M. Frick

On the theory of layered high-temperature superconductors

Assuming that charge carriers form a Fermi liquid state, we study a model for layered high-temperature superconductors with unretarded intralayer and interlayer pairing. Guided by band structure calculations and inverse photoemission experiments, we adopt a tight binding band with nearest and next-nearest neighbors hopping within the sheets and weak interlayer hopping. The gap equations are solved numerically, without imposing a cutoff energy, characteristic to phonon mediated superconductivity. On this basis we calculate the gap parameters,Tc, the tunneling conductance, infrared absorption and the coherence length for various band fillings ρ=1/2−x by introducing excess holes of concentrationx. Assuming the interlayer coupling strength to be smaller than the intralayer one, our main results are as follows:Tc is dominated by the intralayer properties, reaching a maximum atx≈0.3, where strong coupling features appear. In the presence of interlayer pairing, the gap becomes anisotropic perpendicular to the layers, and standard BCS-behavior is modified. In particular the BCS-square root singularity in the density of states and in the tunneling conductance is replaced by van Hove singularities characterizing the anisotropic gap. In particular, we investigate the anisotropy of the tunneling conductance for specular and diffuse tunneling for a junction parallel or perpendicular to the layers, infrared absorption, as well as the coherence length, parallel and perpendicular to the layers.

High-temperature superconductivity in the apex-oxygen model: a quantum Monte Carlo study

The Projector Quantum Monte Carlo Method is applied to examine the existence of superconductivity in the Apex-Oxygen-Model which describes the physics of the correlated carriers in the CuO2-planes coupled to the anharmonic vibrations of the apex oxygen in the hightemperature superconductors. The simulations show clear evidence for extendeds-wave superconductivity in the 100 K temperature range for realistic choice of coupling parameters.

On the theory of layered high-temperature superconductors: Finite temperature properties

We extend the study of a model for layered high-temperature superconductors to finite temperatures. The model assumes Fermi liquid properties for the carriers, which form a narrow tight-binding band. The carriers are subject to on-site intralayer and nearest neighbor interlayer interactions. The previous studies of the zero temperature properties, revealing remarkable agreement with experimental data, are extended to finite temperatures. These properties include the tunneling conductance for diffuse and specular transmission in a normal isolator superconductor junction, specific heat, nuclear spin relaxation time and the London penetration depth. Our results are compared with experimental findings.

Local anharmonic vibrations strong correlations and superconductivity : a quantum simulation study

We investigate the importance of local anharmonic vibrations of the bridging oxygen in the copper oxide high-Tc materials in the context of superconductivity. For the numerical simulation we employ the projector quantum Monte Carlo method to study the ground state properties of the coupled electron-phonon system. The quantum Monte Carlo simulation allows an accurate treatment of electronic interactions which investigates the influence of strong correlations on superconductivity mediated by additional quantum degrees of freedom. As a generic model for such a system, we study the two-dimensional single band Hubbard model coupled to local pseudo spins (bridging oxygen), which mediate an effective attractive electron-electron interaction leading to superconductivity. The results are compared to those of an effective negativeU model.

QUANTUM SIZE EFFECTS IN THE ATTRACTIVE HUBBARD-MODEL

We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data.

A model for layered high-temperature superconductors with two CuO2 layers per unit cell

We extend a model for layered high-temperature superconductors to systems with two CuO2 layers per unit cell and two interlayer spacings with different physical properties. The carriers are assumed to occupy Fermi liquid states, forming narrow tight-binding bands. The layers are coupled by weak interlayer-hopping matrix elements between adjacent sheets, as well as by an attractive interaction between carriers in neighboring layers in addition to an on-site intralayer coupling. We solve the Gorkov equations for this model to obtain the critical temperature and the density of states of the oneparticle excitations from the superconducting condensate, and discuss various parameter regimes concerning the coupling between the two layers. We compare our results with current experimental findings for high-temperature superconductors. The presence of two CuO2 layers leads to multi-peak features in the superconducting density of states, as has been observed in recent tunneling measurements.

ANHARMONIC PHONONS AND STRONG ELECTRONIC CORRELATIONS IN HIGH-TC SUPERCONDUCTORS - A QUANTUM MONTE-CARLO STUDY

We present results of quantum simulations for a system of strongly correlated fermions coupled to anharmonic phonons. The projector Quantum Monte Carlo (PQMC) method has been employed to study ground state properties. In a parameter regime relevant for the high-Tc superconductors, the system exhibits superconductivity, characterized by off-Diagonal Long Range Order (ODLRO). Several features of the high-Tc materials can be understood.

Quantum Monte Carlo Simulations for High-Tc Models

Abstract Numerical simulations were carried out using a projector quantum Monte Carlo method pioneered by Sorella et al. Ground state energies are presented for the single band Hubbard model for system sizes 4 x 4 to 8 x 8. The Hubbard model coupled to a two-level system (e.g. bridging oxygen) was also studied. Enhancement of superconducting susceptibilities indicates the possibility of high-Tc superconductivity.

OFF-DIAGONAL LONG RANGE ORDER IN AN ELECTRON-PHONON MODEL FOR HIGH-Tc SUPERCONDUCTORS

We study a model for high-Tc superconductors describing both the strong electronic correlations and a coupling of the carriers to anharmonic phonons. The Projector Quantum Monte Carlo Scheme has been employed to investigate ground state properties. We analyze the superconducting properties of the model by directly addressing to the existence of Off-Diagonal Long Range Order (ODLRO). We review the numerical algorithm and discuss the possibility to observe ODLRO. In the presented model, we find ODLRO pointing towards superconductivity instead of the presence of strong electronic correlations. We discuss several features of the superconducting condensate.