We performed third-order electrical conductivity measurements on the organic conductor $α$-(BEDT-TTF)$_2$I$_3$ using an ac bridge technique sensitive to nonlinear signals. Third-order conductance $G_3$ is clearly observed even at low electric fields, and interestingly, $G_3$ is critically enhanced above the charge-order transition temperature $T_{\rm CO}=136$~K. The observed frequency dependence of $G_3$ is incompatible with a percolation model, in which a Joule heating in a random resistor network is relevant to the nonlinear conduction. We instead argue the nonlinearity of the relaxation time according to a phenomenological model on the mobility in materials with large dielectric constants, and find that the third-order conductance $G_3$ corresponds to the third-order electric susceptibility $χ_3$. Since the nonlinear susceptibility is known as a probe for higher-order multipole ordering, the present observation of the divergent behavior of $G_3$ above $T_{\rm CO}$ reveals an underlying quadrupole instability at the charge-order transition of the organic system.
Raman signatures of the strong intra- and inter-molecular charge oscillations in bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) \k{appa}-phase salts
A detailed investigation of the out-of-plane electrical properties of charge-ordered alpha-(BEDT-TTF)2I3 provides clear evidence for ferroelectricity. Similar to multiferroic alpha-(BEDT-TTF)2Cu[N(CN)2]Cl, the polar order in this material is ascribed to the occurrence of bond- and site-centered charge order. Dielectric response typical for relaxor ferroelectricity is found deep in the charge-ordered state. We suggest an explanation in terms of the existence of polar and nonpolar stacks of the organic molecules in this material, preventing long-range ferroelectricity. The results are discussed …
The Dirac electron in the organic conductor $α$-(BEDT-TTF)$_2$I$_3$ under pressure is analyzed using a tight-binding model with nearest-neighbor transfer energies and four molecules per unit cell. By noting that the Dirac point between the first and second energy bands emerges or merges followed by the level crossing at a time-reversal invariant momentum (TRIM), an effective Hamiltonian is derived on the basis of these two wave functions at the TRIM, which have different parities associated with an inversion symmetry around the inversion center. We demonstrate that the Dirac point is determine…
To determine how electron correlations open a gap in two-dimensional massless Dirac electrons in the organic compounds $α$-(BEDT-TTF)$_2$I$_3$ [$α$-(ET)$_2$I$_3$] and $α$-(BEDT-TSeF)$_2$I$_3$ [$α$-(BETS)$_2$I$_3$], we derive and analyze $ab$ $initio$ low-energy effective Hamiltonians for these two compounds. We find that the horizontal stripe charge ordering opens a gap in the massless Dirac electrons in $α$-(ET)$_2$I$_3$, while an insulating phase without explicit symmetry breaking appears in $α$-(BETS)$_2$I$_3$. We clarify that the combination of the anisotropic transfer integrals and the el…
We present high-resolution measurements of the relative length change as a function of temperature of the organic charge-transfer salt $κ$-(BEDT-TTF)$_2$Hg(SCN)$_2$Cl. We identify anomalous features at $T_g \approx\,63$ K which can be assigned to a kinetic glass-like ordering transition. By determining the activation energy $E_A$, this glass-like transition can be related to conformational degrees of freedom of the ethylene endgroups of the organic building block BEDT-TTF. As opposed to other $κ$-(BEDT-TTF)$_2X$ salts, we identify a peculiar ethylene endgroup ordering in the present material i…
We theoretically investigate possible photoinduced topological phase transitions in the organic salt $α$-(BEDT-TTF)$_2$I$_3$, which possesses a pair of inclined massless Dirac-cone bands between the conduction and valence bands under uniaxial pressure. The Floquet analyses of a driven tight-binding model for this material reveal rich photoinduced variations of band structures, Chern numbers, and Hall conductivities under irradiation with elliptically polarized light. The obtained phase diagrams contain a variety of nonequilibrium steady phases, e.g., the Floquet Chern insulator, Floquet semime…
We report the effect of Dirac cone tilting on interlayer magnetoresistance in α-(BEDT-TTF)$_2$I$_3$, which is a Dirac semimetal under pressure. Fitting of the experimental data by the theoretical formula suggests that the system is close to a type-II Dirac semimetal.
We compare the photoluminescence spectra of the low-temperature Mott insulator \etcl (T_{MIT}=40 K) with spectra of metallic κ-(BEDT-TTF)_2Cu[N(CN)_2]Br, which is superconducting below T_c=11.8 K, in the temperature range between 300 and 20 K. In the Mott insulating state of κ-(BEDT-TTF)_2Cu[N(CN)_2]Cl we observe a luminescence band at 1.95 eV due to the recombination of an exciton created by a HOMO-LUMO optical excitation. This luminescence is quenched both in the high-temperature bad metal state of κ-(BEDT-TTF)_2Cu[N(CN)_2]Cl and in metallic κ-(BEDT-TTF)_2Cu[N(CN)_2]Br. The observation of th…
The quasi-two-dimensional organic semiconductor α-(BEDT-TTF)2I3 [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] has an anisotropic linear dispersion with a zero energy gap near the Fermi level. Owing to the vanishing density of states at the Fermi level, the Coulomb interaction is unscreened in this material. We theoretically study the effect of the long-range Coulomb interaction and the low-energy/long-wavelength behavior of α-(BEDT-TTF)2I3 using the renormalization group analysis. The nearly logarithmic enhancement of the velocity reshapes tilted Dirac cones, and changes the low-temperature…
We investigated the interlayer magnetoresistance in an organic massless Dirac electron system $α$-(BEDT-TTF)$_2$I$_3$ under pressure. We experimentally demonstrate that the width of the zero mode owing to carrier scattering is much narrower than that of the other Landau levels.
Low temperature scanning tunneling spectroscopy reveals the local density of states of the organic superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, that was cut in-situ in ultra-high vacuum perpendicular to the superconducting BEDT-TTF layers. The spectra confirm that superconductivity is confined to the conducting BEDT-TTF layers, while the Cu[N(CN)$_2$]Br anion layers are insulating. The density of states comprises a twofold superconducting gap, which is attributed to the two separated bands crossing the Fermi surface.
We investigate the spin-orbit coupling (SOC) effects in $α$- and $κ$-phase BEDT-TTF and BEDT-TSF organic salts. Contrary to the assumption that SOC in organics is negligible due to light C, S, H atoms, we show the relevance of such an interaction in a few representative cases. In the weakly correlated regime, SOC manifests primarily in the opening of energy gaps at degenerate band touching points. This effect becomes especially important for Dirac semimetals such as $α$-(ET)$_2$I$_3$. Furthermore, in the magnetic insulating phase, SOC results in additional anisotropic exchange interactions, wh…
The organic salt $α$-(BEDT-TTF)$_2$I$_3$ is considered a model system for metal-insulator transition due to electronic charge ordering at $T_{\rm CO}=135$~K. The optical properties obtained from polarized reflection measurements above and below $T_{\rm CO}$ can be well described by calculations based on first-principle density-functional theory (DFT). We discuss the effect of electronic correlations on the metal-insulator transition.
Since the first observation of weak ferromagnetism in the charge-transfer salt kappa-(BEDT-TTF)2-Cu[N(CN)2]Cl [U. Welp et al., Phys. Rev. Lett. 69, 840 (1992)], no further evidence of ferromagnetism in this class of organic materials has been reported. Here we present static and dynamic spin susceptibility measurements on kappa-(BEDT-TTF)2Hg(SCN)2Br revealing weak ferromagnetism below about TWF = 20 K. We suggest that frustrated spins in the molecular dimers suppress long-range order, forming a spin-glass ground state in the insulating phase.
The low-temperature state of the quantum spin liquid candidate $κ$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ emerges via an anomaly at $T^{*}\sim6$ K. Although signatures of this anomaly have been revealed in various quantities, its origin has remained unclear. Here we report inelastic neutron scattering measurements on single crystals of $κ$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, aiming at studying phonon renormalization effects at $T^{*}$. A drastic change was observed in the phonon damping across $T^{*}$ for a breathing mode of BEDT-TTF dimers at $E=4.7$ meV. The abrupt change in the phonon damping i…
We examine the edge states of the Dirac electrons in the molecular material α-(BEDT-TTF)2I3 with electron-electron interactions. Based on the analysis of the extended Hubbard model with the Hartree-Fock approximation, we show that the charge-ordered phase has the gapless edge states only in the vicinity of the phase boundary between the zero-gap state and the charge-ordered phase. We also show a peculiar flux phase caused by the long-range Coulomb interaction with the same mechanism as topological Mott insulator phase.
Utilizing infrared vibrational spectroscopy we have investigated dimerized two-dimensional organic salts in order to search for possible charge redistribution that might cause electronic dipoles and ferroelectricity: the quantum spin liquid κ-(BEDT-TTF)2Cu2(CN)3, the antiferromagnetic Mott insulator κ-(BEDT-TTF)2$Cu[N(CN)2]Cl, and the superconductor κ-(BEDT-TTF)2$Cu[N(CN)2]Br. None of them exhibit any indication of charge disproportionation upon cooling down to low temperatures. No modification in the charge distribution is observed around T = 6 K where a low-temperature anomaly has been repor…
K(BEDT-TTF)2Cu(NCS)2 has been investigated by Raman scattering in both bulk and nanoparticle compounds. Phonon modes from 20 to 1600 cm-1 have been assigned. Focusing on the unexplored low frequency phonons, a plateau in frequencies is observed in the bulk phonons between 50 and 100 K and assigned to the signature of the bad metal phase. Nanoparticles of K(BEDT-TTF)2Cu(NCS)2 exhibit anomalies at 50 K associated to the crossover from a bad metal to a Fermi liquid whose origins are discussed.
In most Dirac semimetals, time-reversal and inversion symmetries are believed to play a crucial role in their stability. We demonstrate that these symmetries are broken in Dirac fermions in the organic conductor $α$-(BEDT-TTF)$_2$I$_3$ due to the strong electronic correlation. The system is a three-dimensional type-II Dirac semimetal in the coherent inter-layer tunneling regime. A chiral anomaly is predicted to be observed in the magnetoresistance when the magnetic field is tuned to the inter-layer tunneling direction. Our result suggests that $α$-(BEDT-TTF)$_2$I$_3$ is a useful platform to ex…
The electronic properties of molecular conductors can be readily varied via physical or chemical pressure as it increases the bandwidth W; this enables crossing the Mott insulator-to-metal phase transition by reducing electronic correlations U/W. Here we introduce an alternative path by increasing the molecular orbitals when partially replacing sulfur by selenium in the constituting bis-(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) molecules of the title compound. We characterize the tuning of the insulating quantum spin liquid state via a Mott transition to the metallic Fermi-liquid state by…
The electronic structure of weak charge-ordering (CO) state just below the critical pressure in an organic conductor α-(BEDT-TTF)_2I_3 was experimentally investigated using peak structure in the temperature dependence of interlayer magnetoresistance (MR). Based on a minimal model considering multiple Landau levels (LLs), we discuss herein the MR peak as characteristic to multilayer massless/massive Dirac fermion (DF) systems. MR measured in the weak CO state exhibited a clear MR peak, and its magnetic-field dependence was consistent with the LL behavior of a massive DF with a small gap. Result…
Theoretical and experimental studies have supported that the electronic structure of $α$-(BEDT-TTF)$_2$I$_3$ under pressure is described by two-dimensional Dirac fermions. When the interlayer tunneling is coherent, the electronic structure of the system becomes three-dimensional, and we expect the peak structure to appear in the interlayer resistivity under magnetic fields. We theoretically and experimentally show that the peak appears in the interlayer resistivity at low temperatures and high magnetic fields. From the experiment, we estimate that the magnitude of the interlayer tunneling is $…
The organic charge-transfer salt $κ$-(BEDT-TTF)$_{2}$Hg(SCN)$_{2}$Br is a quasi two-dimensional metal with a half-filled conduction band at ambient conditions. When cooled below $T=80$ K it undergoes a pronounced transition to an insulating phase where the resistivity increases many orders of magnitude. In order to elucidate the nature of this metal-insulator transition we have performed comprehensive transport, dielectric and optical investigations. The findings are compared with other dimerized $κ$-(BEDT-TTF) salts, in particular the Cl-analogue, where a charge-order transition takes place a…
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 present ab initio two-dimensional extended Hubbard-type multiband models for EtMe_3Sb[Pd(dmit)_2]_2 and κ-(BEDT-TTF)_2Cu(NCS)_2, after a downfolding scheme based on the constrained random phase approximation (cRPA) and maximally-localized Wannier orbitals, together with the dimensional downfolding. In the Pd(dmit)_2 salt, the antibonding state of the highest occupied molecular orbital (HOMO) and the bonding/antibonding states of the lowest unoccupied molecular orbital (LUMO) are considered as the orbital degrees of freedom, while, in the κ-BEDT-TTF salt, the HOMO-antibonding/bonding states …
The critical cooling rate $R_{\rm c}$ above which charge ordering is kinetically avoided upon cooling, which results in charge-glass formation, was investigated for the geometrically frustrated system $θ$-(BEDT-TTF)$_2X$. X-ray diffraction experiments revealed that $θ$-(BEDT-TTF)$_2$TlCo(SCN)$_4$ exhibits a horizontally charge-ordered state, and kinetic avoidance of this state requires rapid cooling of faster than 150 K/min. This value is markedly higher than that reported for two other isostructural $θ$-type compounds, thus demonstrating the lower charge-glass-forming ability of $X$ $=$ TlCo(…
The Mott insulator κ-(BEDT-TTF)2Cu[N(CN)2]Cl consists of molecular dimers arranged on an anisotropic triangular lattice and develops a canted antiferromagnetic ground state. It has recently been suggested that this system features purely electronic ferroelectricity which requires an electric dipole moment. Optical spectroscopy clearly rules out charge imbalance in this system, which excludes the existence of quantum electric dipoles on the dimers and subsequently a dipolar spin coupling. We suggest that the prominent in-plane dielectric response in κ-(BEDT-TTF)2Cu[N(CN)2]Cl is due to short-ran…
The organic conductor $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_{3}$ seems to form a quantum spin liquid, although at low temperatures unusual properties are seen in the charge, spin and lattice degrees of freedom. Here we report results of X-band ESR studies of $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_{3}$ single crystals as a function of temperature and angle. We find indications of two anisotropic relaxation mechanisms at low temperatures and compare them to the spin-liquid behavior observed in other strongly correlated systems. In addition, we can recognize charge inhomogeneities in the copper ions of the anion …
In order to understand the physical properties of the series of organic conductors $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]$X$ with $X$ = Cl, Br, and I, not only electronic correlations but also the effect of disorder has to be taken into account. While for Cl- and Br-containing salts the influence of both parameters were investigated and a universal phase diagram was proposed, the position of $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]I is still not settled. Here we have conducted transport, infrared, and dielectric measurements on single crystals of the title compound to clarify its electronic state at low tempe…
We report the band structure calculations and the experimental results of resistivity and magnetic susceptibility in a spin-1/2 (BEDT-TTF)$^{\bullet +}$ monomer Mott insulator (BEDT-TTF)Cu[N(CN)$_2$]$_2$. The band calculations indicate a Dirac semimetal state with nodal lines at the Fermi level. The resistivity and the magnetic susceptibility as functions of temperature are well interpreted in terms of the monomer Mott insulating state instead of the expected semimetal state probably owing to strong electron correlation. In addition, we find that an Arrhenius-type steep reduction of the parama…
The charge-ordered insulator $α$-(BEDT-TTF)$_2$I$_3$ gradually evolves to a metal when pressure is applied, and at low temperatures the electronic bands form tilted Dirac-like cones. A metallic state with a frequency-independent optical conductivity indicates the coexistence of the trivial and massless Dirac electrons in the system. Our infrared investigations also reveal that at the boundary between insulating and metallic states an energy gap opens due to correlated massive Dirac fermions, which is gradually suppressed when pressure increases.
We have measured and analyzed the dielectric constant of the dimer Mott insulator $κ-$(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, which is known as a playground for a spin-liquid state. Most unexpectedly, this particular organic salt has nontrivial charge degrees of freedom, being characterized by a dipole-glass-like dielectric relaxation below around 60 K. This is ascribed to the charge disproportionation within the dimer due to the intersite Coulomb repulsion. In this respect, the dipole observed here is purely quantum mechanical, and thereby exhibits unexpected responses.
The ground state of $λ$-(BEDT-TTF)$_2$GaCl$_4$, which has the same structure as the organic superconductor $λ$-(BETS)$_2$GaCl$_4$, was investigated by magnetic susceptibility and $^{13}$C NMR measurements. The temperature dependence of the magnetic susceptibility revealed an antiferromagnetic (AF) correlation with $J/k_{\rm B} \simeq$ 98 K. NMR spectrum splitting and the divergence of $1/T_1$ were observed at approximately 13 K, which is associated with the AF transition. We found that the AF structure is commensurate according to discrete NMR peak splitting, suggesting that the ground state o…
By applying measurements of the dielectric constants and relative length changes to the dimerized molecular conductor $κ$-(BEDT-TTF)$_2$Hg(SCN)$_2$Cl, we provide evidence for order-disorder type electronic ferroelectricity which is driven by charge order within the (BEDT-TTF)$_2$ dimers and stabilized by a coupling to the anions. According to our density functional theory calculations, this material is characterized by a moderate strength of dimerization. This system thus bridges the gap between strongly dimerized materials, often approximated as dimer-Mott systems at 1/2 filling, and non- or …
Photoinduced melting of horizontal-stripe charge orders in quasi-two-dimensional organic conductors θ-(BEDT-TTF)2RbZn(SCN)4[BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene] and α-(BEDT-TTF)2I3 is investigated theoretically. By numerically solving the time-dependent Schrödinger equation, we study the photoinduced dynamics in extended Peierls-Hubbard models on anisotropic triangular lattices within the Hartree-Fock approximation. The melting of the charge order needs more energy for θ-(BEDT-TTF)2RbZn(SCN)4 than for α-(BEDT-TTF)2I3, which is a consequence of the larger stabilization energy in θ-(B…
