We suggest that superconductivity (SC) in the organic charge transfer solids (CTS) is reached from a Bond-Charge Density Wave (BCDW). We discuss an effective model for the BCDW to SC transition, an attractive U extended Hubbard Hamiltonian with repulsive nearest neighbor interaction V. We discuss experimental consequences of the theory for different classes of CTS superconductors as well as related inorganic materials.
We show that superconductivity is absent within the 1/2-filled band triangular lattice repulsive Hubbard model that has been proposed for organic charge-transfer solids. We posit that organic superconductivity is rather reached from a Bond-Charge Density Wave that either constitutes the insulating state proximate to superconductivity, or is extremely close in energy to the antiferromagnetic state, and replaces the latter under pressure. The Bond-Charge Density Wave can be described within an effective attractive $U$ extended Hubbard Hamiltonian with repulsive nearest neighbor interaction $V$. …
We study electron correlation driven superconductivity on a decorated honeycomb lattice (DHL), which has a low-energy flat band. On doping, we find singlet superconductivity with extended-s, extended-d and f-wave symmetry mediated by magnetic exchange. f-wave singlet pairing is enabled by the lattice decoration. The critical temperature is predicted to be significantly higher than on similar lattices lacking flat bands. We discuss how high-temperature superconductivity could be realized in the DHL materials such as Rb3TT. 2 H2O and Mo3S7(dmit)3.
Unconventional density waves (UDW) are one of the ground states in metallic crystalline solids and have been speculated already in 1968. However, more focused studies on UDW started only recently, perhaps after the identification of the low temperature phase in alpha-(BEDT-TTF)_2KHg(SCN)_4 as unconventional charge density wave (UCDW) in 2002. More recently, the metallic phase of Bechgaard salts (TMTSF)_2X with X=PF_6 and ReO_4 under both pressure and magnetic field appears to be unconventional spin density wave (USDW). The pseudogap regime of high T_c superconductors LSCO, YBCO, Bi2212 and the…
The phase diagram of the layered organic superconductor $κ$-(ET)$_{2}$Cu[N(CN)$_{2}$]Cl has been accurately measured from a combination of $^{1}$H NMR and AC susceptibility techniques under helium gas pressure. The domains of stability of antiferromagnetic and superconducting long-range orders in the pressure {\it vs} temperature plane have been determined. Both phases overlap through a first-order boundary that separates two regions of inhomogeneous phase coexistence. The boundary curve is found to merge with another first order line related to the metal-insulator transition in the paramagnet…
This Letter theoretically discusses quasiparticle states and nuclear spin relaxation rates $T_1^{-1}$ in a quasi-one-dimensional superconductor (TMTSF)$_2$PF$_6$ under a magnetic field applied parallel to the conduction chains. We study the effects of Josephson-type vortices on $T_1^{-1}$ by solving the Bogoliubov de Gennes equation for $p$-, $d$- or $f$-wave pairing interactions. In the presence of line nodes in pairing functions, $T_1^{-1}$ is proportional to $T$ in sufficiently low temperatures because quasiparticles induced by vortices at the Fermi energy relax spins. We also try to identi…
By using a renormalized mean-field theory, we investigate the phase diagram of $t$-$t'$-$J$-$J'$ model on two dimensional Shastry-Sutherland lattice which are topologically equivalent to synthesized material $\mathrm{SrCu_2(BO_3)_2}$. We find that the symmetry of superconductivity ground state depends on the frustration amplitude $η=t'/t$ and doping concentration. For weak to intermediate frustration, $d_{x^2-y^2}$-wave pairing symmetry is robust in a large parameter region. Around the symmetric point $|η|=1$, d-wave, $s$-s-wave pairing as well as staggered flux may serve as ground state by va…
We study spin fluctuation (SF) mediated superconductivity (SC) in a half-filled square lattice Hubbard model with the transfer matrices -t between nearest neighbor sites and -t' between a half of next nearest neighbor sites neighboring along only one of the <1,1> directions, considering application of this model to organic kappa-(BEDT-TTF)2X compounds. Varying the t'/t value from 0 to 1, one can interpolate between a square and an equilateral triangular lattice, the latter giving frustration to antiferromagnetically (AF) coupled spin systems. Within the fluctuation exchange (FLEX) approximatio…
We study theoretically the shift of the superconducting transition temperature (Tc) under uniaxial compression in beta-type organic superconductors, beta-(BEDT-TTF)2I3 and beta-(BDA-TTP)2X[X=SbF6,AsF6], in order to clarify the electron correlation, the spin frustration and the effect of dimerization. The transfer integrals are calculated by the extended Huckel method assuming the uniaxial strain and the superconducting state mediated by the spin fluctuation is solved using Eliashberg's equation with the fluctuation-exchange approximation. The calculation is carried out on both the dimerized (o…
We present a study of the effects of simultaneous charge- and spin-frustration on the two-dimensional strongly correlated quarter-filled band on an anisotropic triangular lattice. The broken-symmetry states that dominate in the weakly frustrated region near the rectangular lattice limit are the well known antiferromagnetic state with in-phase lattice dimerization along one direction, and the Wigner crystal state with the checkerboard charge order. For moderate to strong frustration, however, the dominant phase is a novel spin-singlet paired-electron crystal (PEC), consisting of pairs of charge…
Recently, the superconductivity in a metal-organic framework (MOF) has been discovered for the first time in copper(II) benzenehexathiolate ([Cu$_3$(C$_6$S$_6$)]$_n$, Cu-BHT). The Cu atoms form a two-dimensional perfect Kagome lattice, which has the potential to host a metallic quantum spin liquid state. Here we present high-precision measurements of in-plane magnetic penetration depth $λ$ in Cu-BHT films down to 40\,mK. The temperature dependence of $λ$ shows a non-exponential, quasi-linear behavior at low temperatures, suggesting that unconventional superconductivity with low-energy quasipar…
We review the interplay of frustration and strong electronic correlations in quasi-two-dimensional organic charge transfer salts, such as k-(BEDT-TTF)_2X and Et_nMe_{4-n}Pn[Pd(dmit)2]2. These two forces drive a range of exotic phases including spin liquids, valence bond crystals, pseudogapped metals, and unconventional superconductivity. Of particular interest is that in several materials there is a direct transition as a function of pressure from a spin liquid Mott insulating state to a superconducting state. Experiments on these materials raise a number of profound questions about the quantu…
We present a novel route for attaining unconventional superconductivity (SC) in a strongly correlated system without doping. In a simple model of a correlated band insulator (BI) at half-filling we demonstrate, based on a generalization of the projected wavefunctions method, that SC emerges when e-e interactions and the bare band-gap are both much larger than the kinetic energy, provided the system has sufficient frustration against the magnetic order. As the interactions are tuned, SC appears sandwiched between the correlated BI followed by a paramagnetic metal on one side, and a ferrimagneti…
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 describe…
We present a review of quasi-two-dimensional organic superconductors. These systems exhibit many interesting phenomena, including reduced dimensionality, strong electron-electron and electron-phonon interactions and the proximity of antiferromagnetism, insulator states and superconductivity. Moreover, it has been possible to measure the electronic bands of many of the organics in great detail, in contrast to the situation in other well-known systems in which similar phenomena occur. We describe the crystal structure and normal-state properties of the organics, before presenting the experimenta…
We introduce and analyze a variational wave function for quasi two-dimensional kappa-ET organic salts containing strong local and nonlocal correlation effects. We find an unconventional superconducting ground state for intermediate charge carrier interaction, sandwiched between a conventional metal at weak coupling and a spin liquid at larger coupling. Most remarkably, the excitation spectrum is dramatically renormalized and is found to be the driving force for the formation of the unusual superconducting state.
We review the current understanding of superconductivity in the quasi-one-dimensional organic conductors of the Bechgaard and Fabre salt families. We discuss the interplay between superconductivity, antiferromagnetism, and charge-density-wave fluctuations. The connection to recent experimental observations supporting unconventional pairing and the possibility of a triplet-spin order parameter for the superconducting phase is also presented.
Metal-organic frameworks (MOFs), which are self-assemblies of metal ions and organic ligands, provide a tunable platform to search a new state of matter. A two-dimensional (2D) perfect kagome lattice, whose geometrical frustration is a key to realizing quantum spin liquids, has been formed in the $π$-${d}$ conjugated 2D MOF [Cu$_{3}$(C$_{6}$S$_{6}$)]$_{n}$ (Cu-BHT). The recent discovery of its superconductivity with a critical temperature $T_{\rm c}$ of 0.25\,kelvin raises fundamental questions about the nature of electron pairing. Here, we show that Cu-BHT is a strongly correlated unconventio…
Recently many people discuss unconventional density waves (i.e. unconventional charge density waves (UCDW) and unconventional spin density waves (USDW)). Unlike in conventional density waves, the quasiparticle spectrum in these systems is gapless. Also these systems remain metallic. Indeed it appears that there are many candidates for UDW. The low temperature phase of alpha-(BEDT-TTF)_2KHg(SCN)_4, the antiferromagnetic phase in URu_2Si_2, the CDW in transition metal dichalcogenite NbSe_2, the pseudogap phase in high T_c cuprate superconductors, the glassy phase in organic superconductor kappa-…
There is intense controversy around the unconventional superconductivity in strontium ruthenate, where the various theoretical and experimental studies suggest diverse and mutually exclusive pairing symmetries. Currently, the investigation is solely focused on only one material, Sr2RuO4, and the field suffers from the lack of comparison targets. Here, employing a density functional theory based analysis, we show that the heterostructure composed of SrRuO3 and SrTiO3 is endowed with all the key characteristics of Sr2RuO4, and, in principle, can host superconductivity. Furthermore, we show that …
Over the past two decades, unconventional superconductivity with gap symmetry other than s-wave has been found in several classes of materials, including heavy fermion (HF), high-T_c, and organic superconductors. Unconventional superconductivity is characterized by anisotropic superconducting gap functions, which may have zeros (nodes) along certain directions in the Brillouin zone. The nodal structure is closely related to the pairing interaction, and it is widely believed that the presence of nodes is a signature of magnetic or some other exotic, rather than conventional phonon-mediated, pai…
We review recent progress in understanding the different spatial broken symmetries that occur in the normal states of the family of charge-transfer solids (CTS) that exhibit superconductivity (SC), and discuss how this knowledge gives insight to the mechanism of the unconventional SC in these systems. We show that a unified theory of the diverse broken symmetry states necessarily requires explicit incorporation of strong electron-electron interactions and lattice discreteness, and most importantly, the correct bandfilling of one-quarter. Uniquely in the quarter-filled band, there is a very str…
The study of non-s-wave unconventional superconductivities in strongly correlated-electron systems has been a central issue in condensed matter physics for more than 30 years. In such unconventional superconductivities, d-wave Cooper pairing with antiparallel spins has been often observed in various quasi-two-dimensional (quasi-2D) bulk systems. Interestingly, many theories predicted that the triangular lattice causes the d-wave pairing to be unstable and may lead to more exotic pairing such as parallel spin (spin-triplet) pairing. Here we focus on a bulk organic triangular-lattice system in w…
A frustrated, effective 1/2-filled band Hubbard-Heisenberg model has been proposed to describe the strongly dimerized charge-transfer solid families kappa-(ET)_2X and Z[Pd(dmit)_2]_2. In addition to unconventional superconductivity these materials also exhibit antiferromagnetism, candidate spin-liquid phases, and in the case of Z=EtMe_3P, a so-called valence-bond solid phase. We show that neither superconductivity nor the valence-bond solid phase occurs within the Hubbard-Heisenberg model, indicating that the effective 1/2-filled band model is unsuitable for these materials.
We discuss the possibility of deciding on the symmetry of the superconducting phase in the organic superconductors (Bechgaard salts), using tunnelling experiments. We first briefly review the properties of organic superconductors, and the possibility to have unconventional (triplet) superconductivity in these systems. We then present a simple scheme for computing the full current-voltage characteristics for tunnelling experiments within the framework of the non-equilibrium Keldysh Green function formalism. This formalism is flexible enough to address different pairing symmetries combined with …
Josephson effect in junctions of quasi one-dimensional triangular lattice superconductors is discussed, where the theoretical model corresponds to organic superconductors (TMTSF)_2PF_6. We assume the quarter-filling electron band and p, d and f wave like pairing symmetries in organic superconductors. To realize the electronic structures in organic superconductors, we introduce the asymmetric hopping integral, (t') among second nearest lattice sites. At t'=0, the Josephson current in the d wave symmetry saturates in low temperatures, whereas those in the p and the f wave symmetries show the low…
The fascinating electronic properties of the family of layered organic molecular crystals kappa-(BEDT-TTF)2X where X is an anion (e.g., X=I3, Cu[N(CN)2]Br, Cu(SCN)2) are reviewed. These materials are particularly interesting because of similarities to the high-$T_c$ cuprate superconductors including unconventional metallic properties and competition between antiferromagnetism and superconductivity. The temperature dependence of electrical transport, optical, and nuclear magnetic resonance properties deviate significantly from those of a conventional metal. In particular, there appears to be an…
Layered organic superconductors of the BEDT family are model systems for the interplay of the Mott transition with superconductivity, magnetic order and frustration. Recent experimental studies on a hole-doped version of BEDT compounds reveal an enhancement of superconductivity and a rapid crossover between two different conducting phases above the superconducting dome. One of these phases is a Fermi liquid, the other not. Using plaquette cellular dynamical mean field theory with state of the art continuous-time quantum Monte Carlo calculations, we study this problem with the two-dimensional H…
The possibility of superconductivity in doped and undoped triangular antiferromagnets is discussed. Using the Bethe-Salpeter (B-S) equation, it is shown that the exchange of RPA paramagnons on a triangular lattice Hubbard model leads to strong pairing correlations at and near half-filling. The dominant states for this system correspond to d-wave singlet (even-frequency) and s-wave triplet (odd-frequency) pairing. Analytical techniques applied to the hole-doped t-J model yield similar results. A t_1-t_2 Hubbard model interpolating between square (t_1=0) and triangular (t_1=t_2) lattices has a t…
The charge frustration with the mixed-valence state inherent to LiTi$_2$O$_4$, which is found to be a unique spinel oxide superconductor, is the impetus for paying special attention to reveal the existence of intriguing superconducting properties. Here, we report a pronounced fourfold rotational symmetry of the superconductivity in high-quality single-crystalline LiTi$_2$O$_4$ (001) thin films. Both the magnetoresistivity and upper critical field under an applied magnetic field manifest striking fourfold oscillations deep inside the superconducting state, whereas the anisotropy vanishes in the…
Half-filled two-leg Hubbard ladders have spin-gapped short-range antiferromagnetic correlations while three-leg ladders have power law antoferromagnetic correlations, and both systems have d_{x^2-y^2}-power law pairing correlations when they are doped. Thus these ladders exhibit some of the phenomenology seen in the layered cuprates. Here we report results for half-filled frustrated Hubbard ladders, based upon ladder segments taken from a tight-binding model of kappa-BEDT-TTF. Although these ladders are half-filled, varying the degree of frustration can drive them across an insulator-metal tra…
We demonstrate a robust frustration-driven charge-order to superconductivity transition in the half-filled negative-U extended Hubbard model. Superconductivity extends over a broad region of the parameter space. We argue that the model provides the correct insight to understanding unconventional superconductivity in the organic charge-transfer solids and other quarter-filled systems.
The suppression of superconductivity by nonmagnetic disorder is investigated systematically in the organic superconductor $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$. We introduce a nonmagnetic disorder arising from molecule substitution in part with deuterated BEDT-TTF or BMDT-TTF for BEDT-TTF molecules and molecular defects introduced by X-ray irradiation. A quantitative evaluation of the scattering time $τ_{\rm dHvA}$ is carried out by de Haas-van Alphen (dHvA) effect measurement. A large reduction in $T_{\rm c}$ with a linear dependence on $1/τ_{\rm dHvA}$ is found in the small-disorder region below $1/…
A mechanism of superconductivity is proposed for the Kondo lattice which has semi-metallic conduction bands with electron and hole Fermi surfaces. At high temperatures, the $f$ electron's localized spins/pseudospins are fluctuating between electron and hole Fermi surfaces to seek for a partner to couple with. This system tries to resolve this frustration at low temperatures and chooses to construct a quantum mechanically entangled state composed of the Kondo singlet with electron surface and that with hole surface, to break the U(1) gauge symmetry. The corresponding order parameter is given by…
Is the mechanism of unconventional superconductivity in Sr$_2$RuO$_4$ closer in spirit to superfluid $^3$He, or to the cuprates, pnictides, and organic superconductors? We challenge prevailing assumptions in this field and using well-controlled perturbative renormalization group calculations, we suggest that superconductivity in Sr$_2$RuO$_4$ resembles more closely the quasi-one dimensional organic superconductors. Our theory has certain phenomenological consequences that are consistent with the experimentally observed phenomena.
Transport of charge carriers can be controlled by doping through chemical and physical means. Unlike chemical doping, physical doping is carried out by a special technique through gate voltages in a field-effect transistor geometry. This technique keeps the carrier channels free from defects without complications from the crystalline structure and the dopant impurity sites. In this paper we discuss the occurrence of superconductivity at the interface of a device by an unconventional technique. We examine a dynamical pairing mechanism governed by the excitons in the active device. The pairing o…
The two-dimensional organic superconductor $λ$-(BETS)$_2$GaCl$_4$ exhibits pronounced charge fluctuations below $T \approx 150$~K, in contrast to the sibling compound $κ$-(BETS)$_2$GaCl$_4$ that remains metallic down to milli-Kelvin. Infrared spectroscopy reveals only minor splitting in the vibrational features of the latter compound, common to other strongly dimerized $κ$-salts. When the organic molecules are arranged in the $λ$-pattern, however, a strong vibrational $ν_{27}(b_{1u})$ mode is present, that forms a narrow doublet. %indicating static charge imbalance of about 2\%. Most important…
Conventional superconductivity, as used in this review, refers to electron-phonon coupled superconducting electron-pairs described by BCS theory. Unconventional superconductivity refers to superconductors where the Cooper pairs are not bound together by phonon exchange but instead by exchange of some other kind, e. g. spin fluctuations in a superconductor with magnetic order either coexistent or nearby in the phase diagram. Such unconventional superconductivity has been known experimentally since heavy fermion CeCu2Si2, with its strongly correlated 4f electrons, was discovered to superconduct …
It is generally believed that superconducting materials are divided into two classes: `conventional' and `unconventional'. Conventional superconductors (the elements and thousands of compounds including $MgB_2$) are described by conventional London-BCS-Eliashberg electron-phonon theory. There is no general agreement as to what mechanism or mechanisms describe `unconventional' superconductors such as the heavy fermions, organics, cuprate and pnictide families. However all superconductors, whether `conventional' or `unconventional', exhibit the Meissner effect. I argue that there is a single mec…
Failed superconductivity in a Mott spin liquid material
National High Magnetic Field Laboratory, Florida State University（佛罗里达州立大学国家高磁场实验室）；Department of Physics, Florida State University（佛罗里达州立大学物理系）；Physikalisches Institut, Universität Stuttgart（斯图加特大学第一物理研究所）；Department of Physics, Hokkaido University（北海道大学物理系）；Institute of Solid State Physics, Vienna University of Technology（维也纳工业大学固体物理研究所）
We discover superconductivity in alkali-earth metals doped phenanthrene. The superconducting critical temperatures \emph{T}$_c$ are 5.6 K and 5.4 K for Sr$_{1.5}$phenanthrene and Ba$_{1.5}$phenanthrene, respectively. The shielding fraction of Ba$_{1.5}$phenanthrene exceeds 65%. The Raman spectra show 8 cm$^{-1}$/electron and 7 cm$^{-1}$/electron downshifts for the mode at 1441 cm$^{-1}$ due to the charge transfer to organic molecules from the dopants of Ba and Sr. Similar behavior has been observed in A$_3$phenanthrene and A$_3$C$_{60}$(A = K and Rb). The positive pressure effect in Sr$_{1.5}$…
A consistent microscopic theory of pseudogap phenomena and novel Bose-liquid superconductivity (superfluidity) is presented, based on the fact that in high-$T_c$ cuprates and related systems the energy $\varepsilon_A$ of the effective attraction between fermions is comparable with their Fermi energy $\varepsilon_F$ and the bosonic Cooper pairs are formed above $T_c$ and then a part of such Cooper pairs condense into a Bose superfluid at $T_c$. High-$T_c$ cuprates and other systems with low Fermi energies ($\varepsilon_F\sim\varepsilon_A$) are bosonic superconductors/superfluids and exhibit pse…
Temperature dependent anisotropy and two-band superconductivity revealed by lower critical field in organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br
Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here we report unbiased Quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same onsite symmetries as the standard Hubbard model on a 2D square lattice. Using QMC, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting ant…
