1H NMR and static susceptibility measurements have been performed in an organic Mott insulator with a nearly isotropic triangular lattice, kappa-(BEDT-TTF)2Cu2(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 approximately 250 K. Regardless of the large magnetic interactions, the 1H NMR spectra show no indication of long-range magnetic ordering down to 32 mK, which is 4 orders of magnitude smaller than J. These results suggest that a quantum spin liquid state is realized in the close proximity of the superconducting state appearing under pressure.

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Pressure-temperature phase diagram of the organic Mott insulator κ-(ET)2Cu2(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 spinlattice relaxation rate and resistivity. The characteristic curvature of Mott boundary in the phase diagram highlights a crucial effect of the spin frustration on the Mott transition. The layered organic conductor κ-(ET) 2 Cu 2 (CN) 3 is the only spin-liquid system to exhibit the Mott transition, to the authors' knowledge [5]. The conduction layer in κ-(ET) 2 Cu 2 (CN) 3 consists of strongly dimerized ET [bis(ethlylenedithio)-tetrathiafulvalene] molecules with one hole per a dimer site, so that the on-site Coulomb repulsion inhibits the hole transfer [6]. In fact, it is a Mott insulator at ambient pressure and becomes a metal/superconductor under pressure [7]. Taking the dimer as a unit, the network of inter-dimer transfer integrals forms a nearly isotropic triangular lattice, and therefore the system can be modeled to a half-filled band system with strong spin frustration on the triangular lattice. At ambient pressure, the magnetic susceptibility behaved as the triangular-lattice Heisenberg model with an AFM interaction energy J ∼ 250 K [5,8]. Moreover, the 1 H NMR measurements provided no indication of long-range magnetic order down to 32 mK. These results suggested the spin liquid state at ambient pressure. Then Mott transition or crossover lines were identified as the temperature where 1/T1T and dR/dT show the maximum as described in the text. The upper limit of the Fermi liquid region was defined by the temperatures where 1/T1T and R deviate from the Korringa's relation and R0 + AT 2 , respectively. The onset superconducting transition temperature was determined from the in-plane resistance measurements.

Changing the interactions between particles in an ensemble--by varying the temperature or pressure, for example--can lead to phase transitions whose critical behaviour depends on the collective nature of the many-body system. Despite the diversity of ingredients, which include atoms, molecules, electrons and their spins, the collective behaviour can be grouped into several families (called 'universality classes') represented by canonical spin models. One kind of transition, the Mott transition, occurs when the repulsive Coulomb interaction between electrons is increased, causing wave-like electrons to behave as particles. In two dimensions, the attractive behaviour responsible for the superconductivity in high-transition temperature copper oxide and organic compounds appears near the Mott transition, but the universality class to which two-dimensional, repulsive electronic systems belongs remains unknown. Here we present an observation of the critical phenomena at the pressure-induced Mott transition in a quasi-two-dimensional organic conductor using conductance measurements as a probe. We find that the Mott transition in two dimensions is not consistent with known universality classes, as the observed collective behaviour has previously not been seen. This peculiarity must be involved in any emergent behaviour near the Mott transition in two dimensions.

The static and dynamic local spin susceptibility of the organic Mott insulator κ-(ET)2Cu2(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.PACS numbers: 75.45.+j, 75.50.Mm, 74.70.Kn Intensive research for exotic and unconventional superconductivity in layered cuprates and organic conductors has fertilized the physics of quantum antiferromagnets that may be a key to elucidate the mechanism of the electron pairing in the neighboring superconducting state and to find novel quantum states. Of great interest is the realization of quantum spin liquids in two dimensions without any symmetry breaking since the proposal on the spin-1/2 triangular-lattice antiferromagnet (TLA).1 The succeeding theoretical studies of TLA, however, prefer a long-range spiral order at least in the Heisenberg model with nearest-neighbor exchange interactions 2 , while the quantum disordered states with broken symmetry in translation, 3 chirality 4 and rotation 5 have been proposed. The model including the higherorder exchanges 6,7 or the Hubbard model 8 has predicted a quantum disordered ground state. In contrast to the significant theoretical progress, a few model materials of the spin-1/2 TLA have been discovered to exhibit quantum disordered states only recently, including the 3 He monolayer, 9 Cs 2 CuCl 4 10 and organic conductors. 11,12The organic Mott insulator κ-(ET) 2 Cu 2 (CN) 3 is a promising system of the triangular-lattice spin liquid, 11 where ET denotes the organic molecule, bis(ethylenedithio)tetrathiafulvalene.The quasi-2D crystal structure consists of conducting ET layer and insulating Cu 2 (CN) 3 layer. In the conduction layer, strongly dimerized ET molecules are arranged in a checkerboard pattern, and the transfer integrals between the dimers form a triangular lattice with a half-filled band. In fact, the magnetic susceptibility behaves as the TLA Heisenberg model with an exchange interaction energy J of 250 K.11,14 Nevertheless, the long-range magnetic order was not observed down to 32 mK (∼ 10 −4 J) in the 1 H NMR measurements. 11 Moreover, the residual spin susceptibility and the power-law temperature dependence in the spin-lattice relaxation rate at low temperatures imply the low-energy spin excitations. Under a relatively low pressure, this material exhibits the Mott transition and the superconductivity without passing through the magnetically ordered state.13,15 The positive slope of the Mott transition phase boundary in the pressuretemperature phase diagram shows the large residu...

A many-body quantum system on the verge of instability between two competing ground states may exhibit quantumcritical phenomena 1,2 , as has been intensively studied for magnetic systems. The Mott metal-insulator transition 3 , a phenomenon that is central to many investigations of strongly correlated electrons, is also supposed to be quantum critical, although this has so far not been demonstrated experimentally. Here, we report experimental evidence for the quantum-critical nature of the Mott instability, obtained by investigating the electron transport of three organic systems with di erent ground states under continuously controlled pressure. The resistivity obeys the material-independent quantum-critical scaling relation bifurcating into a Fermi liquid or Mott insulator, irrespective of the ground states. Electrons on the verge of becoming delocalized behave like a strange quantum-critical fluid before becoming a Fermi liquid.Mutually interacting electrons with sufficiently strong Coulomb repulsion U fall into the Mott insulating state when the carrier density corresponds to an electron per site (a half-filled band) 3 . As the bandwidth W is increased by pressure or chemical substitution, the electrons gain kinetic energy and become itinerant at a critical value of W/U . The Mott transition, a marked phase transition between a metal and an insulator, is a collective manifestation of imbalance in the particle-wave duality of electrons. As one of the main issues in the quantum physics of condensed matter, the quantumcritical nature of the Mott transition awaits clarification. In contrast to intensive theoretical studies 4-6 , however, this issue has not yet been addressed experimentally because most Mott transitions in real systems have critical points at finite temperatures 7-11 ; thus, they are not genuine quantum phase transitions.In general, quantum criticality is observed at the temperature T sufficiently lower than the competing energy scales underlying the phase transition 1,2 , which are the bandwidth W and on-site Coulomb energy U in the case of the Mott transition. Thus, even if the system's critical point, T c , is finite, unlike the genuine quantum phase transition, in the case that T c is orders of magnitude lower than W and U , there is a vast temperature region of T c < T U , W , where the system can experience quantum criticality (Fig. 1a). Indeed, using dynamical mean field theory (DMFT), which can properly describe the Mott transition 12 , the authors of refs 4,13 have suggested the scaling of transport for quantum criticality in an intermediate temperature range well above T c .To explore the possible Mott quantum criticality from the experimental side, we performed pressure studies of the electron transport for three different quasi-two-dimensional organic Mott insulators with anisotropic triangular lattices, κ-(ET) 2 Cu 2 (CN) 3 , κ-(ET) 2 Cu[N(CN) 2 ]Cl and EtMe 3 Sb[Pd(dmit) 2 ] 2 (hereafter abbreviated to κ-Cu 2 (CN) 3 , κ-Cl and EtMe 3 Sb-dmit, respectively), where

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.

. This momentum leads to a spatially inhomogeneous state consisting of periodically alternating 'normal' and 'superconducting' regions. Here, we establish that the hallmark of this state is the appearance of spatially localized and spin-polarized quasiparticles forming the so-called Andreev bound states (ABS). These are detected through our nuclear magnetic resonance (NMR) measurements.The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is expected to occur in the vicinity of the upper critical magnetic field (H c2 ) when Pauli pair breaking dominates over orbital (vortex) effects [2][3][4][5] . Pauli pair breaking prevails in fields that exceed the Pauli limit (H p ) for which the Zeeman energy is strong enough to break the Cooper pair by flipping one spin of the singlet. Intense efforts have been invested to search for indisputable evidence for the existence of the FFLO states. Examples include a theoretical proposal for detecting modulated superfluid phases in optical lattices 6 ; tunnelling in superconducting (SC) films 7 ; mapping of the phase diagram of CeCoIn 5 (refs 8,9), and studies of layered organic superconductors [10][11][12][13] . However, clear microscopic evidence for an FFLO phase is still missing. In the FFLO state, in the vicinity of the transition from the SC to FFLO state, nodes in the order parameter form the domain walls, where the superconducting phase changes by π . This phase twist leads to a local modification of the electronic density of states (DOS) and the creation of new topological ABS (ref. 14), the observation of which we report here.Besides CeCoIn 5 , where a putative FFLO state coexists with long-range magnetism, the organic compound, κ-(BEDT-TTF) 2 Cu(NCS) 2 (hereafter referred to as κ-(ET) 2 X) exhibits the clearest thermodynamic evidence for the existence of a narrow intermediate SC phase 11 . Because this SC phase is stabilized in magnetic fields (H ) that exceed the Pauli limit, H p ≈ 20.7 T (ref. 15), as illustrated in Fig. 1, it has been identified as an FFLO phase. Recent measurements of NMR spectra gave evidence that the phase transition within the SC state is Zeeman-driven 16 , but failed to provide a clear hallmark of the FFLO state. Our main discovery is that the NMR spin-lattice relaxation rate (T significantly enhanced, as compared to its normal-state value, in the SC state for fields exceeding H p . We deduce that the enhancement stems from the ABS of polarized quasiparticles spatially localized in the nodes of the order parameter in an FFLO state. Furthermore, we reveal that these topological ABS are profoundly different from the sub-gap states found in vortex cores, as they are shifted in energy away from the Fermi level by an amount controlled by the magnetic field. We first examine the NMR spectral lineshapes in different regimes at 22 T, shown in the inset to Fig. 2, to demonstrate the sensitivity of our measurements to different superconducting phases in this compound. These 13 C NMR spectra reflect the distribution of the hyperfine fields and are thus a sen...