Pair-pair Correlations Research Articles

Stripes in the extended $t-t^\prime$ Hubbard model: A Variational Monte Carlo analysis

By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping \delta=1/8δ=1/8, with both nearest- (tt) and next-nearest-neighbor hopping (t^\primet′). Stripes with different wavelengths \lambdaλ (denoting the periodicity of the charge inhomogeneity) and character (bond- or site-centered) are stabilized for sufficiently large values of the electron-electron interaction U/tU/t. The general trend is that \lambdaλ increases going from negative to positive values of t^\prime/tt′/t and decreases by increasing U/tU/t. In particular, the \lambda=8λ=8 stripe obtained for t^\prime=0t′=0 and U/t=8U/t=8 [L.F. Tocchio, A. Montorsi, and F. Becca, SciPost Phys. 21 (2019)] shrinks to \lambda=6λ=6 for U/t\gtrsim 10U/t≳10. For t^\prime/t<0t′/t<0, the stripe with \lambda=5λ=5 is found to be remarkably stable, while for t^\prime/t>0t′/t>0, stripes with wavelength \lambda=12λ=12 and \lambda=16λ=16 are also obtained. In all these cases, pair-pair correlations are highly suppressed with respect to the uniform state (obtained for large values of |t^\prime/t||t′/t|), suggesting that striped states are not superconducting at \delta=1/8δ=1/8.

Nanopore facilitated monohydrocalcitic amorphous calcium carbonate precipitation.

Predicting the precipitation of solids is important in both natural systems and subsurface energy applications. The factors controlling reaction mechanisms, phase selection and conversion between phases are particularly important. In this contribution the precipitation and growth of an amorphous calcium carbonate species from flowing aqueous solution in a nanoporous controlled pore glass is followed in situ with differential X-ray pair distribution function analysis. It is discovered that the local atomic structure of this phase indicates monohydrocalcite-like pair-pair correlations, yet is functionally amorphous because it lacks long-range structure. The unexpected occurrence of synthetic proto-monohydrocalcite amorphous calcium carbonate, precipitated from a solution undersaturated with respect to published solubilities, suggests that nanopore confinement facilitates formation of an amorphous phase at the expense of more favorable crystalline ones. This result illustrates that confinement and interface effects are physical factors exerting control on mineral nucleation behavior in natural and geological systems.

Superconductivity in the doped quantum spin liquid on the triangular lattice

Broad interest in quantum spin liquid (QSL) phases was triggered by the notion that they can be viewed as insulating phases with preexisting electron pairs, such that upon light doping they might automatically yield high temperature superconductivity. Yet despite intense experimental and numerical efforts, definitive evidence showing that doping QSLs leads to superconductivity has been lacking. We address the problem of a lightly doped QSL through a large-scale density-matrix renormalization group study of the t-J model on finite-circumference triangular cylinders with a small but nonzero concentration of doped holes. We provide direct evidences that doping QSL can naturally give rise to d-wave superconductivity. Specifically, we find power-law superconducting correlations with a Luttinger exponent, Ksc ≈ 1, which is consistent with a strongly diverging superconducting susceptibility, {chi }_{sc} ,sim, {T}^{-(2,-,{K}_{sc})} as the temperature T → 0. The spin–spin correlations—as in the undoped QSL state—fall exponentially which suggests that the superconducting pair-pair correlations evolve smoothly from the insulating parent state.

Intertwined charge, spin, and pairing orders in doped iron ladders

Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe$_2$S$_3$. The model is constructed by using {\it ab initio} hopping parameters and the ground state properties are investigated using the density matrix renormalization group method. We show that the $(\pi,0)$ magnetic ordering at half-filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard $U$ coupling, other magnetic patterns, such as $(0,\pi)$, are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interaction strength, indicating hole pairing. Due to the crystal-field split among orbitals, the holes primarily reside in one orbital, with the other one remaining half-filled. This resembles orbital selective Mott states. The formation of tight hole pairs continues with increasing hole density, as long as the magnetic order remains antiferromagnetic in one direction. The study of pair-pair correlations indicates the dominance of the intra-orbital spin-singlet channel, as opposed to other pairing channels. Although in a range of hole doping pairing correlations decay slowly, our results can also be interpreted as corresponding to a charge-density-wave made of pairs, a precursor of eventual superconductivity after interladder couplings are included. Such scenario of intertwined orders has been extensively discussed before in the cuprates, and our results suggest a similar physics could exist in ladder iron-based superconductors. Finally, we also show that a robust Hund's coupling is needed for pairing to occur.

Negative charge-transfer gap and even parity superconductivity in Sr2RuO4

A comprehensive theory of superconductivity in Sr$_2$RuO$_4$ must explain experiments that suggest even parity superconducting order and others that suggest broken time reversal symmetry. Completeness further requires that the theory applies to Ca$_2$RuO$_4$, a Mott-Hubbard semiconductor that exhibits an unprecedented insulator-to-metal transition driven by very small electric field, and also by doping with very small concentration of electrons, leading to a metallic state proximate to ferromagnetism. A valence transition model, previously proposed for superconducting cuprates [Phys. Rev. B {\bf 98}, 205153] is extended to Sr$_2$RuO$_4$ and Ca$_2$RuO$_4$. The insulator to metal transition is distinct from that expected from the simple melting of the Mott-Hubbard semiconductor. Rather, the Ru ions occur as low spin Ru$^{4+}$ in the semiconductor, and as high spin Ru$^{3+}$ in the metal, the driving force behind the valence transition being the strong spin-charge coupling and consequent large ionizaton energy in the low charge state. Metallic and superconducting ruthenates are two-component systems in which the half-filled high spin Ru$^{3+}$ ions determine the magnetic behavior but not transport, while the charge carriers are entirely on on the layer oxygen ions, which have an average charge -1.5. Spin singlet superconductivity evolves from the correlated lattice frustrated 3/4 filled band of layer oxygen ions alone, in agreement with quantum many body calculations that have demonstrated enhancement by electron-electron interactions of superconducting pair-pair correlations tions uniquely at or very close to this filling [Phys. Rev. B {\bf 93}, 165110 and {\bf 93}, 205111]. Several model specific experimental predictions are made, including that spin susceptibility due to Ru ions will remain unchanged as Sr$_2$RuO$_4$ is taken through superconducting Tc.

Effect of annealing on magnetic properties in ferrimagnetic GdCo alloy films with bulk perpendicular magnetic anisotropy

Magnetic properties in ferrimagnetic GdCo alloy films with bulk perpendicular magnetic anisotropy (PMA) are investigated as a function of annealing temperature (Tanneal) and annealing time for several capping layers. Magnetic properties in films capped by TaOx vary markedly with Tanneal; the saturation magnetization and coercivity vary progressively with increasing Tanneal up to 300°C, and above that temperature, PMA is lost abruptly. By comparing the annealing temperature dependence for Co-dominated and Gd-dominated compositions close to the magnetization compensation point, the data are readily explained by preferential oxidation of Gd during annealing. When films are capped by a Ta/Pt bilayer, the film properties are stable up Tanneal = 300 °C, indicating that oxidation at high temperatures is effectively blocked, but the abrupt loss of PMA for Tanneal > 300 °C is still observed. X-ray diffraction measurement reveals that the amorphous structure of the films remains the same after high-temperature annealing that is sufficient to remove PMA, indicating that crystallization from the amorphous phase is not responsible for the lack of PMA. Instead, our results suggest that high annealing temperatures may cause segregation of Co and Gd atoms in the films, which reduces anisotropic pair-pair correlations responsible for the observed bulk PMA in the as-grown state.

Pairing tendencies in a two-orbital Hubbard model in one dimension

The recent discovery of superconductivity under high pressure in the ladder compound BaFe$_2$S$_3$ has opened a new field of research in iron-based superconductors with focus on quasi one-dimensional geometries. In this publication, using the Density Matrix Renormalization Group technique, we study a two-orbital Hubbard model defined in one dimensional chains. Our main result is the presence of hole binding tendencies at intermediate Hubbard $U$ repulsion and robust Hund coupling $J_H/U=0.25$. Binding does not occur neither in weak coupling nor at very strong coupling. The pair-pair correlations that are dominant near half-filling, or of similar strength as the charge and spin correlation channels, involve hole-pair operators that are spin singlets, use nearest-neighbor sites, and employ different orbitals for each hole. The Hund coupling strength, presence of robust magnetic moments, and antiferromagnetic correlations among them are important for the binding tendencies found here.

Coulomb enhancement of superconducting pair-pair correlations in a34-filled model forκ−(BEDT-TTF)2X

We present the results of precise correlated-electron calculations on the monomer lattices of the organic charge-transfer solids $\kappa$-(BEDT-TTF)$_2$X for 32 and 64 molecular sites. Our calculations are for band parameters corresponding to X = Cu[N(CN)$_2$]Cl and Cu$_2$(CN)$_3$, which are semiconducting antiferromagnetic and quantum spin liquid, respectively, at ambient pressure. We have performed our calculations for variable electron densities $\rho$ per BEDT-TTF molecule, with $\rho$ ranging from 1 to 2. We find that $d$-wave superconducting pair-pair correlations are enhanced by electron-electron interactions only for a narrow carrier concentration about $\rho=1.5$, which is precisely the carrier concentration where superconductivity in the charge-transfer solids occurs. Our results indicate that the enhancement in pair-pair correlations is not related to antiferromagnetic order, but to a proximate hidden spin-singlet state that manifests itself as a charge-ordered state in other charge-transfer solids. Long-range superconducting order does not appear to be present in the purely electronic model, suggesting that electron-phonon interactions also must play a role in a complete theory of superconductivity.

Coulomb-enhanced superconducting pair correlations and paired-electron liquid in the frustrated quarter-filled band

A necessary condition for superconductivity (SC) driven by electron correlations is that electron-electron (e-e) interactions enhance superconducting pair-pair correlations, relative to the noninteracting limit. We report high-precision numerical calculations of the ground state within the frustrated two-dimensional (2D) Hubbard Hamiltonian for a wide range of carrier concentration $\rho$ (0 < $\rho$ <1) per site. We find that long range superconducting pair correlations are enhanced only for $\rho$ $\simeq$ 0.5. At all other fillings e-e interactions mostly suppress pair correlations. The enhancement of pair correlations is driven by the strong tendency to local singlet bond formation and spin gap (SG) in $\rho$ = 0.5, in lattices with quantum fluctuation. We also report determinantal quantum Monte Carlo (DQMC) calculations that are in strong agreement with our ground state results. Our work provides a key ingredient to the mechanism of SC in the 2D organic charge-transfer solids (CTS), and many other unconventional superconductors with frustrated crystal lattices and $\rho$ $\simeq$ 0.5, while explaining the absence of SC in structurally related materials with substantially different $\rho$.

Absence of long-range superconducting correlations in the frustrated half-filled-band Hubbard model

We present many-body calculations of superconducting pair-pair correlations in the ground state of the half-filled-band Hubbard model on large anisotropic triangular lattices. Our calculations cover nearly the complete range of anisotropies between the square and isotropic triangular lattice limits. We find that the superconducting pair-pair correlations decrease monotonically with increasing on site Hubbard interaction $U$ for interpair distances greater than nearest neighbor. For the large lattices of interest here the distance dependence of the correlations approaches that for noninteracting electrons. Both these results are consistent with the absence of superconductivity in this model in the thermodynamic limit. We conclude that the effective $\frac{1}{2}$-filled band Hubbard model, suggested by many authors to be appropriate for the $\ensuremath{\kappa}$-(BEDT-TTF)-based organic charge-transfer solids, does not explain the superconducting transition in these materials.

Interferometric scanning microscopy for the study of disordered materials

We demonstrate an interferometric optical technique that probes pair-pair correlations in disordered materials. Fraunhofer diffraction patterns, using coherent double-probe illumination, exhibit Young’s interference fringes whose strength is influenced by structural correlations between the two probed regions. Fourier transforms of diffraction patterns exhibit holographic sidebands, and the strength of correlations is proportional to the sideband intensity. Autoregression analysis of the correlation strength provides a direct measure of the characteristic ordering length scales. This technique is extendable in principle to x-ray and electron probes for studying materials at atomic length scales.

Asymmetric Bethe-Salpeter Equation for Pairing and Condensation

The Martin-Schwinger hierarchy of correlations are reexamined and the three-particle correlations are investigated under various partial summations. Besides the known approximations of screened, ladder and maximally crossed diagrams the pair-pair correlations are considered. It is shown that the recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical repeated collisions is derived as a result of the hierarchical dependencies of correlations. Exceeding the parquet approximation we show that an asymmetry appears in the selfconsistent propagators. This form is superior over the symmetric selfconsistent one since it provides the Nambu-Gorkov equations and gap equation for fermions and the Beliaev equations for bosons while from the symmetric form no gap equation results. The selfenergy diagrams which account for the subtraction of unphysical repeated collisions are derived from the pair-pair correlation in the three-particle Green’s function. It is suggested to distinguish between two types of selfconsistency, the channel-dressed propagators and the completely dressed propagators, with the help of which the asymmetric expansion completes the Ward identity and is Φ-derivable.

Absence of Superconductivity in the Half-Filled Band Hubbard Model on the Anisotropic Triangular Lattice

We report exact calculations of magnetic and superconducting pair-pair correlations for the half-filled band Hubbard model on an anisotropic triangular lattice. Our results for the magnetic phases are similar to those obtained with other techniques. The superconducting pair-pair correlations at distances beyond nearest neighbor decrease monotonically with increasing Hubbard interaction U for all anisotropy, indicating the absence of frustration-driven superconductivity within the model.

Second generation of Moore-Read quasiholes in a composite-fermion liquid

Two- and three-body correlations of incompressible quantum liquids are studied numerically. Pairing of composite fermions (CFs) in the 1/3-filled second CF Landau level is found at nu_e=4/11. It is explained by reduced short-range repulsion due to ring-like single-particle charge distribution. Although Moore-Read state of CFs is unstable in the 1/2-filled second CF level, condensation of its quasiholes is a possible origin of incompressibility at nu_e=4/11. Electron pairing occurs at nu_e=7/3 and 13/3, but with different pair-pair correlations. Signatures of triplets are found at higher fillings.

Photoemission, inverse photoemission and superconducting correlations in Hubbard and t-J ladders: role of the anisotropy between legs and rungs

Several experiments in the context of ladder materials have recently shown that the study of simple models of anisotropic ladders (i.e. with different couplings along legs and rungs) is important for the understanding of these compounds. In this paper Exact Diagonalization studies of the one-band Hubbard and t-J models are reported for a variety of densities, couplings, and anisotropy ratios. The emphasis is given to the one-particle spectral function A(q,\omega) which presents a flat quasiparticle dispersion at the chemical potential in some region of parameter space. This is correlated with the existence of strong pairing fluctuations, which themselves are correlated with an enhancement of the bulk-extrapolated value for the two-hole binding energy as well as with the strength of the spin-gap in the hole-doped system. Part of the results for the spectral function are explained using a simple analytical picture valid when the hopping along the legs is small. In particular, this picture predicts an insulating state at quarter filling in agreement with the metal-insulator transition observed at this special filling for increasing rung couplings. The results are compared against previous literature, and in addition pair-pair correlations using extended operators are also here reported.

Hole pairs in a spin liquid: Influence of electrostatic hole-hole repulsion

The stability of hole bound states in the t-J model including short-range Coulomb interactions is analyzed using computational techniques on ladders with up to $2 \times 30$ sites. For a nearest-neighbors (NN) hole-hole repulsion, the two-holes bound state is surprisingly robust and breaks only when the repulsion is several times the exchange $J$. At $\sim 10%$ hole doping the pairs break only for a NN-repulsion as large as $V \sim 4J$. Pair-pair correlations remain robust in the regime of hole binding. The results support electronic hole-pairing mechanisms on ladders based on holes moving in spin-liquid backgrounds. Implications in two dimensions are also presented. The need for better estimations of the range and strength of the Coulomb interaction in copper-oxides is remarked.

Phase diagram and superconducting properties of an exactly solvable model with correlated hopping

The model of strongly correlated electrons with the correlated hopping term and an additional interaction between holes $V$ is solved exactly in one dimension at a special point where the number of hole pairs is conserved. As a function of the interaction $V$ the phase diagram has a rich structure. There exist gapless phases with dominating density-density correlations (metallic) or pair-pair correlations (superconducting) as well insulating and phase-separated phases. The stiffness constant of the conductivity, the effective transport mass, and the compressibility are also exactly calculated in several regions of the phase diagram.

Quantum Monte Carlo simulations of Hubbard type models

We present a review of recent Quantum Monte-Carlo results for one- and twodimensional Hubbard models. In one-dimension spectral properties are calculated with the maximum entropy method. At small doping, the one-particle excitations are characterized by a dispersive cosine-like band. Two different velocities for charge and spin-excitations are obtained which lead to a conformal charge c = 0.98 ± 0.05. In two-dimensions, we concentrate on two methods to detect superconducting ground states without prior knowledge of the symmetry of the underlying pair-pair correlations: flux quantization and the temperature derivative of the superfluid density. Both methods are based on extensions of quantum Monte-Carlo algorithms to incorporate magnetic fields. Our main results include numerical data which a) confirm the Kosterlitz-Thouless transition in the attractive Hubbard model b) show the absence of superconductivity in the quarter filled repulsive Hubbard model, and finally c) show no sign of a Kosterlitz-Thouless type transition in the three-band Hubbard model up to βtpd = 12.5 and hole doping δ = 0.25.

Superconductivity as a synchronous spatial alternation of valence bonds

A new theoretical model for superconductivity is proposed which depends on a pairing in real space (valence bonds). Pair-pair correlations establish an ordered array of such pairs and a synchronous alternation among equivalent coherent spatial arrays of valence bonds is considered as the origin of superconductivity. Simple metals with two valence electrons (e.g., Be, Zn, etc.) are used to illustrate the ideas. The new high T c materials (based on substitutions in La 2CuO 4) will be considered elsewhere.

Monte Carlo calculation of order on the triangular Ising lattice with next-nearest-neighbor interactions

This paper presents a comparison of Monte Carlo calculations with the corresponding Bethe-Peierls solution of Campbell and Schick for an Ising-spin system on a triangular lattice with antiferromagnetic nearest-neighbor and ferromagnetic next-nearest-neighbor interactions. The results agree for nonzero external field at a density of one-third. But for zero external field at temperatures below $\frac{\mathrm{kT}}{2J}=0.5$ with densities between one-third and two-thirds, the Monte Carlo calculations differ from the Bethe-Peierls solution. This is probably due to the absence of pair-pair correlations in the latter.