Spatiotemporal observation of quantum crystallization of electrons.

Liquids crystallize as they cool; however, when crystallization is avoided in some way, they supercool, maintaining their liquidity, and freezing into glass at low temperatures, as ubiquitously observed. These metastable states crystallize over time through the classical dynamics of nucleation and growth. However, it was recently found that Coulomb interacting electrons on charge-frustrated triangular lattices exhibit supercooled liquid and glass with quantum nature and they crystallize, raising fundamental issues: what features are universal to crystallization at large and specific to that of quantum systems? Here, we report our experimental challenges that address this issue through the spatiotemporal observation of electronic crystallization in an organic material. With Raman microspectroscopy, we have successfully performed real-space and real-time imaging of electronic crystallization. The results directly capture strongly temperature-dependent crystallization profiles indicating that nucleation and growth proceed at distinctive temperature-dependent rates, which is common to conventional crystallization. However, the growth rate is many orders of magnitude larger than that in the conventional case. The temperature characteristics of nucleation and growth are universal, whereas unusually fast growth kinetics features quantum crystallization where a quantum-to-classical catastrophe occurs in interacting electrons.

An organic superconductor, (TEA)(HEDO-TTF-dc)2·2(H2C2O4), coupled with strong hydrogen-bonding interactions.

A new organic superconductor (TEA)(HEDO-TTF-dc)2·2(H2C2O4) (H2EDO-TTF-dc = ethylenedioxy-tetrathiafulvalene dicarboxylic acids) with an onset TC of 4.0 K, was successfully obtained using oxalic acid and HEDO-TTF-dc anion donor. The crystal structure analysis indicated that strong π-π overlaps and very strong intra- and inter-molecular hydrogen-bonding interactions exist between the HEDO-TTF-dc anion donors and oxalic acid molecules.

Anomalously field-susceptible spin clusters emerging in the electric-dipole liquid candidate κ-(ET)2Hg(SCN)2Br.

Mutual interactions in many-body systems bring about various exotic phases, among which liquid-like states failing to order due to frustration are of keen interest. The organic system with an anisotropic triangular lattice of molecular dimers, κ-(ET)2Hg(SCN)2Br, has been suggested to host a dipole liquid arising from intradimer charge-imbalance instability, possibly offering an unprecedented stage for the spin degrees of freedom. Here, we show that an extraordinary unordered/unfrozen spin state having soft matter-like spatiotemporal characteristics emerges in this system. 1H nuclear magnetic resonance (NMR) spectra and magnetization measurements indicate that gigantic, staggered moments are nonlinearly and inhomogeneously induced by a magnetic field, whereas the moments vanish in the zero-field limit. The analysis of the NMR relaxation rate signifies that the moments fluctuate at a characteristic frequency slowing down to below megahertz at low temperatures. The inhomogeneity, local correlation, and slow dynamics indicative of middle-scale dynamical correlation length of several nanometers suggest novel frustration-driven spin clusterization.

Gapped magnetic ground state in quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3.

Geometrical frustration, quantum entanglement, and disorder may prevent long-range ordering of localized spins with strong exchange interactions, resulting in an exotic state of matter. κ-(BEDT-TTF)2Cu2(CN)3 is considered the prime candidate for this elusive quantum spin liquid state, but its ground-state properties remain puzzling. We present a multifrequency electron spin resonance (ESR) study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at 6 kelvin. This opening of a spin gap, accompanied by structural modifications, is consistent with the formation of a valence bond solid ground state. We identify an impurity contribution to the ESR response that becomes dominant when the intrinsic spins form singlets. Probing the electrons directly manifests the pivotal role of defects for the low-energy properties of quantum spin systems without magnetic order.

Interacting chiral electrons at the 2D Dirac points: a review.

The pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as the massless Dirac or Weyl fermions, constitute various intriguing issues in modern condensed-matter physics. In particular, the issues linked to the Coulomb interaction between the chiral electrons attract great attentions due to their unusual features, namely, the interaction is not screened and has a long-ranged property near the charge-neutrality point, in clear contrast to its screened and short-ranged properties in the conventional correlated materials. In graphene, this long-range interaction induces an anomalous logarithmic renormalization of the Fermi velocity, which causes a nonlinear reshaping of its Dirac cone. In addition, for strong interactions, it even leads to the predictions of an excitonic condensation with a spontaneous mass generation. The interaction, however, would seem to be not that large in graphene, so that the latter phenomenon appears to have not yet been observed. Contrastingly, the interaction is probably large in the pressurized organic materialα-(BEDT-TTF)2I3, where a 2D massless-Dirac-fermion phase emerges next to a correlated insulating phase. Therefore, an excellent testing ground would appear in this material for the studies of both the velocity renormalization and the mass generation, as well as for those of the short-range electronic correlations. In this review, we give an overview of the recent progress on the understanding of such interacting chiral electrons in 2D, by placing particular emphasis on the studies in graphene andα-(BEDT-TTF)2I3. In the first half, we briefly summarize our current experimental and theoretical knowledge about the interaction effects in graphene, then turn attentions to the understanding inα-(BEDT-TTF)2I3, and highlight its relevance to and difference from graphene. The second half of this review focusses on the studies linked to the nuclear magnetic resonance experiments and the associated model calculations inα-(BEDT-TTF)2I3. These studies allow us to discuss the anisotropic reshaping of a tilted Dirac cone together with various electronic correlations, and the precursor excitonic dynamics growing prior to a condensation. We see these provide unique opportunities to resolve the momentum dependence of the spin excitations and fluctuations that are strongly influenced by the long-range interaction near the Dirac points.

Anomalous 2D-Confined Electronic Transport in Layered Organic Charge-Glass Systems.

To get insight into the nature of the electronic fluid in the frustration-driven charge glasses, we investigate in-plane and out-of-plane charge transport for several quasitriangular-lattice organic systems: θ-(BEDT-TTF)_{2}X [X=RbZn(SCN)_{4}, CsZn(SCN)_{4}, and I_{3}]. These compounds host a charge order, charge glass, and Fermi liquid, depending on the strength of the charge frustration. We find that the resistivity exhibits extreme 2D anisotropy and contrasting temperature dependence between the in-plane and out-of-plane directions in the charge-glass phase, unlike in the charge order and metallic states. The experimental features indicate that the frustration-induced charge glass carries an anomalous 2D-confined electronic fluid with possible charge excitations other than conventional quasiparticles.

New insights into the structural properties of κ-(BEDT-TTF)2Ag2(CN)3 spin liquid.

Here, the first accurate study is presented of the room-temperature and 100 K structures of one of the first organic spin liquids, κ-(BEDT-TTF)2Ag2(CN)3. It is shown that the monoclinic structure determined previously is only the average one. It is shown that the exact structure presents triclinic symmetry with two non-equivalent dimers in the unit cell. But surprisingly this does not lead to a sizeable charge disproportionation between dimers. The difference from the analogue compound κ-(BEDT-TTF)2Cu2(CN)3 which also presents a spin liquid phase is discussed in detail. The data provided here show the importance of the anionic layer and in particular the transition metal position in the process of symmetry breaking. The possible impact of the symmetry breaking, albeit weak, on the spin-liquid mechanism and the influence of various disorders on the physical properties of this system is also discussed.

Quantum Disordering of an Antiferromagnetic Order by Quenched Randomness in an Organic Mott Insulator.

The behavior of interacting spins subject to randomness is a longstanding issue and the emergence of exotic quantum states is among intriguing theoretical predictions. We show how a quantum-disordered phase emerges from a classical antiferromagnet by controlled randomness. ^{1}H NMR of a successively x-ray-irradiated organic Mott insulator finds that the magnetic order collapses into a spin-glass-like state, immediately after a slight amount of disorder centers are created, and evolves to a gapless quantum-disordered state without spin freezing, spin gap, or critical slowing down, as reported by T. Furukawa et al. [Phys. Rev. Lett. 115, 077001 (2015)]PRLTAO0031-900710.1103/PhysRevLett.115.077001 through sequential reductions in the spin freezing temperature and moment.

Electronic Griffiths Phase in Disordered Mott-Transition Systems.

Solid-state physics and soft-matter physics have been developed independently, with little mutual exchange of the underlying physical concepts. However, after many studies of correlated electron systems, it has been recognized that correlated electrons (especially in Mott-transition systems) in solid matter sometimes show behavior similar to "structured fluids" in soft matter; that is, the electrons exhibit long-length self-organization (but without long-range order) and slow dynamics, which is inevitable for the long-length structures. The essential question is this: what condition causes such behavior in solid matter? We focused on an organic Mott-transition system and demonstrated that the electrons of this system fluctuate very slowly only when the following two factors are met simultaneously: (i) the electronic system is on the metal and Mott-insulator boundary and (ii) the system is subject to quenched disorder. This electronic state with slow dynamics under this condition can be explained by the concept of the "(electronic) Griffiths phase." This concept will potentially be a key in connecting solid-state physics with soft-matter physics.

Single-component molecular conductor [Pt(dmdt)2]-a three-dimensional ambient-pressure molecular Dirac electron system.

The single-component molecular conductor [Pt(dmdt)2] is a sought-after ambient-pressure molecular Dirac electron system, which exhibits a high temperature-insensitive conductivity and temperature-dependent magnetic susceptibility nearly vanishing below 120 K. First-principles DFT calculations reveal that Dirac cones emerge along the a* direction, and form Dirac nodal lines.

Spin-lattice decoupling in a triangular-lattice quantum spin liquid.

A quantum spin liquid (QSL) is an exotic state of matter in condensed-matter systems, where the electron spins are strongly correlated, but conventional magnetic orders are suppressed down to zero temperature because of strong quantum fluctuations. One of the most prominent features of a QSL is the presence of fractionalized spin excitations, called spinons. Despite extensive studies, the nature of the spinons is still highly controversial. Here we report magnetocaloric-effect measurements on an organic spin-1/2 triangular-lattice antiferromagnet, showing that electron spins are decoupled from a lattice in a QSL state. The decoupling phenomena support the gapless nature of spin excitations. We further find that as a magnetic field is applied away from a quantum critical point, the number of spin states that interact with lattice vibrations is strongly reduced, leading to weak spin-lattice coupling. The results are compared with a model of a strongly correlated QSL near a quantum critical point.

Quasi-continuous transition from a Fermi liquid to a spin liquid in κ-(ET)2Cu2(CN)3.

The Mott metal-insulator transition-a manifestation of Coulomb interactions among electrons-is known as a discontinuous transition. Recent theoretical studies, however, suggest that the transition is continuous if the Mott insulator carries a spin liquid with a spinon Fermi surface. Here, we demonstrate the case of a quasi-continuous Mott transition from a Fermi liquid to a spin liquid in an organic triangular-lattice system κ-(ET)2Cu2(CN)3. Transport experiments performed under fine pressure tuning have found that as the Mott transition is approached, the Fermi liquid coherence temperature continuously falls to the scale of kelvins, with a divergent quasi-particle decay rate on the metal side, and the charge gap continuously closes on the insulator side. A Clausius-Clapeyron analysis provides thermodynamic evidence for the extremely weak first-order nature of the transition. These results provide additional support for the existence of a spinon Fermi surface, which becomes an electron Fermi surface when charges are delocalized.

Anomalous spin correlations and excitonic instability of interacting 2D Weyl fermions.

The Coulomb interaction in systems of quasi-relativistic massless electrons has an unscreened long-range component at variance with conventional correlated metals. We used nuclear magnetic resonance (NMR) measurements to reveal unusual spin correlations of two-dimensional Weyl fermions in an organic material, causing a divergent increase of the Korringa ratio by a factor of 1000 upon cooling, in marked contrast to conventional metallic behavior. Combined with model calculations, we show that this divergence stems from an interaction-driven velocity renormalization that almost exclusively suppresses zero-momentum spin fluctuations. At low temperatures, the NMR relaxation rate shows an unexpected increase; numerical analyses show that this increase corresponds to internode excitonic fluctuations, a precursor to a transition from massless to massive quasiparticles.

Anomalous metallic behaviour in the doped spin liquid candidate κ-(ET)4Hg2.89Br8.

Quantum spin liquids are exotic Mott insulators that carry extraordinary spin excitations. Therefore, when doped, they are expected to afford metallic states with unconventional magnetic excitations. Here, we report experimental results which are suggestive of a doped spin liquid with anomalous metallicity in a triangular-lattice organic conductor. The spin susceptibility is nearly perfectly scaled to that of a non-doped spin liquid insulator in spite of the metallic state. Furthermore, the charge transport that is confined in the layer at high temperatures becomes sharply deconfined on cooling, coinciding with the rapid growth of spin correlations or coherence as signified by a steep decrease in spin susceptibility. The present results substantiate the desired doped spin liquid and suggest a strange metal, in which the coherence of the underlying spin liquid promotes the deconfinement of charge from the layers while preserving the non-Fermi-liquid nature.It is expected that introducing charge carriers into an exotic quantum spin liquid state may lead to an unconventional metal but there are no clear realizations of a metallic spin liquid. Here, the authors present a spin liquid candidate that also shows evidence of strange metal behavior.

Slow dynamics of electrons at a metal-Mott insulator boundary in an organic system with disorder.

The Mott transition-a metal-insulator transition caused by repulsive Coulomb interactions between electrons-is a central issue in condensed matter physics because it is the mother earth of various attractive phenomena. Outstanding examples are high-Tc (critical temperature) cuprates and manganites exhibiting colossal magnetoresistance. Furthermore, spin liquid states, which are quantum-fluctuation-driven disordered ground states in antiferromagnets, have recently been found in magnetic systems very near the Mott transition. To date, intensive studies on the Mott transition have been conducted and appear to have established a nearly complete framework for understanding the Mott transition. We found an unknown type of Mott transition in an organic spin liquid material with a slightly disordered lattice. Around the Mott transition region of this material under pressure, nuclear magnetic resonance experiments capture the emergence of slow electronic fluctuations of the order of kilohertz or lower, which is not expected in the conventional Mott transition that appears as a clear first-order transition at low temperatures. We suggest that they are due to the unconventional metal-insulator fluctuations emerging around the disordered Mott transition in analogy to the slowly fluctuating spin phase, or Griffiths phase, realized in Ising spin systems with disordered lattices.

Quantum criticality in an organic spin-liquid insulator κ-(BEDT-TTF)2Cu2(CN)3.

A quantum spin-liquid state, an exotic state of matter, appears when strong quantum fluctuations enhanced by competing exchange interactions suppress a magnetically ordered state. Generally, when an ordered state is continuously suppressed to 0 K by an external parameter, a quantum phase transition occurs. It exhibits critical scaling behaviour, characterized only by a few basic properties such as dimensions and symmetry. Here we report the low-temperature magnetic torque measurements in an organic triangular-lattice antiferromagnet, κ-(BEDT-TTF)2Cu2(CN)3, where BEDT-TTF stands for bis(ethylenedithio)tetrathiafulvalene. It is found that the magnetic susceptibilities derived from the torque data exhibit a universal critical scaling, indicating the quantum critical point at zero magnetic field, and the critical exponents, γ=0.83(6) and νz=1.0(1). These exponents greatly constrain the theoretical models for the quantum spin liquid, and at present, there is no theory to explain the values, to the best of our knowledge.

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor.

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.

Antiferromagnetic Ordering in the Single-Component Molecular Conductor [Pd(tmdt)2].

Crystals of [Pd(tmdt)2] (tmdt = trimethylenetetrathiafulvalenedithiolate) were prepared in order to investigate their physical properties. The electrical resistivity of [Pd(tmdt)2] was measured on single crystals using two-probe methods and showed that the room-temperature conductivity was 100 S·cm(-1). The resistivity behaviors implied that [Pd(tmdt)2] was a semimetal at approximately room temperature and became narrow-gap semiconducting as the temperature was decreased to the lowest temperature. X-ray structural studies on small single crystals of [Pd(tmdt)2] at temperatures of 20-300 K performed using synchrotron radiation at SPring-8 showed no distinct structural change over this temperature region. However, small anomalies were observed at approximately 100 K. Electron spin resonance (ESR) spectra were measured over the temperature range of 2.7-301 K. The ESR intensity increased as the temperature decreased to 100 K and then decreased linearly as the temperature was further decreased to 50 K, where an abrupt decrease in the intensity was observed. To investigate the magnetic state, (1)H nuclear magnetic resonance (NMR) measurements were performed in the temperature range of 2.5-271 K, revealing broadening below 100 K. The NMR relaxation rate gradually increased below 100 K and formed a broad peak at approximately 50 K, followed by a gradual decrease down to the lowest temperature. These results suggest that most of the sample undergoes the antiferromagnetic transition at approximately 50 K with the magnetic ordering temperatures distributed over a wide range up to 100 K. These electric and magnetic properties of [Pd(tmdt)2] are quite different from those of the single-component molecular (semi)metals [Ni(tmdt)2] and [Pt(tmdt)2], which retain their stable metallic states down to extremely low temperatures. The experimental results and the band structure calculations at the density functional theory level showed that [Pd(tmdt)2] may be an antiferromagnetic Mott insulator with a strong electron correlation.

Insulating Nature of Strongly Correlated Massless Dirac Fermions in an Organic Crystal.

Through resistivity measurements of an organic crystal hosting massless Dirac fermions with a charge-ordering instability, we reveal the effect of interactions among massless Dirac fermions on the charge transport. A low-temperature resistivity upturn appears robustly irrespective of the pressure and is enhanced while approaching the critical pressure of charge ordering, indicating that the insulating behavior originates from short-range Coulomb interactions. The observation of an apparently vanishing gap in the charge-ordered phase accords with the theoretical prediction of nontopological edge states.

Single-component molecular conductor [Cu(dmdt)2] with three-dimensionally arranged magnetic moments exhibiting a coupled electric and magnetic transition.

Crystals of the single-component molecular conductor [Cu(dmdt)(2)] (dmdt = dimethyltetrathiafulvalenedithiolate) were prepared as a molecular system, with three-dimensionally arranged magnetic moments embedded in "sea" of π conduction electrons. [Cu(dmdt)(2)] had fairly large room-temperature conductivity (110 S cm(-1)) and exhibited weakly metallic behavior near room temperature. Below 265 K, the resistivity (R) increased very slowly with decreasing temperature and then increased rapidly, indicating a transition from a highly conducting state to an insulating state near 95 K. The magnetic susceptibility showed Curie-Weiss behavior at 100-300 K (C = 0.375 emu/mol, Θ = 180 K). The Curie constant and the high-temperature resistivity behavior indicate that conduction electrons and three-dimensionally arranged magnetic moments coexist in the crystal. The ESR intensity increased down to about 95 K. The ESR signal was broadened and decreased abruptly near 95 K, suggesting that electric and antiferromagnetic transitions occurred simultaneously near 95 K. The crystal structure was determined down to 13 K. To examine the stability of the twisted conformation of Cu complex with dithiolate ligands, the dihedral angle dependence of the conformational energy of an isolated M(L)(2)(n-) molecule was calculated, which revealed the dihedral angle dependence on the ligand (L) and the oxidation state of the molecule (n). High-pressure four-probe resistivity measurements were performed at 3.3-9.3 GPa using a diamond anvil cell. The small resistivity increase observed at 3.3 GPa below 60 K suggested that the insulating transition observed at ambient pressure near 95 K was essentially suppressed at 3.3 GPa. The intermolecular magnetic interactions were examined on the basis of simple mean field theory of antiferromagnetic transition and the calculated intermolecular overlap integrals of the singly occupied molecular orbital (SOMO) of Cu(dmdt)(2).