Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as appears in JSTA

Fermiology and superconductivity studies on the non-tetrachalcogenafulvalene structured organic superconductor beta-(BDA-TTP)_2SbF_6

The quantum oscillatory effect and superconductivity in a non-tetrachalcogenafulvalene (TCF) structure based organic superconductor beta-(BDA-TTP)_2SbF_6 are studied. Here the Shubnikov-de Haas effect (SdH) and angular dependent magnetoresistance oscillations (AMRO) are observed. The oscillation frequency associated with a cylindrical Fermi surface is found to be about 4050 tesla, which is also verified by the tunnel diode oscillator (TDO) measurement. The upper critical field Hc2 measurement in a tilted magnetic field and the TDO measurement in the mixed state reveal a highly anisotropic superconducting nature in this material. We compared physical properties of beta-(BDA-TTP)_2SbF_6 with typical TCF structure based quasi two-dimensional organic conductors. A notable feature of beta-(BDA-TTP)_2SbF_6 superconductor is a large value of effective cyclotron mass m_c^*=12.4+/1.1 m_e, which is the largest yet found in an organic superconductor. A possible origin of the enhanced effective mass and its relation to the superconductivity are briefly discussed.Comment: 8 pages, 10 figure

Small-q phonon-mediated superconductivity in organic \kappa-BEDT-TTF compounds

We propose a mew picture for superconductivity in $\kappa-(BEDT-TTF)_2X$ salts arguing that small-{\bf q} electron-phonon scattering dominates the pairing. We reproduce the distinct X-shaped d-wave gap reported recently by magnetooptic measurements and we argue that the softness of the momentum structure of the gap and the near degeneracy of s- and d-wave gap states may be at the origin of the experimental controversy about the gap symmetry. We show that a magnetic field applied parallel to the planes may induce extended gapless-regions on the FS accounting for the experimental signatures of a Fulde-Ferrel-Larkin-Ovchinikov state and it may induce gap symmetry transitions as well.Comment: 4 pages and 7 figure

Evidence for structural and electronic instabilities at intermediate temperatures in κ\kappa-(BEDT-TTF)2_{2}X for X=Cu[N(CN)2_{2}]Cl, Cu[N(CN)2_{2}]Br and Cu(NCS)2_{2}: Implications for the phase diagram of these quasi-2D organic superconductors

We present high-resolution measurements of the coefficient of thermal expansion $\alpha (T)=\partial \ln l(T)/\partial T$ of the quasi-twodimensional (quasi-2D) salts $\kappa$-(BEDT-TTF)$_2$X with X = Cu(NCS)$_2$, Cu[N(CN)$_2$]Br and Cu[N(CN)$_2$]Cl. At intermediate temperatures (B), distinct anomalies reminiscent of second-order phase transitions have been found at $T^\ast = 38$ K and 45 K for the superconducting X = Cu(NCS)$_2$ and Cu[N(CN)$_2$]Br salts, respectively. Most interestingly, we find that the signs of the uniaxial pressure coefficients of $T^\ast$ are strictly anticorrelated with those of $T_c$. We propose that $T^\ast$ marks the transition to a spin-density-wave (SDW) state forming on minor, quasi-1D parts of the Fermi surface. Our results are compatible with two competing order parameters that form on disjunct portions of the Fermi surface. At elevated temperatures (C), all compounds show $\alpha (T)$ anomalies that can be identified with a kinetic, glass-like transition where, below a characteristic temperature $T_g$, disorder in the orientational degrees of freedom of the terminal ethylene groups becomes frozen in. We argue that the degree of disorder increases on going from the X = Cu(NCS)$_2$ to Cu[N(CN)$_2$]Br and the Cu[N(CN)$_2$]Cl salt. Our results provide a natural explanation for the unusual time- and cooling-rate dependencies of the ground-state properties in the hydrogenated and deuterated Cu[N(CN)$_2$]Br salts reported in the literature.Comment: 22 pages, 7 figure

The Dependence of the Superconducting Transition Temperature of Organic Molecular Crystals on Intrinsically Non-Magnetic Disorder: a Signature of either Unconventional Superconductivity or Novel Local Magnetic Moment Formation

We give a theoretical analysis of published experimental studies of the effects of impurities and disorder on the superconducting transition temperature, T_c, of the organic molecular crystals kappa-ET_2X and beta-ET_2X (where ET is bis(ethylenedithio)tetrathiafulvalene and X is an anion eg I_3). The Abrikosov-Gorkov (AG) formula describes the suppression of T_c both by magnetic impurities in singlet superconductors, including s-wave superconductors and by non-magnetic impurities in a non-s-wave superconductor. We show that various sources of disorder lead to the suppression of T_c as described by the AG formula. This is confirmed by the excellent fit to the data, the fact that these materials are in the clean limit and the excellent agreement between the value of the interlayer hopping integral, t_perp, calculated from this fit and the value of t_perp found from angular-dependant magnetoresistance and quantum oscillation experiments. If the disorder is, as seems most likely, non-magnetic then the pairing state cannot be s-wave. We show that the cooling rate dependence of the magnetisation is inconsistent with paramagnetic impurities. Triplet pairing is ruled out by several experiments. If the disorder is non-magnetic then this implies that l>=2, in which case Occam's razor suggests that d-wave pairing is realised. Given the proximity of these materials to an antiferromagnetic Mott transition, it is possible that the disorder leads to the formation of local magnetic moments via some novel mechanism. Thus we conclude that either kappa-ET_2X and beta-ET_2X are d-wave superconductors or else they display a novel mechanism for the formation of localised moments. We suggest systematic experiments to differentiate between these scenarios.Comment: 18 pages, 5 figure

Pairing Symmetry Competition in Organic Superconductors

A review is given on theoretical studies concerning the pairing symmetry in organic superconductors. In particular, we focus on (TMTSF)$_2$X and $\kappa$-(BEDT-TTF)$_2$X, in which the pairing symmetry has been extensively studied both experimentally and theoretically. Possibilities of various pairing symmetry candidates and their possible microscopic origin are discussed. Also some tests for determining the actual pairing symmtery are surveyed.Comment: 16 pages, 8 figures, to be published in J. Phys. Soc. Jpn., special issue on "Organic Conductors

Superconductivity mediated by charge fluctuations in layered molecular crystals

We consider the competition between superconducting, charge ordered, and metallic phases in layered molecular crystals with the theta and beta" structures. Applying slave-boson theory to the relevant extended Hubbard model, we show that the superconductivity is mediated by charge fluctuations and the Cooper pairs have d(xy) symmetry. This is in contrast to the kappa-(BEDT-TTF)(2)X family, for which theoretical calculations give superconductivity mediated by spin fluctuations and with d(x)2(-y)2 symmetry. We predict several materials that should become superconducting under pressure