance effects in the angular dependence of the upper critical field

We study the anisotropy of the in-plane upper critical magnetic field coupled to the orbital motion and the spins of electrons in a layered d(x2-y2) organic superconductor in the spatially modulated Fulde-Ferrell-Larkin-Ovchinnikov phase. We show that the interplay between the nodal structure of the order parameter and its spatial modulation results in the very peculiar angular dependence of the onset of superconductivity in the high-field regime. The principal axis of the field-direction dependence of the onset of superconductivity is tilted by π/4 in the temperature range 0.056 < or approximately equal T < 0.56. In some cases the resonance between the modulation wavevector and the vector potential of a parallel magnetic field may lead to anomalous cusps in the temperature and in-plane angular dependences of the onset of superconductivity. The obtained results support the interpretation of the recent experiments as evidence of the FFLO state.

Low-field superconducting phase of (TMTSF)2ClO4

The low-field phase of the organic superconductor (TMTSF)(2)ClO(4) is studied by muon-spin rotation. The zero temperature limit of the magnetic penetration depth within the TMTSF layers is obtained to be λ(ab)(0) = 0.86(2) μm. Temperature dependence of the muon-spin relaxation shows no indication of gap nodes on the Fermi surface nor of any spontaneous fields due to time-reversal-symmetry breaking. The weight of evidence suggests that the symmetry of this low-field phase is odd-frequency p-wave singlet, a novel example of odd-frequency pairing in a bulk superconductor.

In-plane magnetic field anisotropy of the Fulde-Ferrell-Larkin-Ovchinnikov state in layered superconductors

There is strong experimental evidence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state formation in layered organic superconductors in a parallel magnetic field. We study theoretically the interplay between the orbital effect and the FFLO modulation in this case and demonstrate that the in-plane critical field anisotropy drastically changes at the transition to the FFLO state. The very peculiar angular dependence of the superconducting onset temperature which is predicted may serve for unambiguous identification of the FFLO modulation. The obtained results permit us to suggest the modulated phase stabilization as the origin of the magnetic-field angle dependence of the onset of superconductivity experimentally observed in (TMTSF)2ClO4 organic conductors.

Upper critical magnetic field far above the paramagnetic pair-breaking limit of superconducting one-dimensional Li0:9Mo6O17 single crystals

The upper critical field H(c2) of purple bronze Li0:9Mo6O17 is found to exhibit a large anisotropy, in quantitative agreement with that expected from the observed electrical resistivity anisotropy. With the field aligned along the most conducting axis, H(c2) increases monotonically with decreasing temperature to a value 5 times larger than the estimated paramagnetic pair-breaking field. Theories for the enhancement of H(c2) invoking spin-orbit scattering or strong-coupling superconductivity are shown to be inadequate in explaining the observed behavior, suggesting that the pairing state in Li0:9Mo6O17 is unconventional and possibly spin triplet.

Inhomogeneous superconductivity in organic conductors: the role of disorder and magnetic field

Several experimental studies have shown the presence of spatially inhomogeneous phase coexistence of superconducting and non-superconducting domains in low dimensional organic superconductors. The superconducting properties of these systems are found to be strongly dependent on the amount of disorder introduced in the sample regardless of its origin. The suppression of the superconducting transition temperature T(c) shows a clear discrepancy with the result expected from the Abrikosov-Gor'kov law giving the behavior of T(c) with impurities. On the basis of the time dependent Ginzburg-Landau theory, we derive a model to account for this striking feature of T(c) in organic superconductors for different types of disorder by considering the segregated texture of the system. We show that the calculated T(c) quantitatively agrees with experiments. We also focus on the effect of superconducting fluctuations on the upper critical fields H(c2) of layered superconductors showing slab structure where superconducting domains are sandwiched by non-superconducting regions. We found that H(c2) may be strongly enhanced by such fluctuations.

Hidden reentrant and Larkin-Ovchinnikov-Fulde-Ferrell superconducting phases in a magnetic field in a (TMTSF)2ClO4

We solve a long-standing problem about a theoretical description of the upper critical magnetic field, parallel to conducting layers and perpendicular to conducting chains, in a (TMTSF)(2)ClO(4) superconductor. In particular, we explain why the experimental upper critical field, H(c2)(b')≃6 T, is higher than both the quasiclassical upper critical field and the Clogston paramagnetic limit. We show that this property is due to the coexistence of the hidden reentrant and Larkin-Ovchinnikov-Fulde-Ferrell phases in a magnetic field in the form of three plane waves with nonzero momenta of the Cooper pairs. Our results are in good qualitative and quantitative agreement with the recent experimental measurements of H(c2)(b') and support a singlet d-wave-like scenario of superconductivity in (TMTSF)(2)ClO(4).

Zeeman-driven phase transition within the superconducting state of κ-(BEDT-TTF)2Cu(NCS)2

(13)C nuclear magnetic resonance measurements were performed on κ-(BEDT-TTF)(2)Cu(NCS)(2), with the external field placed parallel to the quasi-2D conducting layers. The absorption spectrum is used to determine the electronic spin polarization M(s) as a function of external field H at a temperature T=0.35 K. A discontinuity in the derivative dM(s)/dH at an applied field of H(s)=213±3 kOe is taken as evidence for a Zeeman-driven transition within the superconducting state and stabilization of inhomogeneous superconductivity.

Magnetic structure of the antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov state

The properties of incommensurate antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are studied by solving the Bogoliubov-de Gennes (BdG) equations. The relationship between the electronic structure and the magnetic structure is clarified. We find that the magnetic structure in the AFM-FFLO state includes three cases. (I) In the strongly localized case, the AFM staggered moment is confined into the FFLO nodal planes where the superconducting order parameter vanishes. (II) In the weakly localized case, the AFM staggered moment appears in the whole spatial region, and its magnitude is enhanced around the FFLO nodal planes. (III) In the extended case, the AFM staggered moment is nearly homogeneous and slightly suppressed in the vicinity of the FFLO nodal planes. The structure of Bragg peaks in the momentum resolved structure factor is studied in each case. We discuss the possibility of an AFM-FFLO state in the heavy fermion superconductor CeCoIn5 by comparing these results with the neutron scattering data of CeCoIn5. Experimentally the magnetic structure and its dependence on the magnetic field orientation in the high-field superconducting phase of CeCoIn5 are consistent with case (II).

Hidden quasi-one-dimensional superconductivity in Sr₂RuO₄

We show that the interplay between spin and charge fluctuations in Sr₂RuO₄ leads unequivocally to triplet pairing which has a hidden quasi-one-dimensional character. The resulting superconducting state spontaneously breaks time-reversal symmetry and is of the form Δ ~(p(x)+ip(y))z(^) with sharp gap minima and a d vector that is only weakly pinned. The superconductor lacks robust chiral Majorana fermion modes along the boundary. The absence of topologically protected edge modes could explain the surprising absence of experimentally detectable edge currents in this system.

The Fulde-Ferrell-Larkin-Ovchinnikov phase in the presence of pair hopping interaction

The recent experimental support for the presence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in CeCoIn(5) directed attention towards the mechanisms responsible for this type of superconductivity. We investigate the FFLO state in a model where on-site/inter-site pairing coexists with the repulsive pair hopping interaction. The latter interaction is interesting in that it leads to pairing with non-zero momentum of the Cooper pairs even in the absence of the external magnetic field (the so-called η pairing). It turns out that, depending on the strength of the pair hopping interaction, the magnetic field can induce one of two types of the FFLO phase with different spatial modulations of the order parameter. It is argued that the properties of the FFLO phase may give information about the magnitude of the pair hopping interaction. We also show that η pairing and d-wave superconductivity may coexist in the FFLO state. It holds true also for superconductors which, in the absence of magnetic field, are of pure d-wave type.

Strong parity mixing in the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity in systems with coexisting spin and charge fluctuations

We study the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of spin fluctuation mediated pairing, and focus on the effect of coexisting charge fluctuations. We find that (i) consecutive transitions from singlet pairing to FFLO and further to S_{z}=1 triplet pairing can generally take place upon increasing the magnetic field when strong charge fluctuations coexist with spin fluctuations, and (ii) the enhancement of the charge fluctuations lead to a significant increase of the parity mixing in the FFLO state, where the triplet/singlet component ratio in the gap function can be close to unity. We propose that such consecutive pairing state transition and strong parity mixing in the FFLO state may take place in a quasi-one-dimensional organic superconductor (TMTSF)2X.

Anomalous in-plane anisotropy of the onset of superconductivity in (TMTSF)2ClO4

We report the magnetic-field amplitude and field-angle dependence of the superconducting onset temperature Tconset of the organic superconductor (TMTSF)2ClO4 in magnetic fields H accurately aligned to the conductive ab' plane. We revealed that the rapid increase of the onset fields at low temperatures occurs both for H || b' and H || a, irrespective of the carrier confinement. Moreover, in the vicinity of the Pauli-limiting field, we report a shift of a principal axis of the in-plane field-angle dependence of Tconset. This feature may be related to an occurrence of Fulde-Ferrell-Larkin-Ovchinnikov phases.