Phases of matter are usually identified through the lens of spontaneous symmetry breaking, which particularly applies to unconventional superconductivity and the interactions it originates from. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated Sr 2 RuO 4 is uniquely held up as a solid-state analog to superfluid 3 He-A 1, 2 , with an odd-parity vector order parameter that is unidirectional in spin space for all electron momenta and also breaks time-reversal symmetry. This characterization was recently * These authors contributed equally to this work. 1 called into question by a search for, and failure to find, evidence for an expected "split" transition while subjecting a Sr 2 RuO 4 crystal to in-plane uniaxial pressure; instead a dramatic rise and peak in a single transition temperature was observed 3, 4. NMR spectroscopy, which is directly sensitive to the order parameter via the hyperfine coupling to the electronic spin degrees of freedom, is exploited here to probe the nature of superconductivity in Sr 2 RuO 4 and its evolution under strained conditions. A reduction of Knight shifts K is observed for all strain values and temperatures T < T c , consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results are in contradiction with a body of previous NMR work 5 , and with the most prominent previous proposals for the order parameter. Sr 2 RuO 4 is an extremely clean layered perovskite, and the superconductivity emerges from a strongly correlated Fermi Liquid. The present work imposes tight constraints on the order-parameter symmetry of this archetypal system. The normal state of Sr 2 RuO 4 is based on three bands crossing the Fermi level 6, 7 , with pronounced strong-correlation characteristics linked to Hund's Rule coupling of the partially filled Ru t 2g orbitals dominating the Fermi surface. The transition to a superconducting ground state at T c =1.5 K 8 , with indirect evidence for proximity to ferromagnetism, led to the suggestion that the pair wave functions of the superconducting state likely exhibit a symmetric spin part, i.e., triplet 1. Crucial support for the existence of a triplet order parameter rested on NMR spectroscopy, which showed no change in Knight shift between normal and superconducting states 5. Later, several experiments produced evidence for time-reversal symmetry breaking (TRSB) 9, 10. Together, these reports aligned well to the above-mentioned proposal that Sr 2 RuO 4 is a very clean, quasi two

The localization of charge carriers by electronic repulsion was suggested by Mott in the 1930s to explain the insulating state observed in supposedly metallic NiO. The Mott metal-insulator transition has been subject of intense investigations ever since-not least for its relation to high-temperature superconductivity. A detailed comparison to real materials, however, is lacking because the pristine Mott state is commonly obscured by antiferromagnetism and a complicated band structure. Here we study organic quantum spin liquids, prototype realizations of the single-band Hubbard model in the absence of magnetic order. Mapping the Hubbard bands by optical spectroscopy provides an absolute measure of the interaction strength and bandwidth-the crucial parameters that enter calculations. In this way, we advance beyond conventional temperature-pressure plots and quantitatively compose a generic phase diagram for all genuine Mott insulators based on the absolute strength of the electronic correlations. We also identify metallic quantum fluctuations as a precursor of the Mott insulator-metal transition, previously predicted but never observed. Our results suggest that all relevant phenomena in the phase diagram scale with the Coulomb repulsion U, which provides a direct link to unconventional superconductivity in cuprates and other strongly correlated materials.

A strongly frustrated ordered state can be induced in Y3Cu9(OH)19Cl8 by slightly modifying the perfect kagome lattice YCu3(OH)6Cl3.

The Mott insulator κ-(BEDT-TTF)2Ag2(CN)3 forms a highly-frustrated triangular lattice of S = 1/2 dimers with a possible quantum-spin-liquid state. Our experimental and numerical studies reveal the emergence of a slight charge imbalance between crystallographically inequivalent sites, relaxor dielectric response and hopping dc transport. In a broader perspective we conclude that the universal properties of strongly-correlated charge-transfer salts with spin liquid state are an anion-supported valence band and cyanide-induced quasi-degenerate electronic configurations in the relaxed state. The generic low-energy excitations are caused by charged domain walls rather than by fluctuating electric dipoles. They give rise to glassy dynamics characteristic of dimerized Mott insulators, including the sibling compound κ-(BEDT-TTF)2Cu2(CN)3.PACS numbers: 75.10. Kt, 77.22.Gm, Electronic ferroelectricity and multiferroicity attracts great attention of condensed matter physicists due to their fundamental and technological importance. 1-3 They are identified in systems with strong electronic correlations such as transition-metal oxides and low-dimensional charge-transfer molecular solids. In the latter category, electric polarization arises from valence instability and charge ordering. In both cases, breaking the inversionsymmetry results in the concurrence of non-equivalent charge-sites and bonds. 4 There is no doubt that electron correlations are fundamental for stabilizing the ferroelectric ground state, nevertheless, experimental evidence indicates that the delicate interplay of Coulomb forces and structural changes within the coupled molecular-anion system have to be taken into account. Along these lines a solid understanding of electronic ferroelectricity was achieved for the families of quasi-one-dimensional organic charge-transfer salts: (TMTTF) 2 X and TTF-X, but also some layered (BEDT-TTF) 2 X systems. [5][6][7] However, no consensus has been reached yet on the origin of the ferroelectric signatures detected in the strongly dimerized κ-(BEDT-TTF) 2 X salts. [8][9][10][11][12] In these compounds, the BEDT-TTF dimers are arranged in a triangular lattice with a relatively high geometrical frustration. In some of them, indications of charge-ordering phenomena have been reported, but in-depth studies are missing 13,14 . On the other hand, the Mott dimer insulators κ-(BEDT-TTF) 2 Cu[N(CN) 2 ]Cl and κ-(BEDT-TTF) 2 Cu 2 (CN) 3 , called κ-CuCN, have been thoroughly studied because they are discussed as prototypes of a molecular multiferroic and quantum spin liquid (QSL) systems. 9,15 It turns out to be extremely challenging to reconcile the idea of quantum electric dipoles on molecular dimers interacting via dipolar-spin coupling [16][17][18][19] with the experimentally evidenced absence of any considerable charge imbalance. So far no global structural changes and no charge disproportionation between molecular dimer sites larger than 2δ ρ ≈ ±0.01e that could break the symmetry have been found. 20,21 In the case of the QSL κ-...