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.

Nuclear Magnetic Resonance Reveals Disordered Level-Crossing Physics in the Bose-Glass Regime of the Br-Doped Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2} Compound at a High Magnetic Field.

By measuring the nuclear magnetic resonance (NMR) T_{1}^{-1} relaxation rate in the Br (bond) doped DTN compound, Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2}(DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H^{*}≅13.6 T. From its temperature and field dependence, we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017).PRLTAO0031-900710.1103/PhysRevLett.118.067204].

Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy.

Electronic charges introduced in copper-oxide (CuO(2)) planes generate high-transition-temperature (T(c)) superconductivity but, under special circumstances, they can also order into filaments called stripes. Whether an underlying tendency towards charge order is present in all copper oxides and whether this has any relationship with superconductivity are, however, two highly controversial issues. To uncover underlying electronic order, magnetic fields strong enough to destabilize superconductivity can be used. Such experiments, including quantum oscillations in YBa(2)Cu(3)O(y) (an extremely clean copper oxide in which charge order has not until now been observed) have suggested that superconductivity competes with spin, rather than charge, order. Here we report nuclear magnetic resonance measurements showing that high magnetic fields actually induce charge order, without spin order, in the CuO(2) planes of YBa(2)Cu(3)O(y). The observed static, unidirectional, modulation of the charge density breaks translational symmetry, thus explaining quantum oscillation results, and we argue that it is most probably the same 4a-periodic modulation as in stripe-ordered copper oxides. That it develops only when superconductivity fades away and near the same 1/8 hole doping as in La(2-x)Ba(x)CuO(4) (ref. 1) suggests that charge order, although visibly pinned by CuO chains in YBa(2)Cu(3)O(y), is an intrinsic propensity of the superconducting planes of high-T(c) copper oxides.

Field-dependent paramagnetic relaxation enhancement in solutions of Ni(II): What happens above the NMR proton frequency of 1 GHz?

An extended set of paramagnetic relaxation enhancement (PRE) data, up to the field of 32.9 Tesla, is reported for protons in an acidified aqueous solution of a Ni(II) salt in the presence and in the absence of added glycerol. For the 55% w/w glycerol sample, a distinct maximum in the PRE vs magnetic field curve is observed for the first time. The data are analysed using the Swedish slow-motion theory, including both the intramolecular (inner-sphere) and intermolecular (outer-sphere) contributions. The results indicate that estimating the outer-sphere part in the presence of the more efficient inner-sphere term is a difficult task.

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.

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.

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy.

The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order-parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.

Emergence of charge order from the vortex state of a high-temperature superconductor.

Evidence is mounting that charge order competes with superconductivity in high Tc cuprates. Whether this has any relationship to the pairing mechanism is unknown as neither the universality of the competition nor its microscopic nature has been established. Here, we show using nuclear magnetic resonance that charge order in YBa2Cu3Oy has maximum strength inside the superconducting dome, similar to compounds of the La2-x(Sr,Ba)xCuO4 family. In YBa2Cu3Oy, this occurs at doping levels of p=0.11-0.12. We further show that the overlap of halos of incipient charge order around vortex cores, similar to those visualised in Bi2Sr2CaCu2O8+δ, can explain the threshold magnetic field at which long-range charge order emerges. These results reveal universal features of a competition in which charge order and superconductivity appear as joint instabilities of the same normal state, whose relative balance can be field-tuned in the vortex state.