Spin Vortex Crystal Order in Organic Triangular Lattice Compound
Kira Riedl, Elena Gati, David Zielke, Steffi Hartmann, Oleg M. Vyaselev, Nataliya D. Kushch, Harald O. Jeschke, Michael Lang, Roser Valenti, Mark V. Kartsovnik, Stephen M. Winter
Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates, such as $κ$-(ET)$_2$Cu$_2$(CN)$_3$ ($κ$-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring-exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this work, we discuss the properties of the recently synthesized $κ$-(BETS)$_2$Mn[N(CN)$_2$]$_3$ ($κ$-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring-exchange in these materials, and support the proposed chiral spin-liquid scenario for triangular lattice organics.
To verify the effect of geometrical frustration, we artificially distort the triangular lattice of quasi-two-dimensional organic conductor $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ [BEDT-TTF: bis(ethylenedithio)terathiofulvalene] by analogous-molecular substitution and apply $^{13}$C NMR of bulk and substituted sites, electric conductivity, and static magnetic susceptibility measurements. The results indicate that the magnetic characteristics of the substituted sample are quantitatively similar to those of the pure sample. Moreover the magnetic characteristics at the substituted sites are also the same…
We show that the mesoscopic incommensurate $\mathbb{Z}_2$ vortex crystals proposed for layered triangular anisotropic magnets can be most saliently identified by two distinctive signatures in dynamical spin response experiments: The presence of pseudo-Goldstone `phonon' modes at low frequencies $ω$, associated with the collective vibrations of the vortex cores, and a characteristic multi-scattered intensity profile at higher $ω$, arising from a large number of Bragg reflections and magnon bandgaps. These are direct fingerprints of the large vortex sizes and magnetic unit cells and the solitoni…
We theoretically discuss the mechanism for the peculiar nonlinear conduction in quasi-two-dimensional organic conductors θ-(BEDT-TTF)2X [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] through the melting of stripe-type charge order. An extended Peierls-Hubbard model attached to metallic electrodes is investigated by a nonequilibrium Green's function technique. A novel current-voltage characteristic appears in a coexistent state of stripe-type and nonstripe 3-fold charge orders, where the applied bias melts mainly the stripe-type charge order through the reduction of lattice distortion, wherea…
In the quest for materials with unconventional quantum phases, the organic triangular-lattice antiferromagnet $κ$-(ET)$_2$Cu$_2$(CN)$_3$ has been extensively discussed as a quantum spin liquid (QSL) candidate. Recently, an intriguing quantum critical behaviour was suggested from low-temperature magnetic torque experiments. Through microscopic analysis of all anisotropic contributions, including Dzyaloshinskii-Moriya and multi-spin scalar chiral interactions, we highlight significant deviations of the experimental observations from a quantum critical scenario. Instead, we show that disorder-ind…
The triangular-lattice Heisenberg antiferromagnet (HAF) is known to carry topological Z_2 vortex excitations which form a gas at finite temperatures. Here we show that the spin-orbit interaction, introduced via a Kitaev term in the exchange Hamiltonian, condenses these vortices into a triangular $Z_2$ vortex crystal at zero temperature. The cores of the Z_2 vortices show abrupt, soliton-like magnetization modulations and arise by a special intertwining of three honeycomb superstructures of ferromagnetic domains, one for each of the three sublattices of the 120-degree state of the pure HAF. Thi…
Motivated by inelastic neutron scattering data on Cs_2CuCl_4, we explore spin-1/2 triangular lattice antiferromagnets with both spatial and easy-plane exchange anisotropies, the latter due to an observed Dzyaloshinskii-Moriya interaction. Exploiting a duality mapping followed by a fermionization of the dual vortex degrees of freedom, we find a novel "critical" spin-liquid phase described in terms of Dirac fermions with an emergent global SU(4) symmetry minimally coupled to a non-compact U(1) gauge field. This ``algebraic vortex liquid" supports gapless spin excitations and universal power-law …
We explore spin-1/2 triangular antiferromagnets with both easy-plane and lattice exchange anisotropies by employing a dual vortex mapping followed by a fermionization of the vortices. Over a broad range of exchange anisotropy, this approach leads naturally to a ``critical'' spin liquid--the algebraic vortex liquid--which appears to be distinct from other known spin liquids. We present a detailed characterization of this state, which is described in terms of non-compact QED3 with an emergent SU(4) symmetry. Descendant phases of the algebraic vortex liquid are also explored, which include the Ka…
$^{1}$H NMR and static susceptibility measurements have been performed in an organic Mott insulator with nearly isotropic triangular lattice, $κ$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, which is a model system of frustrated quantum spins. The static susceptibility is described by the spin $S$ = 1/2 antiferromagnetic triangular-lattice Heisenberg model with the exchange constant $J$ $\sim$ 250 K. Regardless of the large magnetic interactions, the $^{1}$H NMR spectra show no indication of long-range magnetic ordering down to 32 mK, which is four-orders of magnitude smaller than $J$. These results su…
Polarization selectivity of light-field-induced charge localization was investigated in an organic metal alpha-(BEDT-TTF)2I3 with a triangular lattice. Dependences of transient reflectivity spectra on polarizations of the 7-fs pump and probe lights indicate that a short-range charge order (CO) is efficiently induced from the metallic phase for the pump polarization perpendicular to the 1010-type CO axis. Numerical solution of a time-dependent Schrodinger equation clarified that the 1010-CO is induced by field-induced re-distribution of charges cooperating with competing inter-site Coulomb repu…
Dynamical properties of the classical Heisenberg antiferromagnet on the triangular lattice are investigated by means of a spin-dynamics simulation and an analytical calculation. While the model was suggested to exhibit a topological transition driven by the Z_2-vortex binding-unbinding, weakness of the associated thermodynamic singularity has made it difficult to observe the evidence of the Z_2 vortex experimentally so far, only some indirect support. Here, we show that the signature of the Z_2-vortex excitation and the vortex-induced topological transition can be captured from the dynamical s…
The vortex state in a single crystal of the layered organic superconductor κ-(BEDT-TTF2Cu(NCS)2, where BEDT-TTF (or ET) is bis(ethylenedithio)tetrathiafulvalene, was studied by 1H-NMR. Under a low field region around 0.75 T, the vortex glass-liquid transition was demonstrated by a diverging of the longitudinal nuclear spin relaxation rate and peak-broadening in spectra. Under a high field region near the upper critical field Hc2(0)~7 T, the curvature of nuclear spin relaxation curves showed a drastic change at the temperature where the emergence of the quantum vortex slush state was reported. …
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…
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 report the transport properties in the vortex liquid states induced by quantum fluctuations at low temperature in the layered organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}. A steep drop of the resistivity observed below about 1 K separates the liquid state into two regions. In the low resistance state at lower temperature, a finite resistivity with weak temperature dependence persists down to 100 mK at least. The finite resistivity in the vortex state at T ~= 0 K indicates the realization of quantum vortex liquid assisted by the strong quantum fluctuations instead of the thermal o…
We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials $κ$-(BEDT-TTF)$_2$X. The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs$_2$CuCl$_4$. We find rich phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finit…
The families of organic charge-transfer salts $κ$-(BEDT-TTF)$_2X$ and $κ$-(BETS)$_2X$ have proven to serve as a powerful playground for the investigation of the physics of frustrated Mott insulators. These materials have been ascribed model character, since dimerization of the organic molecules allows to map these materials onto a single band Hubbard model, in which the dimers reside on an anisotropic triangular lattice. By changing the inorganic unit $X$ or applying physical pressure, the correlation strength and anisotropy of the triangular lattice can be varied. This has lead to the discove…
We consider the doped Rokhsar-Kivelson quantum dimer model on the triangular lattice with one mobile hole (monomer) at the Rokhsar-Kivelson point. The motion of the hole is described by two branches of excitations: the hole may either move with or without a trapped Z2 vortex (vison). We perform a study of the hole dispersion in the limit where the hole hopping amplitude is much smaller than the interdimer interaction. In this limit, the hole without vison moves freely and has a tight-binding spectrum. On the other hand, the hole with a trapped vison is strongly constrained due to interference …
We study the competition between magnetic and spin-liquid phases in the Hubbard model on the anisotropic triangular lattice, which is described by two hopping parameters t and t' in different spatial directions and is relevant for layered organic charge-transfer salts. By using a variational approach that includes spiral magnetic order, we provide solid evidence that a spin-liquid phase is stabilized in the strongly-correlated regime and close to the isotropic limit t'/t=1. Otherwise, a magnetically ordered spiral state is found, connecting the (collinear) Néel and the (coplanar) 120° phases. …
The $\EtMeP$ and $\EtMeSb$ nearly triangular organic salts are distinguished from most other Pd[(dmit)$_2$] based salts, as they display valence bond and no long range order, respectively. Under pressure, a superconducting phase is revealed in EtMe$_3$P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperatu…
We investigate the influence of disorders in terminal ethylene groups of BEDT-TTF molecules (ethylene-disorders) on the vortex pinning of the organic superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br. Magnetization measurements are performed under different cooling-processes. The second peak in the magnetization hysteresis curve is observed for all samples studied, and the hysteresis width of the magnetization becomes narrower by cooling faster. In contradiction to the simple pinning effect of disorder, this result shows the suppression of the vortex pinning force by introducing more ethylene-d…
We have theoretically investigated transport properties of the classical Heisenberg antiferromagnet on the triangular lattice in which a binding-unbinding topological transition of $\mathbb{Z}_2$ vortices is predicted to occur at a finite temperature $T_v$. It is shown by means of the hybrid Monte-Carlo and spin-dynamics simulations that the longitudinal spin-current conductivity exhibits a divergence at $T_v$, while the thermal conductivity only shows a monotonic temperature dependence with no clear anomaly at $T_v$. The significant enhancement of the spin-current conductivity is found to be …
We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular-lattices, using high temperature series expansions. We consider a model with two exchange constants, $J_1$ and $J_2$ on a lattice that interpolates between the limits of a square-lattice ($J_1=0$), a triangular-lattice ($J_2=J_1$), and decoupled linear chains ($J_2=0$). In all cases, the susceptibility which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature, $T_p$. Scaling the exchange constants t…
Motivated by the recent quasi-elastic neutron scattering experiment, we extend the spin-dynamics simulation on the triangular-lattice Heisenberg antiferromagnet, to observe a sharp central peak of its energy width $\sim 0.001J$ ($J$ the exchange coupling) of the $Z_2$-vortex origin, consistently with the experiment.
We investigate the Hubbard model on the anisotropic triangular lattice by means of the cellular dynamical mean field theory. The phase diagram determined in the Hubbard interaction versus temperature plane shows novel reentrant behavior in the Mott transition due to the competition between Fermi-liquid formation and magnetic correlations under geometrical frustration. We demonstrate that the reentrant behavior is characteristic of the Mott transition with intermediate geometrical frustration and indeed consistent with recent experimental results of organic materials.
We report the Shubnikov-de Haas (SdH) oscillations observed in the vortex liquid state of the quasi two dimensional organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$. The SdH oscillations can be observed down to about 5 T at 0.5 K, where the flux flow resistivity becomes as small as about 30 % of the normal state value. Below the upper critical field $H_{\rm c2}$ of about 7 T, the additional damping of the SdH oscillation amplitude appears, as well as that of the de Haas-van Alphen (dHvA) oscillations, with respect to the normal state one which is described with the standard Lifshitz-Ko…
The strong coupling phase diagram of the spinless fermions on the anisotropic triangular lattice at half-filling is presented. The geometry of inter-site Coulomb interactions rules the phase diagram. Unconventional charge ordered phases are detected which are the recently reported pinball liquid and the striped chains. Both are induced by the quantum dynamics out of classical disordered states and afford extremely correlated metallic states and the particular domain wall-type of excitations, respectively. The disorder once killed by the quantum effect revives at the finite temperature, which i…
$^{13}$C NMR observation of a nonmagnetic charge-ordered state in the organic conductor $κ$-(ET)$_{2}$Hg(SCN)$_{2}$Cl
University of Tokyo（东京大学）；The Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Institute of Problems of Chemical Physics RAS（俄罗斯科学院化学物理问题研究所）；The Institute for Quantum Matter and the Department of Physics and Astronomy, The Johns Hopkins University（约翰斯·霍普金斯大学量子物质研究所及物理与天文学系）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；University of Stuttgart（斯图加特大学）；Department of Advanced Materials Science, University of Tokyo（东京大学先进材料科学系）
We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum ~ k = 0. This quadratic band touching is protected by the symmetry of the system. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistic…
We present a scenario for the peculiar coexistence of charge fluctuations observed in quasi-2D 1/4-filled organic conductors $θ$-(BEDT-TTF)$_2X$ in the quantum critical regime where the charge ordering is suppressed down to zero temperature. The scenario is explored in the extended Hubbard model including electron-phonon couplings on an anisotropic triangular lattice. We find that the coexisting fluctuations emerge from two different instabilities, the ``Wigner crystallization on lattice'' driven by the off-site Coulomb repulsion and the charge-density-wave formation due to the nesting of the …
We introduce a model of vortices in type-II superconductors with a four-fold anisotropy in the vortex-vortex interaction potential. Using numerical simulations we show that the vortex lattice undergoes structural transitions as the anisotropy is increased, with a triangular lattice at low anisotropy, a rhombic intermediate state, and a square lattice for high anisotropy. In some cases we observe a multi-$q$ state consisting of an Archimedean tiling that combines square and triangular local ordering. At very high anisotropy, domains of vortex chain states appear. We discuss how this model can b…
Although magnetically ordered at low temperatures, the spin-1/2 triangular antiferromagnet Cs_2CuCl_4 exhibits remarkable spin dynamics that strongly suggest proximity to a spin liquid phase. Here we address the question of whether a proximate spin liquid may also occur in an applied magnetic field, leaving a similar imprint on the dynamical spin correlations of this material. Specifically, we explore a spatially anisotropic Heisenberg spin-1/2 triangular antiferromagnet at 1/3 magnetization from a dual vortex perspective, and indeed find a new ``critical'' spin liquid phase described by QED3 …
We investigate the anisotropic triangular lattice that interpolates from decoupled one-dimensional chains to the isotropic triangular lattice and has been suggested to be relevant for various quasi-two-dimensional materials, such as Cs$_2$CuCl$_4$ or $κ$-(ET)$_2$Cu$_2$(CN)$_3$, an organic material that shows intriguing magnetic properties. We obtain an excellent accuracy by means of a novel representation for the resonating valence bond wave function with both singlet and triplet pairing. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure trian…
In order to investigate charge ordering phenomena under electric field, static nonequilibrium Hartree approximation (SNHA) method is formulated on the basis of the nonequilibrium Green's functions introduced by Keldysh. By applying the SNHA to the 3/4-filling extended Hubbard model on anisotropic triangular lattice, we study the stabilities and amplitudes of 3-fold and horizontal charge orders in $θ$ and $θ_d$-(BEDT-TTF)$_2X$ salts under the electric field. The obtained results show that the electric field stabilizes the 3-fold state in comparison to the horizontal state. The amplitude of the …
We show that a magnetic vortex is the ground state of an array of magnetic particles shaped as a hexagonal fragment of a triangular lattice, even for an small number of particles in the array $N \leq 100$. The vortex core appears and the symmetry of the vortex state changes with the increase of the intrinsic magnetic anisotropy of the particle $β$; the further increase of $β$ leads to the destruction of the vortex state. Such vortices can be present in arrays as small in size as dozen of nanometers.
We investigate the Hubbard model on the anisotropic triangular lattice as a suggested effective description of the Mott phase in various triangular organic compounds. Employing the variational cluster approximation and the ladder dual-fermion approach as complementary methods to adequately treat the zero-temperature and the finite-temperature domains, we obtain a consistent picture of the phase diagram as a function of anisotropy and interaction strength. The metal-insulator transition substantially depends on the anisotropy, and so does the nature of magnetism and the emergence of a nonmagnet…
Recent investigations of the magnetic properties and the discovery of superconductivity in quasi-one-dimensional triangular lattice organic charge-transfer solids have indicated the severe limitations of the effective 1/2-filled band Hubbard model for these and related systems. Our computational studies of these materials within a 1/4-filled band Hubbard model in which the organic monomer molecules, and not their dimers, constitute the sites of the Hamiltonian are able to reproduce the experimental results. We ascribe the spin gap transition in kappa-(BEDT-TTF)_2B(CN)_4 to the formation of a t…
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 ground state of an S=1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts or Cs2CuCl4, is numerically studied. We apply a numerical variational method by using a tensor network with entanglement renormalization, which improves the capability of describing a quantum state. Magnetic ground states are identified for 0.7 <= J2/J1 <= 1 in the thermodynamic limit, where J1 and J2 denote the inner-chain and inter-chain coupling constants, respectively. Except for …
Spin fluctuations in the triangular-lattice Heisenberg antiferromagnet NaCrO$_2$ are investigated by means of quasi-elastic neutron scattering with high energy resolution and wide energy band. Two components with the following features are captured separately. They are pronounced at intermediate temperatures of 20-50 K. One with quite an extended lifetime corresponding to $\sim$$0.001E_{\rm ex}$ ($E_{\rm ex}$ the exchange energy) nearly disappears at low temperature 10 K, and the other with an extended lifetime $\sim$$0.01E_{\rm ex}$ survives there, identified as free $Z_2$ vortex and $Z_2$-vo…
Symmetry-Protected Topological Phases in the Triangular Majorana-Hubbard Ladder
Western Washington University（西华盛顿大学）；Stewart Blusson Quantum Matter Institute, University of British Columbia（不列颠哥伦比亚大学斯图尔特·布拉斯量子物质研究所）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
A partial disorder on a layered triangular lattice is theoretically investigated from a viewpoint of toroidal ordering and magnetoelectric effects. We consider an extended periodic Anderson model including a site-dependent antisymmetric spin-orbit coupling between conduction and localized electrons. We show that, by the mean-field approximation, the model exhibits a coplanar vortex-lattice-type magnetic order as observed in a hexagonal uranium compound UNi4B, in the parameter region with intermediate hybridization and electron correlation. This peculiar state accommodates a toroidal order, whi…
The standard theoretical approach to gapless spin liquid phases of two-dimensional frustrated quantum antiferromagnets invokes the concept of fermionic slave particles into which the spin fractionalizes. As an alternate we explore new kinds of gapless spin liquid phases in frustrated quantum magnets with XY anisotropy where the vortex of the spin fractionalizes into gapless itinerant fermions. The resulting gapless fractionalized vortex liquid phases are studied within a slave particle framework that is dual to the usual one. We demonstrate the stability of some such phases and describe their …
Using large-scale dynamical cluster quantum Monte Carlo simulations, we explore the unconventional superconductivity in the hole-doped Hubbard model on the triangular lattice. Due to the interplay of electronic correlations, geometric frustration, and Fermi surface topology, we find a doubly degenerate singlet pairing state at an interaction strength close to the bare bandwidth. Such an unconventional superconducting state is mediated by antiferromagnetic spin fluctuations along the $Γ$-$K$ direction, where the Fermi surface is nested. An exact decomposition of the irreducible particle-particl…
We model the newly predicted high-$T_c$ superconducting candidates constructed by corner-shared trigonal bipyramidal complexes with an effective three-orbital tight-banding Hamiltonian and investigate the pairing symmetry of their superconducting states driven by electron-electron interactions. Our combined weak and strong coupling based calculations consistently identify the chiral $d+id$ superconductivity as the leading pairing symmetry in a wide doping range with realistic interaction parameters. This pairing state has nontrivial topological Chern-number and can host gapless chiral edge mod…
To investigate the possibility of charge order and superconductivity in a doped two-dimensional triangular lattice, we study the extended Hubbard model with variational Monte Carlo method. At n=2/3, a commensurate filling for a triangular lattice, it is shown that the nearest-neighbor Coulomb interaction V induces honeycomb-type charge order and antiferromagnetic spin order at U>10t. We also discuss the possibility of superconductivity induced by charge fluctuation and the relation to the superconductivity in Na_{0.35}CoO_{2}1.3H_{2}O and theta-type organic condoctors.
Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this obs…
The two-dimensional Hubbard model on the anisotropic triangular lattice, with two different hopping amplitudes $t$ and $t^\prime$, is relevant to describe the low-energy physics of $κ$-(ET)$_2$X, a family of organic salts. The ground-state properties of this model are studied by using Monte Carlo techniques, on the basis of a recent definition of backflow correlations for strongly-correlated lattice systems. The results show that there is no magnetic order for reasonably large values of the electron-electron interaction $U$ and frustrating ratio $t^\prime/t = 0.85$, suitable to describe the no…
The $1/4$-filled organic compound, $δ$-(EDT-TTF-CONMe$_{2}$)$_{2}$AsF$_6$ is a frustrated two-dimensional triangular magnetic system as shown by high-frequency (111.2 and 222.4 GHz) electron spin resonance (ESR) and structural data in the literature. The material gradually orders antiferromagnetically below 40~K but some magnetically disordered domains persist down to 4 K. We propose that in defect free regions frustration prevents true magnetic order down to at least 4 K in spite of the large first- and second-neighbor exchange interactions along chains and between chains, respectively. The a…
We present a systematic investigation of the low-frequency charge carrier dynamics in different charge states of the organic conductors $θ$-(BEDT-TTF)$_2$$M$Zn(SCN)$_4$ with $M$=Rb,Tl, which result from quenching or relaxing the charge degrees of freedom on a geometrically frustrated triangular lattice. Due to strong electronic correlations these materials exhibit a charge-ordering transition, which can be kinetically avoided by rapid cooling resulting in a so-called charge-glass state without long-range order. The combination of fluctuation spectroscopy and a heat pulse method allows us to st…
The two-dimensional t-J model on a frustrating lattice is studied using mean-field variational theories with Gutzwiller approximation. We find that a superconducting state with broken time-reversal symmetry (d+id state) is realized in the parameter region close to the triangular lattice. The frustration enlarges the region of superconductivity when $t<0$ for the hole-doped case, which is equivalent to $t>0$ for electron doping. We also discuss the SU(2) degeneracy at half-filling. The d+id state probably corresponds to the spin gap state at half-filling.
We propose that the superconducting pairing symmetry of organic superconductors $κ$-(BEDT-TTF)$_{2}$X can be determined by measuring the position in momentum space of the incommensurate peaks of the spin susceptibility. We show that the positions of these peaks are uniquely determined by the symmetry of the superconducting state and the geometry of Fermi surface. Based on the effective Hubbard model on an anisotropic triangular lattice, we demonstrate the different incommensurate patters of spin responses for $d_{x^{2}-y^{2}}$- and $d_{xy}$-like pairing states. In addition, we predict the none…
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…
Pressure-temperature phase diagram of the organic Mott insulator $κ$-(ET)$_2$Cu$_2$(CN)$_3$, a model system of the spin liquid on triangular lattice, has been investigated by $^1$H NMR and resistivity measurements. The spin-liquid phase is persistent before the Mott transition to the metal or superconducting phase under pressure. At the Mott transition, the spin fluctuations are rapidly suppressed and the Fermi-liquid features are observed in the temperature dependence of the spin-lattice relaxation rate and resistivity. The characteristic curvature of Mott boundary in the phase diagram highli…
We propose a new type of charge liquid state in the spinless fermion system on a triangular lattice under strong inter-site Coulomb interactions, $V$. In the strong coupling limit ($t=0$), the ground state is classical and disordered due to geometrical frustration. The introduction of small t will drive the system to a partially ordered phase which we call a "pinball liquid". A possibly long range ordered Wigner crystal solid coexist with a liquid component which are moving around them like a pinball. This liquid is dominant over wide range of filling, even away from the regular triangle, and …
We study the energetics of Gutzwiller projected BCS states of various symmetries for the triangular lattice antiferromagnet with a four particle ring exchange using variational Monte Carlo methods. In a range of parameters the energetically favored state is found to be a projected $d_{x^2-y^2}$ paired state which breaks lattice rotational symmetry. We show that the properties of this nematic or orientationally ordered paired spin liquid state as a function of temperature and pressure can account for many of the experiments on organic materials. We also study the ring-exchange model with ferrom…
The static and dynamic local spin susceptibility of the organic Mott insulator $κ$-(ET)$_2$Cu$_2$(CN)$_3$, a model material of the spin- 1/2 triangular lattice, is studied by $^{13}$C NMR spectroscopy from room temperature down to 20 mK. We observe an anomalous field-dependent spectral broadening with the continuous and bipolar shift distribution, appearing without the critical spin fluctuations. It is attributable to spatially nonuniform magnetizations induced in the spin liquid under magnetic fields. The amplitude of the magnetization levels off below 1 K, while the low-lying spin fluctuatio…
We study triangular lattice spin-1/2 system with antiferromagnetic Heisenberg and ring exchanges using variational approach focusing on possible realization of spin liquid states. Trial spin liquid wave functions are obtained by Gutzwiller projection of fermionic mean field states and their energetics is compared against magnetically ordered trial states. We find that in a range of the ring exchange coupling upon destroying the antiferromagnetic order, the best such spin liquid state is essentially a Gutzwiller-projected Fermi sea state. We propose this spin liquid with spinon Fermi surface as…
