The Devil Dogs

Non-fiction by William W. Haydock

Local density of states of a d-wave superconductor with inhomogeneous antiferromagnetic correlations

The tunneling spectrum of an inhomogeneously doped extended Hubbard model is calculated at the mean field level. Self-consistent solutions admit both superconducting and antiferromagnetic order, which coexist inhomogeneously because of spatial randomness in the doping. The calculations find that, as a function of doping, there is a continuous cross over from a disordered ``pinned smectic'' state to a relatively homogeneous d-wave state with pockets of antiferromagnetic order. The density of states has a robust d-wave gap, and increasing antiferromagnetic correlations lead to a suppression of the coherence peaks. The spectra of isolated nanoscale antiferromagnetic domains are studied in detail, and are found to be very different from those of macroscopic antiferromagnets. Although no single set of model parameters reproduces all details of the experimental spectrum in BSCCO, many features, notably the collapse of the coherence peaks and the occurence of a low-energy shoulder in the local spectrum, occur naturally in these calculations.Comment: 9 pages, 5 figure

Assessment of the GW Approximation using Hubbard Chains

We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. GW and exchange-only calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable

Method of studying the Bogoliubov-de Gennes equations for the superconducting vortex lattice state

In this paper, we present a method to construct the eigenspace of the normal-state electrons moving in a 2D square lattice in presence of a perpendicular uniform magnetic field which imposes (quasi)-periodic boundary conditions for the wave functions in the magnetic unit cell. An exact unitary transformations are put forward to correlate the discrete eigenvectors of the 2D electrons with those of the Harper's equation. The cyclic-tridiagonal matrix associated with the Harper's equation is then tridiagonalized by another unitary transformation. The obtained eigenbasis is utilized to expand the Bogoliubov-de Gennes equations for the superconducting vortex lattice state, which showing the merit of our method in studying the large-sized system. To test our method, we have applied our results to study the vortex lattice state of an s-wave superconductor.Comment: 8 pages; 3 figure

Analytical calculation of the Green's function and Drude weight for a correlated fermion-boson system

In classical Drude theory the conductivity is determined by the mass of the propagating particles and the mean free path between two scattering events. For a quantum particle this simple picture of diffusive transport loses relevance if strong correlations dominate the particle motion. We study a situation where the propagation of a fermionic particle is possible only through creation and annihilation of local bosonic excitations. This correlated quantum transport process is outside the Drude picture, since one cannot distinguish between free propagation and intermittent scattering. The characterization of transport is possible using the Drude weight obtained from the f-sum rule, although its interpretation in terms of free mass and mean free path breaks down. For the situation studied we calculate the Green's function and Drude weight using a Green's functions expansion technique, and discuss their physical meaning.Comment: final version, minor correction

Homogenization of Maxwell's equations in periodic composites

We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a computationally-efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically-measurable quantities rather than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some color figures in this preprint may be easier to read because here we utilize solid color lines, which are indistinguishable in black-and-white printin

Analytic Trajectories for Mobility Edges in the Anderson Model

A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent site-energies, and so take definite values rather than distributions of values. The transformed Hamiltonian is ordered, and may be interpreted as an itinerant electron interacting with a spin on each site. In this new basis, the distinction between extended and localized states is clear, and edges of the bands of extended states, the mobility edges, are calculated as a function of disorder. In two dimensions these edges have been found in both analytic and numerical applications of tridiagonalization, but they have not been found in analytic approaches based on perturbation theory, or the single-parameter scaling hypothesis; nor have they been detected in numerical approaches based on scaling or critical distributions of level spacing. In both two and three dimensions the mobility edges in this work are found to separate with increasing disorder for all disorders, in contrast with the results of calculation using numerical scaling for three dimensions. The analytic trajectories are compared with recent results of numerical tridiagonalization on samples of over 10^9 sites. This representation of the Anderson model as an ordered interacting system implies that in addition to transitions at mobility edges, the Anderson model contains weaker transitions characterized by critical disorders where the band of extended states decouples from individual sites; and that singularities in the distribution of site energies, rather than its second moment, determine localization properties of the Anderson model.Comment: 32 pages, 2 figure

Krylov Subspace Method for Molecular Dynamics Simulation based on Large-Scale Electronic Structure Theory

For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the essential character of the Hamiltonian within a limited number of basis set. Its validation is confirmed by the convergence property of the density matrix within the subspace. The following quantities are calculated; energy, force, density of states, and energy spectrum. Molecular dynamics simulation of Si(001) surface reconstruction is examined as an example, and the results reproduce the mechanism of asymmetric surface dimer.Comment: 7 pages, 3 figures; corrected typos; to be published in Journal of the Phys. Soc. of Japa

Site dilution of quantum spins in the honeycomb lattice

We discuss the effect of site dilution on both the magnetization and the density of states of quantum spins in the honeycomb lattice, described by the antiferromagnetic Heisenberg spin-S model. For this purpose a real-space Bogoliubov-Valatin transformation is used. In this work we show that for the S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin S=1/2, however, the linear spin wave approximation breaks down. In this case, we have studied the effect of dilution on the staggered magnetization using the Stochastic Series Expansion Monte Carlo method. Two main results are to be stressed from the Monte Carlo method: (i) a better value for the staggered magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the staggered magnetization of the percolating cluster at the classical percolation threshold, showing that there is no quantum critical transition driven by dilution in the Heisenberg model. In the solution of the problem using linear the spin wave method we pay special attention to the presence of zero energy modes. Using a combination of linear spin wave analysis and the recursion method we were able to obtain the thermodynamic limit behavior of the density of states for both the square and the honeycomb lattices. We have used both the staggered magnetization and the density of states to analyze neutron scattering experiments and Neel temperature measurements on quasi-two- -dimensional honeycomb systems. Our results are in quantitative agreement with experimental results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.Comment: 21 pages (REVTEX), 16 figure

Magnetic anisotropy of vicinal (001) fcc Co films: role of crystal splitting and structure relaxation in step-decoration effect

The uniaxial in-plane magnetic anisotropy (UIP-MA) constant is calculated for a single step on the (001) surface of fcc Co($N$) films. The calculations are done for both an undecorated step and the step decorated with one or more, up to 7, Cu wires. Our objective is to explain the mechanisms by which the decoration decreases the UIP-MA constant, which is the effect observed experimentally for ultrathin Co films deposited on vicinal (001) Cu surfaces and can lead to reorientation of magnetization within the film plane. Theoretical calculations performed with a realistic tight-binding model show that the step decoration changes the UIP-MA constant significantly only if the splitting between the on-site energies of various $d$-orbitals is included for atoms located near the step edge. The local relaxation of atomic structure around the step is also shown to have a significant effect on the shift of the UIP-MA constant. The influence of these two relevant factors is analyzed further by examining individual contributions to the UIP-MA constant from atoms around the step. The magnitude of the obtained UIP-MA shift agrees well with experimental data. It is also found that an additional shift due to possible charge transfer between Cu and Co atoms is very small.Comment: 12 pages,9 figures, RevTeX, submitted to Physical Review B version 3: additions to content version 2: minor correction