Resonating Valence Bond Research Articles

Erratum: Consistent theory of underdoped cuprates: Evolution of the resonating valence bond state from half filling [Phys. Rev. B82, 014504 (2010)

Erratum: Consistent theory of underdoped cuprates: Evolution of the resonating valence bond state from half filling [Phys. Rev. B<b>82</b>, 014504 (2010)

Loss of nodal quasiparticle integrity in underdoped YBa2Cu3O6+x

Arguably the most intriguing aspect of the physics of cuprates is the close proximity between the record high-Tc superconductivity (HTSC) and the antiferromagnetic charge-transfer insulating state driven by Mott-like electron correlations. These are responsible for the intimate connection between high and low-energy scale physics, and their key role in the mechanism of HTSC was conjectured very early on. More recently, the detection of quantum oscillations in high-magnetic field experiments on YBa2Cu3O6+x (YBCO) has suggested the existence of a Fermi surface of well-defined quasiparticles in underdoped cuprates, lending support to the alternative proposal that HTSC might emerge from a Fermi liquid across the whole cuprate phase diagram. Discriminating between these orthogonal scenarios hinges on the quantitative determination of the elusive quasiparticle weight Z, over a wide range of hole-doping p. By means of angle-resolved photoemission spectroscopy (ARPES) on in situ doped YBCO, and following the evolution of bilayer band-splitting, we show that the overdoped metal electronic structure (0.25<p<0.37) is in remarkable agreement with density functional theory and the Z=2p/(p+1) mean-field prediction. Below p~0.10-0.15, we observe the vanishing of the nodal quasiparticle weight Z_N; this marks a clear departure from Fermi liquid behaviour and -- consistent with dynamical mean-field theory -- is even a more rapid crossover to the Mott physics than expected for the doped resonating valence bond (RVB) spin liquid.

Comparisons between Haydeeite, α-Cu3Mg(OD)6Cl2, and Kapellasite, α-Cu3Zn(OD)6Cl2, Isostructural S = 1/2 Kagome Magnets

The search for new S = 1/2 kagome antiferromagnets has been an ongoing challenge for the researchers interested in frustrated magnetism. Intrigue has surrounded these materials since the proposal that the high frustration of the kagome antiferromagnet and quantum fluctuations could prevent the formation of conventional Neel order and allow the formation of the resonating valence bond (RVB) state at low temperatures. There remain relatively few examples of S = 1/2 kagome magnets with crystal structures that have 3-fold symmetry, as many feature distortions that lower the crystal symmetry to monoclinic and reduce the degeneracy of the kagome lattice. In this article, we detail the synthesis and preliminary magnetic investigations of a new quantum kagome magnet, haydeeite, α-Cu3Mg(OH)6Cl2. Comparisons with the isomagnetic and isostructural analogue kapellasite, α-Cu3Zn(OH)6Cl2, are discussed.

Pinwheel valence-bond solid and triplet excitations in the two-dimensional deformed kagome lattice

Determining ground states of correlated electron systems is fundamental to understanding novel phenomena in condensed matter physics. A difficulty, however, arises in a geometrically frustrated system in which the incompatibility between the global topology of an underlying lattice and local spin interactions gives rise to macroscopically degenerate ground states, potentially prompting the emergence of quantum spin states, such as resonating valence bond (RVB) and valence bond solid (VBS). Although theoretically proposed to exist in a kagome lattice -- one of the most highly frustrated lattices in two dimensions (2D) being comprised of corner-sharing triangles -- such quantum-fluctuation-induced states have not been observed experimentally. Here we report the first realization of the "pinwheel" VBS ground state in the S=1/2 deformed kagome lattice antiferromagnet Rb2Cu3SnF12. In this system, a lattice distortion breaks the translational symmetry of the ideal kagome lattice and stabilizes the VBS state.

Spin Hamiltonians with Resonating-Valence-Bond Ground States

Quantum dimer models exhibit quantum critical points and liquid states when the ground state is the resonating-valence bond (RVB) state. We construct SU(2)-invariant spin-1/2 Hamiltonians with the same RVB ground state. The main technical obstacle overcome is the fact that different dimer configurations in the spin model are not orthogonal. We show that the physics depends on how dimers are related to the spins, and find a Hamiltonian that is likely to be quantum critical.

Signature of pseudogap formation in the density of states of underdoped cuprates

The resonating valence bond spin liquid model for the underdoped cuprates has as an essential element, the emergence of a pseudogap. This energy scale introduces asymmetry in the quasiparticle density of states because it is associated with the antiferromagnetic Brillouin zone. By contrast, superconductivity develops on the Fermi surface and this largely restores the particle-hole symmetry for energies below the superconducting energy-gap scale. In the highly underdoped regime, these two scales can be separately identified in the density of states and also partial density of states for each fixed angle in the Brillouin zone. From the total density of states, we find that the pseudogap energy scale manifests itself differently as a function of doping for positive and negative biases. Furthermore, we find evidence from recent scanning tunneling spectroscopy data for asymmetry in the positive and negative biases of the extracted $\ensuremath{\Delta}(\ensuremath{\theta})$ which is in qualitative agreement with this model. Likewise, the slope of the linear low-energy density of states is nearly constant in the underdoped regime while it increases significantly with overdoping in agreement with the data.

Schwinger boson mean field theories of spin liquid states on a honeycomb lattice: Projective symmetry group analysis and critical field theory

Motivated by the recent numerical evidence[1] of a short-range resonating valence bond state in the honeycomb lattice Hubbard model, we consider Schwinger boson mean field theories of possible spin liquid states on honeycomb lattice. From general stability considerations the possible spin liquids will have gapped spinons coupled to Z$_2$ gauge field. We apply the projective symmetry group(PSG) method to classify possible Z$_2$ spin liquid states within this formalism on honeycomb lattice. It is found that there are only two relevant Z$_2$ states, differed by the value of gauge flux, zero or $\pi$, in the elementary hexagon. The zero-flux state is a promising candidate for the observed spin liquid and continuous phase transition into commensurate N\'eel order. We also derive the critical field theory for this transition, which is the well-studied O(4) invariant theory[2-4], and has an irrelevant coupling between Higgs and boson fields with cubic power of spatial derivatives as required by lattice symmetry. This is in sharp contrast to the conventional theory[5], where such transition generically leads to non-colinear incommensurate magnetic order. In this scenario the Z$_2$ spin liquid could be close to a tricritical point. Soft boson modes will exist at seven different wave vectors. This will show up as low frequency dynamical spin susceptibility peaks not only at the $\Gamma$ point (the N\'eel order wave vector) but also at Brillouin zone edge center $M$ points and twelve other points. Some simple properties of the $\pi$-flux state are studies as well. Symmetry allowed further neighbor mean field ansatz are derived in Appendix which can be used in future theoretical works along this direction.

Consistent theory of underdoped cuprates: Evolution of the resonating valence bond state from half filling

We have been able to resolve two long-standing issues that are central to the theory of high Tc superconductivity: (1) How is the physics of the doped region connected to that of the Mott insulator? (2) What is the origin of the two-dimensionality of the normal state? Specifically, based on the t-J model, we derive a renormalized Hamiltonian to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the bosonic RVB state of Arovas and Auerbach. Moving holes are assumed to destroy long-range magnetic order, which leads to a gap in the spinon spectrum. The presence of the spin gap allows us to derive a constrained Hamiltonian which describes sublattice-preserving hopping by renormalized holons and holon pairs, accompanied by spinon singlet backflows. Below the singlet condensation, i.e, the psudogap (as distinct from the spin gap), temperature T*, holons form a spinless Fermi liquid without an observable small Fermi surface. Above T* holons are localized, giving rise to a (gauge) insulator, which we identify with the strange metal phase. Holon pair hopping leads to a robust d-wave superconductor, its symmetry determined primarily by the symmetry of the RVB state at half filling. The predictions of the theory are shown to be consistent with the results of nmr, tunneling and transport experiments. Remarkably, the existence of the spin gap provides a natural explanation for the two-dimensionality of the normal state. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.

Effect of pseudogap formation on the superconducting gap in underdoped cuprates

Many anomalous properties of the normal and superconducting state of underdoped cuprates can be understood qualitatively within a resonating valence bond spin liquid model which incorporates pseudogap formation below a quantum-critical point. It also contains band narrowing, and reduction in coherence, both effects captured through Gutzwiller factors. The superconducting state is treated phenomenologically within the usual BCS model with a $d$-wave superconducting gap. Here we solve a generalized gap equation which explicitly incorporates the emergence of a pseudogap in the electronic structure. The magnitude of the pairing potential is found to still be increasing as the bottom underdoped edge of the superconducting dome is approached. Consequently, it is the Mott physics with implied reduction in metallicity which drives the superconducting critical temperature ${T}_{c}$ to zero. The superconducting gap contains many higher harmonics, is nonmonotonic as the magnetic coherence length increases, although its amplitude remains finite everywhere on the Fermi contour even in the antinodal direction where the pseudogap is largest. The superconducting gap to critical temperature ratio increases strongly with decreasing doping.

Hidden Fermi liquid; the moral: a good effective low-energy theory is worth all of MonteCarlo with Las Vegas thrown in

We present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in thet–J model which is widely believed to underlie the phenomenology of the high-Tc cuprates. We suggest that a true Bardeen–Cooper–Schrieffer condensationfrom a Fermi liquid state takes place, but in the unphysical space prior toprojection. At low doping, however, instead of a hidden Fermi liquid one getsa ‘hidden’ non-superconducting resonating valence bond state which developshole pockets upon doping. The theory which results upon projection does notfollow conventional rules of diagram theory and in fact in the normal state is aZ = 0 non-Fermi liquid. Anomalous properties of the ‘strange metal’ normal state are predictedand compared against experimental findings.

Holographic superconductor/insulator transition at zero temperature

We analyze the five-dimensional AdS gravity coupled to a gauge field and a charged scalar field. Under a Scherk-Schwarz compactification, we show that the system undergoes a superconductor/insulator transition at zero temperature in 2 + 1 dimensions as we change the chemical potential. By taking into account a confinement/deconfinement transition, the phase diagram turns out to have a rich structure. We will observe that it has a similarity with the RVB (resonating valence bond) approach to high-T c superconductors via an emergent gauge symmetry.

Possible high-temperature superconducting state with ad+idpairing symmetry in doped graphene

Graphene is at the forefront of condensed matter sciences, because of a variety of interesting phenomena it supports. If graphene could support high Tc superconductivity, after doping for example, it will make it even more valuable. Some authors have suggested possibility of superconductivity in graphite like systems. However, an early suggestion of one of us (Baskaran) was unique in the sense it combined Pauling's classic idea of resonating valence bond physics with band theory to obtain some exciting results for superconductivity. Black-Schaffer and Doniach took this approach further and found an unconventional d + id order parameter. To sharpen our theory and get more convincing and reliable results for superconductivity, we introduce a correlated variational BCS ground state wavefunction and perform extensive Monte Carlo study of the repulsive Hubbard model on the honeycomb lattice. We find that undoped graphene is not a superconductor, consistent with experiments and also mean field results. Interestingly, an appreciable superconducting order is obtained around an optimal doping. This result and a supportive slave particle analysis together suggest the possibility of high temperature superconductivity in doped graphene.

Resonating Valence Bond and σ-Charge Density Wave Phases in a Benzannulated Phenalenyl Radical

We report the preparation of the first benzannulated phenalenyl neutral radical conductor (18), and we show that the compound displays unprecedented solid state behavior: the structure is dominated by two sets of intermolecular interactions: (1) a pi-chain structure with superimposed pi-overlap of the benzannulated phenalenyls along [0 0 1], and (2) an interchain overlap involving a pair of carbon atoms (C4) along [0 1 0]. The pi-chain-type stacking motif is reminiscent of previously reported phenalenyl radicals and the room temperature structure (space group P2/c) together with the conductivity of sigma(RT) = 0.03 S/cm and the Pauli-like magnetic susceptibility are best described by the resonating valence bond (RVB) model. The interchain interaction is unstable with respect to the formation of a sigma-charge density wave (sigma-CDW) involving pairs of C4 carbon atoms between adjacent radicals and this phase is characterized by the P2(1)/c space group which involves a doubling of the unit cell along the [0 1 0] direction. The RVB and CDW phases compete for structural occupancy throughout the whole temperature range (15-293 K) with the RVB phase predominating at 15 and 293 K and the sigma-CDW phase achieving a maximum structural occupancy of about 60% at 150 K where it produces clearly discernible effects on the magnetism and conductivity.

Effect of pseudogap formation on the penetration depth of underdoped high-Tccuprates

The penetration depth is calculated over the entire doping range of the cuprate phase diagram with emphasis on the underdoped regime. Pseudogap formation on approaching the Mott transition, for doping below a quantum critical point, is described within a model based on the resonating valence bond spin liquid which provides an ansatz for the coherent piece of the Green's function. Fermi-surface reconstruction, which is an essential element of the model, has a strong effect on the superfluid density at $T=0$ producing a sharp drop in magnitude but does not change the slope of the linear low-temperature variation. Comparison with recent data on Bi-based cuprates provides validation of the theory and shows that the effects of correlations, captured by Gutzwiller factors, are essential for a qualitative understanding of the data. We find that the Ferrell-Glover-Tinkham sum rule still holds and we compare our results with those for the Fermi arc and the nodal liquid models.

Variational Monte Carlo study of the spin liquid state with one-dimensionalization

We investigate ground state properties of triangular lattice spin-1/2 systems with one-dimensional (1D) anisotropy by use of variational Monte Carlo method. Using resonating-valence-bond (RVB) state as a trial wave-function, we focus on the optimization of the complex pairing function Δ ij ≡ 〈 c i ↑ c j ↓ 〉 and compare the results to those of our previous RVB mean-field analysis. As the anisotropy parameter ( J ′ / J ) deviates from unity, strong “one-dimensionalization” is found in the pairing function and strong suppression of “spin-gap” can be expected even near the isotropic point ( J ′ / J = 1 ). Implications for recent experiments on spin liquid states with anomalously small spin-gap, found in organic conductors κ ‐ ( ET ) 2 Cu 2 ( CN ) 3 , is discussed.

フェナレニルを基盤とする非局在型一重項ビラジカルの化学

Main issue described in this article is clarification of spin-spin interactions in delocalized singlet biradical species, especially co-existence of intra- and inter-molecular interactions. For the end, we designed and prepared some singlet biradical molecules thermodynamically stabilized by utilizing spin-delocalizing character of phenalenyl radical. These species were found to be stable in air and could be isolated in a crystalline form. X-ray crystallographic analysis revealed the abnormally short π-π contact between molecules, suggesting a strong intermolecular spin-spin interaction, even though the species had a strong intramolecular spin-spin interaction. Co-existence of both the interactions led to lower energy shift of HOMO-LUMO absorption bands in a solid state with respect to solution bands. These findings indicate that covalent bonding character is operative within and between molecules in molecular aggregates of delocalized singlet biradicals. This new aspect was supported by variable-temperature X-ray crystallography and reflectivity measurement on single crystals which had one-dimensional π-π chains of the delocalized singlet biradicals, and we concluded that the electronic structure of the 1-D chain could be represented by the Resonating Valence Bond model proposed by Pauling.

Frustrated Electron Liquids in the Hubbard Model

The ground state of the Hubbard model is studied within the constrained Hilbert space where no order parameter exists. The self-energy of electrons is decomposed into the single-site and multisite self-energies. The calculation of the single-site self-energy is mapped to a problem of self-consistently determining and solving the Anderson model. When an electron reservoir is explicitly considered, it is proved that the single-site self-energy for the ground state is that of a normal Fermi liquid even if the multisite self-energy is so anomalous that the ground state itself is not a normal Fermi liquid. Thus, the ground state is a normal Fermi liquid in the supreme single-site approximation (S 3 A). In the strong-coupling regime, the Fermi liquid is stabilized by the Kondo effect in the S 3 A and further stabilized by the Fock-type term of the superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond the S 3 A. The stabilized Fermi liquid is frustrated as much as an RVB spin liquid in the Heisenberg model, and is a relevant unperturbed state that can be used to study a normal or anomalous Fermi liquid and an ordered state in the entire Hilbert space by the Kondo lattice theory. Even if multisite terms of higher order than the Fock-type term are considered, the ground state cannot be an insulator with a complete gap nor a Mott insulator. It can only be a gapless semiconductor even if the multisite self-energy is so anomalous that it is divergent at the chemical potential. A Mott insulator is only possible as a high-temperature phase.

Bose-Hubbard model on a star lattice

We analyze the Bose-Hubbard model of hardcore bosons with nearest-neighbor hopping and repulsive interactions on a star lattice using both quantum Monte Carlo simulation and dual vortex theory. We obtain the phase diagram of this model as a function of the chemical potential and the relative strength of hopping and interaction. In the strong-interaction regime, we find that the Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their counterparts on square, triangular, and kagome lattices, are either translationally invariant resonant valence bond (RVB) phases with no density-wave order or have coexisting density-wave and RVB orders. We also find that upon increasing the relative strength of hopping and interaction, the translationally invariant Mott states undergo direct second-order superfluid-insulator quantum phase transitions. We compute the critical exponents for these transitions and argue using the dual vortex picture that the transitions, when approached through the tip of the Mott lobe, belong to the inverted XY universality class.

AB2Hubbard chains in the strong-coupling limit: Ferrimagnetism, Nagaoka and RVB states, phase separation, and Luttinger-liquid behavior

We present a functional-integral formalism suitable to describe the strong-coupling regime below half filling of $A{B}_{2}$ Hubbard chains, with experimental realizations in inorganic and organic polymeric compounds. At half filling (one electron per site: $\ensuremath{\delta}=0$), we obtain the long-range-ordered ferrimagnetic ground state and correctly reproduce the associated quantum nonrelativistic nonlinear $\ensuremath{\sigma}$ model, with presence of topological Wess-Zumino terms, which has been also found in a coherent-state representation, restricted however to treat the case of localized spins. A fully polarized (Nagaoka) ferromagnetic state is obtained in the infinite-coupling regime near half filling, and at doping $\ensuremath{\delta}=1/3$ (two electrons per unit cell) insulating short-range resonating-valence-bond (RVB) singlet states take place. Competition between Nagaoka and RVB mechanisms can lead to phase separation for $0&lt;\ensuremath{\delta}&lt;1/3$. By increasing the hole doping, a crossover regime for $1/3&lt;\ensuremath{\delta}&lt;2/3$ anticipates the emergence of Luttinger-liquid behavior for $\ensuremath{\delta}\ensuremath{\ge}2/3$. In particular, at $\ensuremath{\delta}=2/3$ (one electron per cell) the system behaves similarly to a critical spin-1/2 antiferromagnetic linear chain. All these results find support in numerical studies both in the half filling and doped regimes.

Spinon excitation spectra of the resonating valence bond states in the high temperature superconducting cuprates

Magnetic excitations of the resonating valence bond (RVB) states were searched in high temperature superconducting cuprates by Raman scattering. Ho et al. [C.-M. Ho et al., Phys. Rev. Lett. 86 (2001) 1626] disclosed that the spin excitation in the two-dimensional resonating valence bond state has a magnon-like dispersion and a spinon continuum above it. The density of states of the spin excitation has a peak at 1.5J which is lower than the 2.36J of the spin wave. We found that the A1g spectra have a broad peak at 1.5J in common at the underdoped region of p⩽0.15 in LSCO, Bi2201, and Bi2212 and p⩽0.1 in YBCO. The B1g peak and the B2g peak in the two-magnon region have a fine structure of the spin wave. The carrier density dependence is discussed.