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A family of molecular Mott insulators on triangular lattice provided a few S=1/2 triangular quantum spin liquid candidates, with $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ being the most studied material of this group. The large number experimental works present a conflicting set of evidence, with some suggesting spin liquid behavior, while others point towards a valence bond solid with orphan spins. In this work we use Raman scattering spectroscopy to probe both local charge on molecular sites and lattice phonons as a function of temperature down to 6~K. Based on the analysis of the line shape of the BEDT-TTF charge sensitive vibration $\nu_2$ on cooling below 40 K, we suggest a development of disordered fluctuating charge disproportionation on (BEDT-TTF)$_2$ dimers of amplitude as small as 0.06$e$. The lattice phonons show strong anomalous broadening on cooling only in the (c,c) scattering channel, associated with the developing charge disproportionation. We suggest an interpretation, where the coupling of disordered charge dipoles on dimers to the lattice results in anisotropic modulation of charge transfer integrals between dimer lattice sites. Such fluctuations would result in modulation of magnetic coupling between spins which can produce fluctuating charge ordered spin-singlet pairs.

It has been more than 40 years since superconductivity was discovered in organic conductors, and the way scientists view organic superconductors has changed over time. At first, the fact that organic conductors exhibit superconductivity was a novelty in itself, and subsequently it was shown that behind the superconductivity is the physics of electron correlation, which has been a focus in condensed matter physics at large. Amid the remarkable development of correlation physics, the unique characteristics of organic conductors, e.g., a variety of lattice geometries and the highly compressible feature, led to the elucidation of fundamental principles and the finding of new phenomena, such as bandwidth-controlled Mott transitions and possible quantum spin liquids. However, most organic superconductors have commensurate band fillings, such as a half or a quarter, whereas inorganic superconductors, such as high-$T_{\rm c}$ cuprates and iron-based superconductors, have often been investigated under the variation of their band fillings. Thus, the physical linkage between organic and inorganic superconductors has remained unresolved. In this review article, we focus on the layered nonstoichiometric superconductor, $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$, which is exceptional among organic conductors in that the nonstoichiometry serves as doping to a half-filled band. Moreover, the strong correlation of electrons and a geometrically frustrated triangular lattice make this system exhibit the unique phenomena involved in Mottness, spin liquidity, and superconductivity, which are key concepts of correlated electron physics. This review will summarize what we learned from the pressure study of $\kappa$-(BEDT-TTF)$_4$Hg$_{2.89}$Br$_8$ and how they relate to the extensively studied issues in inorganic materials.

Glass, a ubiquitous state of matter like a frozen liquid, is a seminal issue across fundamental and applied sciences and has long been investigated in the framework of classical mechanics. A challenge in glass physics is the exploration of the quantum-mechanical behaviour of glass. Experimentally, however, the real quantum manifestation of glass and the relationship between classical and quantum glass are totally unknown and remain to be observed in real systems. Here, we report the direct observation of classical-to-quantum evolution in the frustration-induced charge glass state exhibited by interacting electrons in organic materials. We employ Raman spectroscopy to capture a snapshot of the charge density distribution of each molecule in a series of charge glasses formed on triangular lattices with different geometrical frustrations. In less frustrated glass, the charge density profile exhibits a particle-like two-valued distribution; however, it becomes continuous and narrowed with increasing frustration, demonstrating the classical-to-quantum crossover. Moreover, the charge density distribution shows contrasting temperature evolution in classical and quantum glasses, enabling us to delineate energy landscapes with distinct features. The present result is the first to experimentally identify the quantum charge glass and show how it emerges from classical glass., Comment: 33 pages including 13 figures

Quantum spin liquid states, in which spins are quantum-mechanically delocalized in direction, have been so far studied for charge-localized Mott insulators arising from strong repulsive interaction. Recently, however, it was found that the doped Mott insulator with a triangular lattice, $\kappa$-(ET)$_4$Hg$_{2.89}$Br$_8$, exhibits both spin-liquid-like magnetism and metallic electrical conduction. Thus, it is now possible to experimentally explore how the spin liquidity affects the electrical conduction, an issue that has received a great deal of theoretical attention. Here, with a newly developed method to combine uniaxial and hydrostatic pressures, we investigate the electrical conduction in the doped Mott insulator with controlling the triangular lattice geometry and the repulsion strength which determines the spin-liquidity and Mottness, respectively. We found that, in a strongly interacting regime, the electronic state drastically changes from an insulator to a Fermi liquid via a non-Fermi liquid with varying geometrical frustration, which suggests that spin liquidity promotes delocalization of charges. This result indicates that frustration in spin degrees of freedom has a decisive impact on the transport of charges through the entanglement of spin and charge in a doped Mott insulator.

Mutual interactions in many-body systems bring about a variety of exotic phases, among which liquid-like states failing to order due to frustration are of keen interest. Recently, an organic system with an anisotropic triangular lattice of molecular dimers 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 is substantiated in this system. $^1$H NMR spectra and magnetization measurements indicate that gigantic, staggered moments are non-linearly and inhomogeneously induced by 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 MHz at low temperatures. The inhomogeneity, local correlation, and slow dynamics indicative of middle-scale dynamical correlation length suggest a novel frustration-driven spin clusterization., Comment: 13 pages, 11 figures, 1 table

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 are the first to successfully perform 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. Remarkably, however, the growth rate is many orders of magnitude larger than that in the conventional case, which is attributable to the quantum effect. 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., Comment: 31 pages, 11 figures

We investigated microscopic lattice states in the donor-acceptor ionic Mott insulator, TTF-BA, by $^{79}$Br-NQR spectroscopy to explore cross-correlated fluctuations between spin, charge and lattice. A ferroelectric transition with lattice dimerization is captured by a NQR line splitting with the critical exponent $\beta$ of 0.40, as expected in the 3D Ising universality class, and a peak formation in the spin-lattice relaxation rate $T_1^{-1}$ at the transition temperature, $T_\mathrm{c}$, of 53 K. Notably, $T_1^{-1}$ does not obey the conventional $T^2$ law expected for the Raman process of phonons even far above $T_\mathrm{c}$, indicating the emergence of extraordinary lattice fluctuations. They are very probably associated with polar fluctuations in the paraelectric and paramagnetic phase of TTF-BA and explain the previous observation of the anomalously suppressed paramagnetic spin susceptibility, which was conjectured to be due to the local spin-singlet pairing prior to the nonmagnetic ferroelectric order [K. Sunami $et$ $al$., Phys. Rev. Res. 2, 043333 (2020)]., Comment: 4 pages, 4 figures

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 quasi-triangular-lattice organic systems, $\theta$-(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 charge frustration. We find that the resistivity exhibits extremely two-dimensional (2D) anisotropy and contrasting temperature dependence between in the in-plane and out-of-plane directions in the charge glass phase, qualitatively distinguished from 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., Comment: 5 pages, 4 figures

The Mott metal-insulator transition-a drastic manifestations of Coulomb interactions among electrons-is the first-order transition of clear discontinuity, as shown by various experiments and the celebrated dynamical mean-field theory. Recent theoretical works, however, suggest that the transition is continuous if the Mott insulator carries an exotic 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 k-(ET)2Cu2(CN)3. Transport experiments performed under fine pressure tuning find that, as the Mott transition is approached, the Fermi-liquid coherence temperature continuously falls to the scale of kelvins with divergent quasi-particle decay rate in the metal side and the charge gap gradually closes in the insulator side. The Clausius-Clapeyron analysis of the pressure-temperature phase diagram provides thermodynamic evidence for the extremely weak first-order nature of the Mott transition. These results suggest that the spin liquid hosts a spinon Fermi surface, which turns into an electron Fermi surface when charges are Mott delocalized.

$^{13}$C nuclear magnetic resonance measurements were performed for a single-component molecular material Zn(tmdt)$_{2}$, in which tmdt's form an arrangement similar to the so-called ${\kappa}$-type molecular packing in quasi-two-dimensional Mott insulators and superconductors. Detailed analysis of the powder spectra uncovered local spin susceptibility in the tmdt ${\pi}$ orbitals. The obtained shift and relaxation rate revealed the singlet-triplet excitations of the ${\pi}$ spins, indicating that Zn(tmdt)$_{2}$ is a spin-gapped Mott insulator with exceptionally large electron correlations compared to conventional molecular Mott systems., Comment: 14 pages, 6 figures

Recent advances in the study of nodal Weyl fermions (WFs), quasi-relativistic massless particles, constitute a novel realm of quantum many-body phenomena. The Coulomb interaction in such systems, having a zero density of states at the Fermi level, is of particular interest, since in contrast to conventional correlated metals, its long-ranged component is unscreened. Here, through nuclear-magnetic-resonance (NMR) measurements, we unveil the exotic spin correlations of two-dimensional WFs in an organic material, causing a divergent increase of the Korringa ratio by a factor of 1000 upon cooling, in striking contrast with conventional metallic behaviors. Combined with model calculations, we show that this divergence stems from the interaction-driven velocity renormalization that almost exclusively suppresses the zero-momentum spin fluctuations. At low temperatures, the NMR rate shows a remarkable increase, which is shown by numerical analyses to correspond to inter-node excitonic fluctuations, precursor of a transition from massless to massive quasiparticles.

The spin excitations from the nonmagnetic charge-ordered insulating state of $\alpha$-(BEDT-TTF)$_2$I$_3$ at ambient pressure have been investigated by probing the static and low-frequency dynamic spin susceptibilities via site-selective nuclear magnetic resonance at $^{13}$C sites. The site-dependent values of the shift and the spin-lattice relaxation rate $1/T_1$ below the charge-ordering transition temperature ($T_{CO} \approx$ 135 K) demonstrate a spin density imbalance in the unit cell, in accord with the charge-density ratio reported earlier. The shift and $1/T_1$ show activated temperature dependence with a static (shift) gap $\Delta_S \approx$ 47-52 meV and a dynamic ($1/T_1$) gap $\Delta_R \approx$ 40 meV. The sizes of the gaps are well described in terms of a localized spin model, where spin one-half antiferromagnetic dimer chains are weakly coupled with each other., Comment: 22 pages, 7 figures, and 1 table

A weird electronic state accompanied with an anomalous superconducting precursor and/or exotic orders, called the pseudogap state, arises prior to a superconducting condensate in underdoped cuprates that are situated near Mott transition. Another way to make the system approach the Mott transition is the variation of bandwidth or correlation strength, which gives a new dimension to exploring this exotic state. Here we report nuclear magnetic resonance (NMR) studies on layered organic superconductors with half-filled bands whose widths are pressure-tuned near the Mott transition. The system situated on the verge of the Mott transition shows a pseudogap-like anomalous suppression of spin excitations on cooling from well above the superconducting critical temperature $T_{\mathrm{c}}$. The pressure variation of the NMR relaxation rate shows that the pseudogap-like behavior is rapidly suppressed by applying pressure. The NMR experiments under various magnetic fields varied up to 18 T proves the absence of symmetry breaking orders that compete with superconductivity, such as charge orders, in the metallic phase. Remarkably, the pseudogap-like behavior above $T_{\mathrm{c}}$ and the superconducting condensate fade out in parallel under ascending magnetic fields with similar field-orientation dependence, indicating a superconducting precursor is the predominant origin of the pseudogap. Our further investigation of different materials, which take different "distances" from the Mott transition by chemical pressure, confirms that the superconducting precursor is not the conventional amplitude fluctuations arising from low dimensionality but unconventional preformation of Cooper pairs enhanced near the Mott transition. These findings conclude that preformed Cooper pairs persist up to twice as high as $T_{\mathrm{c}}$ on the verge of the bandwidth-controlled Mott transition., Comment: 16 pages, 13 figures

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 novel magnetism revealed here, can be ubiquitous and vital for many Dirac materials., Comment: 43 pages, 6 figures, 1 table; to appear in Nature Communications

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

The magnetic state of the single-component molecular compound, [Cu(tmdt)$_{2}$], is investigated by means of $^{1}$H-NMR. An abrupt spectral broadening below 13 K and a sharp peak in nuclear spin-lattice relaxation rate, $T_{1}^{-1}$, at 13 K are observed as clear manifestations of a second-order antiferromagnetic transition, which is consistent with the previously reported magnetic susceptibility and EPR measurement. The ordered moment is estimated at $0.22-0.45$ ${\mu}_{\rm B}$/molecule. The temperature-dependence of $T_{1}^{-1}$ above the transition temperature indicates one-dimensional spin dynamics and supports that the spins are on the central part of the molecule differently from other isostructural compounds., Comment: 13pages, 5 figures

The magnetic field-induced superconductor-insulator-metal transition (SIMT) in partially deuterated $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, which is just on the Mott boundary, has been observed using the infrared magneto-optical imaging spectroscopy. The infrared reflectivity image on the sample surface revealed that the metallic (or superconducting) and insulating phases coexist and they have different magnetic field dependences. One of the magnetic field dependence is SIMT that appeared on part of the sample surface. The SIMT was concluded to originate from the balance of the inhomogenity in the sample itself and the disorder of the ethylene end groups resulting from fast cooling., Comment: 5 pages, 5 figures, to appear in Phys. Rev. B

The static and dynamic local spin susceptibility of the organic Mott insulator $\kappa$-(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 fluctuations survive toward the ground state, as indicated by the temperature profile of the relaxation rates., Comment: 4 pages, 4 figures