James F. Annett

Symmetry of the order parameter for high-temperature superconductivity

Abstract Whatever its microscopic origins, it seems likely that the superconductivity in the copper-oxides can be described by an appropriate Ginzburg-Landau theory. The possible order parameters and free energies are then determined by the symmetry breaking of the phase transition alone. The group-theoretically allowed states are enumerated here for singlet and triplet superconductors in orthorhombic and tetragonal crystals. As well as broken gauge, time reversal and rotational symmetries, broken translational symmetry states are also investigated. Experiments that might distinguish the various possible states are reviewed, concentrating especially on experiments where the outcomes are determined by the symmetry properties of the order parameter alone. These include Josephson effects, transition splitting, spontaneous strain and magnetism, critical and Gaussian fluctuations, collective modes and vortices. Current experimental results on the high-Tc materials are discussed where relevant, although in many...

Alkali-metal-plated graphite surfaces: He interaction and diffraction

Abstract Theoretical calculations and experimental data are reported for He scattering from a graphite surface covered with an alkali-metal overlayer. The computed interaction potential has a very shallow well depth (⩽, 1 meV) in the case of a (2 × 2) layer. The predicted corrugation is also very small, corresponding to rather weak elastic diffraction beams. The calculated diffraction intensity is less than 2 percent of the specular intensity for a 17.4 meV He beam. No He diffraction was observed in the experiment on K, Rb, and Cs overlayers, indicating that these surfaces are even less corrugated than the calculation predicts.

The superconducting state of YBa2Cu3O7−δ

Many low temperature properties of high Tc superconductors deviate significantly from the detailed predictions of BCS theory. Here we discuss whether these effects could be caused by either: (a) an unconventional pairing state, or (b) local randomness in the gap function due to the intrinsic disorder. We review recent experiments pertinent to these questions: Josephson effects in (001) oriented planar junctions between YBa2Cu3O7-δ and classic superconductors and the temperature dependence of the a-b plane electro-magnetic penetration depth at low temperatures. We also calculate the density of states of s-wave superconductors with local quenched disorder in the gap function so as to determine whether s-wave pairing could be consistent with the low energy quasiparticle excitations seen in many experiments.

Efficiency of algorithms for Kohn-Sham density functional theory

Abstract Recent developments in numerical methods for computing Kohn-Sham electronic structure have substantially increased the sizes of systems which can be studied. In addition to fast Car-Parinello and conjugate gradient algorithms, there have been several innovative proposals aimed at achieving order N scaling in computer time, where N is the number of atoms in the cell. These developments demand a better understanding of the convergence properties of different numerical approaches to Kohn-Sham density functional calculations. In particular the non-linearities of the Kohn-Sham equations lead to non-trivial dependence of convergence times on the system size. The number of iterations required to converge the self-consistent Kohn-Sham equations is shown to grow like N 2 3 for insulators and like N for metals. If each iteration can be carried out in order N time, the total computational effort to solve a given system will thus scale like N 5 3 or N2 for insulators or metals respectively. A similar analysis of conjugate gradient minimization methods shows that, in the worst case, of order O(N 1 3 ) energy and gradient evaluations are needed to converge the energy. Only in insulating systems which are “Wannier representable” (WR) is the number of iterations of O(1), allowing true order N calculations. A different approach, based upon conjugate gradient minimization with respect to variations in the single particle potential rather than the wave functions, is also found to scale like N 1 3 for insulators and scales as N for metals. Slower scaling with N will also be found in systems in which one dimension of the unit cell is much longer than the others, or for metals where the Fermi energy lies close to a van Hove singularity. These results are quite independent of calculational details, such as choice of basis set, but simply follow from the scaling with N of the relevant Jacobian or Hessian matrices.

Zero-point vibrational energy of an adsorbed film

The ground-state energy of a submonolayer4He film is studied, taking into account vibration perpendicular to the surface. We use an adiabatic approximation that evaluates thez motion with the surface-parallel coordinatesx, y of the atoms held fixed. The coupled atoms dynamical equations are solved using various assumptions, all of which yield a similar result. The numerical results for the zero point energy indicate that4He does not form a 2D liquid at zero temperature on K, Rb, or Cs surfaces; instead it is a quantum gas.

Effective single band Hamiltonian for electron-phonon coupling in cuprate superconductors

We derive an effective single-band Hubbard type Hamiltonian for CuO2 planes. The Hamiltonian includes both electron-electron repulsion and electron-phonon coupling to oxygen vibrational modes. We start with first-principles density functional theory parameters and then map onto a single-band model. Unlike previous mappings to a single-band Hamiltonian, ours explicitly preserves the Fermi surface shape and matrix elements of the many-band Hamiltonian. We consider both in-plane oxygen breathing modes as well as out-of-plane tilting modes. The latter modes have a quadratic electron-phonon coupling, and are also highly anharmonic in La2CuO4 based superconductors. The coupling to breathing modes is too small to account for highTc, while the coupling to quadratic modes is much stronger even though they would be neglected in a standard Migdal-Eliashberg approach to superconductivity.

Valence density functionals

Since the inception of Density Functional Theory (DFT) the remarkable success of the Local Density Approximation (LDA) has been difficult to improve in a systematic way. Originally Hohenberg, Kohn and Sham introduced LDA as the first term in a gradient expansion of the exchange-correlation energy functional[1]. It success in a wide variety of systems, such as atoms molecules and solids[2, 3], was somewhat surprising, since the density gradients are not small. The accuracy of LDA was attributed to the sum rules which it satisfies[4] and to the range of validity of the small gradient approximation being larger than expected[5, 6]. Well defined gradient expansions[7] were carried out, however the most accurate numerical results for real systems require either a semi-empirical approach[8] or a detailed model for the exchange-correlation hole[9]. A large number of exact constraints have also been placed upon the possible functionals which are beginning to lead to more systematic improvements[10].

Unconventional pairing in YBa2Cu3O7-d?☆

Abstract We review a variety of experimental data capable of indicating the pairing state of YBa2Cu3O7-δ. Using the results of a group theoretic analysis we summarise the possible interpretations of these data, and concluded that, at present, there is no firm evidence that the pairing is conventional.

What is the essential many-body Hamiltonian for copper-oxide superconductors?

Abstract We discuss how the many-body Hamiltonian derived from constrained density functional calculations can be reduced to simpler two or three band effective Hamiltonians, and we give realistic parameters. The reduction to fewer bands leads to longer ranged hopping terms.