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 $V$. A first-order transition from the insulating to the superconducting state occurs within the model with increasing frustration.
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.
It is shown that unconventional critical phenomena commonly observed in paramagnetic metals YbRh2Si2, YbRh2(Si0.95Ge0.05)2, and beta-YbAlB4 is naturally explained by the quantum criticality of Yb-valence fluctuations. We construct the mode coupling theory taking account of local correlation effects of f electrons and find that unconventional criticality is caused by the locality of the valence fluctuation mode. We show that measured low-temperature anomalies such as divergence of uniform spin susceptibility $χT^{-ζ)$ with $ζ~0.6$ giving rise to a huge enhancement of the Wilson ratio and the em…
I study an Extended Periodic Anderson Model (EPAM) with non-local hybridisation, $V_{fc}$, and a coulomb interaction, $U_{fc}$, between localised $f$ electrons and wide band conduction ($c$) electrons. Within DMFT, a quantum phase transition (QPT) driven by soft $f$-valence fluctuations, accompanied by a discontinuous jump in the Fermi volume, is found as $V_{fc}$ is tuned across a critical value. Near the associated QCP, an unconventional superconductive instability, driven by these extended, singular valence fluctuations, naturally emerges. {\it All} these phenomena are representative of obs…
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…
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 develop a model approach to describe charge fluctuations and different charge phases in strongly correlated 3d oxides. As a generic model system one considers that of centers each with three possible valence states described in frames of pseudo-spin (isospin) formalism by an effective anisotropic non-Heisenberg Hamiltonian. Simple uniform mean-field phases include an insulating monovalent phase, mixed-valence binary disproportionated phase, and mixed-valence ternary under-disproportionated phase. We consider two first phases in more details focusing on the problem of electron/hole states an…
We have measured the superconducting penetration depth~$Λ(T)$ in the heavy-fermion/intermediate-valent superconducting alloy series~Ce$_{1-x}$Yb$_x$CoIn$_5$ using transverse-field muon spin relaxation, to study the effect of intermediate-valent Yb doping on Fermi-liquid renormalization. From $Λ(T)$ we determine the superfluid density $ρ_s(T)$, and find that it decreases continuously with increasing nominal Yb concentration~$x$, i.e., with increasing intermediate valence. The temperature-dependent renormalization of the "normal" fluid density~$ρ_N(T) = ρ_s(0) - ρ_s(T)$ in both the heavy-fermion…
Electronic structure calculations combining the local-density approximation with an exact diagonalization of the Anderson impurity model show an intermediate 5f^5-5f^6-valence ground state and delocalization of the 5f^5 multiplet of the Pu atom 5f-shell in PuCoIn_5, PuCoGa_5, and δ-Pu. The 5f-local magnetic moment is compensated by a moment formed in the surrounding cloud of conduction electrons. For PuCoGa_5 and δ-Pu the compensation is complete and the Anderson impurity ground state is a singlet. For PuCoIn_5 the compensation is partial and the Pu ground state is magnetic. We suggest that th…
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 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-…
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…
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…
We review the evidence supporting valence-fluctuation mediated superconductivity in CeCu2Si2 and CeCu2Ge2, where Tc reaches 2.4 K at high pressure. In these systems the valence and magnetic critical points, at p_V and p_c respectively, are well separated. Characteristic signatures associated with both phenomena are distinct. In contrast, the valence and spin fluctuation regions appear much closer in most Ce based compounds. Concerning d-transition metals, superconductivity in pure iron emerges in the pressure window 15-30 GPa with the onset of Tc up to almost 3 K. All relevant observations poi…
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…
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…
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 construct a van der Waals heterostructure consisting of three graphene layers stacked with alternating twisting angles $\pmθ$. At the average twist angle $θ\sim 1.56^{\circ}$, a theoretically predicted magic angle for the formation of flat electron bands, narrow conduction and valence moiré bands appear together with a linearly dispersing Dirac band. Upon doping the half-filled moiré valence band with holes, or the half-filled moiré conduction band with electrons, displacement field tunable superconductivity emerges, reaching a maximum critical temperature of 2.1 K at optimal doping and dis…
We briefly overview the importance of Hubbard and Anderson-lattice models as applied to explanation of high-temperature and heavy-fermion superconductivity. Application of the models during the last two decades provided an explanation of the paired states in correlated fermion systems and thus extended essentially their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. In second part, we also present some of the new results concerning the unconventional superconductivity and obtained very recently in our group. A comparison with e…
We show that the mean-field resonating valence bond approximation proposed in 1987 by Baskaran, Zou, and Anderson describes gapless charge pair excitations confined to the boundaries of the spinon Brillouin zone. The existence of such pairs accounts for all the essential anomalous electronic properties of cuprates, with superconductivity arising due to the charge drag by the spinon superflow. This mechanism may be relevant to other unconventional superconductors.
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…
Conventional and unconventional superconductivity, respectively, arise from attractive (electron-phonon) and repulsive (many-body Coulomb) interactions with fixed-sign and sign-reversal pairing symmetries. Although heavy-fermions, cuprates, and pnictides are widely believed to be unconventional superconductors, recent evidence in one of the heavy fermion superconductor (CeCu$_2$Si$_2$) indicate the presence of a novel conventional type pairing symmetry beyond the electron-phonon coupling. We present a new mechanism of attractive potential between electrons, mediated by emergent boson fields (v…
We present an resonating valence bond (RVB) theory of superconductivity for the Hubbard--Heisenberg model on an anisotropic triangular lattice. We show that these calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta', kappa and lambda phases of (BEDT-TTF)_2X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)_2X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a d_{x^2-y^2} superconductor with a small superfluid stiffness and a pseudogap with d_{x^2-y^2} symmetry…
A Hubbard model at half-filling on an anisotropic triangular lattice has been proposed as the minimal model to describe conducting layers of $κ-(BEDT-TTF)_2X$ organic materials. The model interpolates between the square lattice and decoupled chains. The $κ-(BEDT-TTF)_2X$ materials present many similarities with cuprates, such as the presence of unconventional metallic properties and the close proximity of superconducting and antiferromagnetic phases. As in the cuprates, spin fluctuations are expected to play a crucial role in the onset of superconductivity. We perform a weak-coupling renormali…
An unconventional superconducting phase is explored developing out of a non Fermi-liquid phase of the two-channel Anderson lattice model. It is characterized by a composite order parameter comprising of a local spin or orbital degree of freedom bound to triplet Cooper pairs with an isotropic and a nearest neighbour form factor. The superconducting transition temperature peaks in the moderate intermediate valence regime and vanishes at integral valence. The gap function is non analytic and odd in frequency, and a pseudo-gap develops in the conduction electron density of states which vanishes as…
Resonating Valence Bond states are quantum spin liquids, having low energy spin-half (spinon) or spin-1 excitations. Although spins are `disordered', they posses subtle topological orders and some times chiral orders. RVB states are easily appreciated and seem natural in the quantum fluctuation dominated 1D world. In 2 and 3D, competing orders such as antiferromagnetism, charge order or even superconductivity often hide an underlying robust quantum spin liquid state. Introduction of additional spin interactions or doping of delocalized charges, or finite temperatures, could frustrate the long …
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…
We review the role of strong electronic correlations in quasi--two-dimensional organic charge transfer salts such as (BEDT-TTF)$_2X$, (BETS)$_2Y$ and $β'$-[Pd(dmit)$_2$]$_2Z$. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerised and is described by a half-filled Hubbard model; the second class is not strongly dimerised and is described by a quarter filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-fille…
We show that the two-channel Anderson lattice model leads to the development of an unconventional superconductivity out of a metallic non Fermi-liquid phase. It is characterized by a composite order parameter comprising of a local spin or orbital degree of freedom bound to triplet Cooper pairs with an isotropic and a nearest neighbour form factor. The superconducting transition temperature is band filling dependent and peaks for half filling in the extrem intermediate valence regime and vanishes at integral valence. The gap function is non analytic and odd in frequency, and a pseudo-gap develo…
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 $1/…
The charge frustration with the mixed-valence state inherent to LiTi$_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…
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.
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.
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…
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…
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 …
We report on a pressure-induced evolution of exotic superconductivity and spin correlations in CeIr(In$_{1-x}$Cd$_{x}$)$_5$ by means of In-Nuclear-Quadrupole-Resonance (NQR) studies. Measurements of an NQR spectrum and nuclear-spin-lattice-relaxation rate $1/T_1$ have revealed that antiferromagnetism induced by the Cd-doping emerges locally around Cd dopants, but superconductivity is suddenly induced at $T_c$ = 0.7 and 0.9 K at 2.34 and 2.75 GPa, respectively. The unique superconducting characteristics with a large fraction of the residual density of state at the Fermi level that increases wit…
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…
We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian which includes nearest neighbor hopping and an interaction term which explicitly favors nearest neighbor spin-singlets through the well-known resonance valence bond (RVB) character of planar organic molecules. Treating this Hamiltonian in mean-field theory, allowing for bond-dependent variation of the RVB order parameter, we show that both s- and d-wave superconducting states are possible. The d-wave solution belongs to a two-dime…
