Pairing, Charge, and Spin Correlations in the Three-Band Hubbard Model

Using the Constrained Path Monte Carlo (CPMC) method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion $V_{pd}$ between charges on neighboring Cu and O lattice sites. As a function of distance, both the $d_{x^2 - y^2}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing $V_{pd}$ decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing $V_{pd}$ increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also increasing $V_{pd}$ suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of anti-ferromagnetic correlations.Comment: Revtex, 8 pages with 15 figure

Quantum Monte Carlo Study of Hole Binding and Pairing Correlations in the Three-Band Hubbard Model

We simulated the 3-band Hubbard model using the Constrained Path Monte Carlo (CPMC) method in search for a possible superconducting ground state. The CPMC is a ground state method which is free of the exponential scaling of computing time with system size. We calculated the binding energy of a pair of holes for systems up to $6 \times 4$ unit cells. We also studied the pairing correlation functions versus distance for both the d-wave and extended s-wave channels in systems up to $6 \times 6$. We found that holes bind for a wide range of parameters and that the binding increased as the system size is increased. However, the pairing correlation functions decay quickly with distance. For the extended s channel, we found that as the Coulomb interaction $U_d$ on the Cu sites is increased, the long-range part of the correlation functions is suppressed and fluctuates around zero. For the $d_{x^2 - y^2}$ channel, we found that the correlations decay rapidly with distance towards a small positive value. However, this value becomes smaller as the interaction $U_d$ or the system size is increased.Comment: 21 pages, 13 Postscript figures, Submitted to Phys. Rev.

Oxide mediated spectral shifting in aluminum resonant optical antennas

As a key feature among metals showing good plasmonic behavior, aluminum extends the spectrum of achievable plasmon resonances of optical antennas into the deep ultraviolet. Due to degradation, a native oxide layer gives rise to a metal-core/oxide-shell nanoparticle and influences the spectral resonance peak position. In this work, we examine the role of the underlying processes by applying numerical nanoantenna models that are experimentally not feasible. Finite-difference time-domain simulations are carried out for a large variety of elongated single-arm and two-arm gap nanoantennas. In a detailed analysis, which takes into account the varying surface-to-volume ratio, we show that the overall spectral shift toward longer wavelengths is mainly driven by the higher index surrounding material rather than by the decrease of the initial aluminum volume. In addition, we demonstrate experimentally that this shifting can be minimized by an all-inert fabrication and subsequent proof-of-concept encapsulation. © 2015 Optical Society of America

A new approach for perovskites in large dimensions

Using the Hubbard Hamiltonian for transition metal-3d and oxygen-2p states with perovskite geometry, we propose a new scaling procedure for a nontrivial extension of these systems to large spatial dimensions $D$. The scaling procedure is based on a selective treatment of different hopping processes for large $D$ and can not be generated by a unique scaling of the hopping element. The model is solved in the limit $D \rightarrow \infty$ by the iterated perturbation theory and using an extended non-crossing approximation. We discuss the evolution of quasi particles at the Fermi-level upon doping, leading to interesting insight into the dynamical character of the charge carriers near the metal insulator instability of transition metal oxide systems, three dimensional perovskites and other strongly correlated transition metal oxides.Comment: 5 pages (TeX) with 2 figures (Postscript

Superconductivity of the One-Dimensional d-p Model with p-p transfer

Using the numerical diagonalization method, we investigate the one-dimensional $d$-$p$ model, simulating a Cu-O linear chain with strong Coulomb repulsions. Paying attention to the effect of the transfer energy $t_{pp}$ between the nearest neighbor oxygen-sites, we calculate the critical exponent of correlation functions $K_{\rho}$ based on the Luttinger liquid relations and the ground state energy $E_0(\phi)$ as a function of an external flux $\phi$. We find that the transfer $t_{pp}$ increases the charge susceptibility and the exponent $K_{\rho}$ in cooperation with the repulsion $U_{d}$ at Cu-site. We also show that anomalous flux quantization occurs for $K_{\rho}>1$. The superconducting region is presented on a phase diagram of $U_{d}$ vs. $t_{pp}$ plane.Comment: 4 pages, RevTex + 5 PS figures include

The incommensurate charge-density-wave instability in the extended three-band Hubbard model

The infinite-U three-band Hubbard model is considered in order to describe the CuO_2 planes of the high temperature superconducting cuprates. The charge instabilities are investigated when the model is extended with a nearest-neighbor repulsion between holes on copper d and oxygen p orbitals and in the presence of a long-range Coulombic repulsion. It is found that a first-order valence instability line ending with a critical point is present like in the previously investigated model without long-range forces. However, the dominant critical instability is the formation of incommensurate charge-density-waves, which always occur before the valence-instability critical point is reached. An effective singular attraction arises in the proximity of the charge-density wave instability, accounting for both a strong pairing mechanism and for the anomalous normal state properties.Comment: 15 pages in RevteX. Figures available from M. Grill

Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods

We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to the Fermionic Gaussian state that optimally approximates the quantum state of the fermions. The methods apply to relatively large systems, since their complexity only scales quadratically with the number of lattice sites. Moreover, they are specially suited to describe inhomogenous systems, as those typically found in recent experiments with atoms in optical lattices, at least in the weak interaction regime. As a benchmark, we have applied them to the two-dimensional Hubbard model on a 10x10 lattice with and without an external confinement.Comment: 16 pages, 22 figure

The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram

One central challenge in high-$T_c$ superconductivity (SC) is to derive a detailed understanding for the specific role of the $Cu$-$d_{x^2-y^2}$ and $O$-$p_{x,y}$ orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-$T_c$ cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from "high-energy" excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are "universal". On the other hand, we expect the differences - and thus, the material dependence to show up in the "non-universal" finite-T phase diagram ($T_c$-values).Comment: 17 pages, 9 figure

Superconductivity in the Two-Band Hubbard Model in Infinite Dimensions

We study a two-band Hubbard model in the limit of infinite dimensions, using a combination of analytical methods and Monte-Carlo techniques. The normal state is found to display various metal to insulators transitions as a function of doping and interaction strength. We derive self-consistent equations for the local Green's functions in the presence of superconducting long-range order, and extend previous algorithms to this case. We present direct numerical evidence that in a specific range of parameter space, the normal state is unstable against a superconducting state characterized by a strongly frequency dependent order-parameter.Comment: 12 pages (14 figures not included, available upon request), Latex, LPTENS Preprint 93/1

Differences Between Hole and Electron Doping of a Two-Leg CuO Ladder

Here we report results of a density-matrix-renormalization-group (DMRG) calculation of the charge, spin, and pairing properties of a two-leg CuO Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms are included along with near-neighbor and oxygen-hopping matrix elements. This system allows us to study the effects of hole and electron doping on a system which is a charge transfer insulator at a filling of one hole per Cu and exhibits power law, d-wave-like pairing correlations when doped. In particular, we focus on the differences between doping with holes or electrons.Comment: REVTEX 4, 10 pages, 13 figure