London Approximation Research Articles

Ring Currents in Icosahedral C 60

A new formulation of the current within the London approximation allows the calculation of ring currents in topologically complex molecules. Application of this theory to C(60) demonstrates the existence of remarkable pi electron ring currents. Paramagnetic currents, in size comparable to the ones in benzene, flow within the pentagons, whereas weaker diamagnetic currents flow all around the C.(60) molecule. The overall vanishing ring-current magnetic susceptibility results from a cancellation of diamagnetic and paramagnetic contributions. The presence of ring currents significantly affects chemical shifts as measured in nuclear magnetic resonance experiments. In contrast to the magnetic susceptibility, which is a property of the molecule as a whole, chemical shifts are sensitive to the local magnetic field and the effect of ring currents does not vanish.

Flux-line lattice in uniaxial superconductors at low magnetic inductions.

Within the London approximation, we predict the geometry of the flux lattice in anisotropic, strongly type-II superconductors for arbitrary field orientation and intensity. At low magnetic fields, the scaling of the lattice parameters with field differs markedly from the ordinary ${\mathit{B}}^{\mathrm{\ensuremath{-}}1/2}$ dependence. We also calculate the form factors and reflectivities for neutron diffraction. The dependence of the reflectivity on the angle between the magnetic field and the c axis, and on the field intensity, is calculated.

Interacting loop-current model of superconducting networks

We review our recent approximation scheme to calculate the normal-superconducting phase boundary, T c(H), of a superconducting wire network in a magnetic field in terms of interacting loop currents. The theory is based on the London approximation of the linearized Ginzburg-Landau equation. An approximate general formula is derived for any two-dimensional space-filling lattice comprising tiles of two shapes. We provide many examples illustrating the use of this method with a particular emphasis on the fluxoid distribution. In addition to periodic lattices, we also discuss quasiperiodic lattices and fractal Sierpinski gaskets.

Squeezed vortex in a layered structure of type-II superconductors

London approximation is used to solve the problem of magnetic vortex destroying order parameter in a superconducting layer of arbitrary thickness embedded between bulk superconducting screens. Like the well-known 2D-vortices in layered superconductors, the vortices under consideration interact logarithmically at large distances and carry magnetic flux θ< θ 0, the unit flux quantum. The stability of long vortices in a layered superconductor is discussed with respect to the decay of shorter vortices.

Numerical study of two-dimensional flux-line lattice structures in the London approximation.

Within the London approximation, we present the basic equations for the numerical determination of flux-line lattices in inhomogeneous materials. After describing the general formalism and the numerical techniques used, we illustrate our method by presenting results for simple inhomogeneous systems. These systems include models for grain and twin boundaries. For the twin-boundary model, we find that a higher density of vortices exists in the interface region than in the host material. This result agrees with experimental observation.

The vortex's supercurrent density in uniaxial superconductors

We study the supercurrent density component along the vortex line for uniaxial superconductors in the London approximation and determine where it vanishes for the case of a tilted magnetic induction.

Surface effects in vortex patterns of uniaxial superconductors

We generalize E.H. Brandt's study of an interface superconductor-vacuum in the London approximation for the case of mass anisotropy orthogonal to the surface. We find the long-range surface interaction between two line segments orthogonal to the surface, ( Φ 2 0 8π 2λ 2 1ϱ )[1-exp( −ϱ λ 1 )] , where λ 1 is London's penetration along the surface.

The supercurrent streamlines of the single vortex in uniaxial superconductors

Vortices in uniaxial superconductors can attract each other if they are tilted with respect to the principal crystal's directions according to Grishin et al. and Kogan et al. Here we interpret such special property in terms of the family of supercurrent streamlines surrounding the isolated tilted vortex. Several numerical and analytical results determining the orientation of the supercurrent with respect to the principal crystal's directions are presented in the framework of the London approximation.

Fast convergent free energy expansion for uniaxial superconductors in the London approximation

A fast convergent expansion for the free energy of uniaxial superconductors in the London approximation is obtained here. The free energy formula is invariant under different choices of unit cell describing the same physical vortex lattice. To illustrate the method some numerical calculations are done in the case of one vortex per unit cell. In the limit of high values of the magnetic induction the resulting vortex pattern approaches the distorted triangular lattice of Campbell, Doria and Kogan. The author find that for low enough values of the magnetic induction, any two vortices located in adjacent chains are highly uncorrelated. Numerical evidence shows the existence of a rectangular lattice configuration that extremizes the free energy for any orientation of the magnetic induction.

Numerical computation of the flux-line-lattice structure of an inhomogeneous material in the London approximation.

We present the basic equations that permit the efficient simulation of vortex structures in inhomogeneous materials whose superconducting behavior is described by the London equations. In analogy to homogeneous materials, we show that the energy of such structures is the sum of a self-interaction part, which depends on the local variation of the penetration depth, and a sum of pair interactions, which are the Green's functions of the London equation for an inhomogeneous material. This formalism permits simulations in which the exact, long-range London interactions between flux lines are used. In addition, the realistic modeling of defects by allowing the penetration depth to vary spatially is possible, and pinning, instead of being assumed, arises in a natural manner by local variations in Lorentz forces. The equations were solved for a variety of one-dimensional models of inhomogeneities, and physically reasonable flux-line lattices were found. A suggestion for the use of the formalism to study the dynamic properties of flux-line lattices is made.

Phase boundary of superconducting networks: A new approximation scheme.

We calculate the normal-superconducting phase boundary of a superconducting wire network in arbitrary magnetic fields using the London approximation of the linearized Ginzburg-Landau equation. Our formulation in terms of the constituent loop currents allows an iteration procedure to calculate the energy of a network, which in turn determines the mean-field transition temperature ${\mathit{T}}_{\mathit{c}}$(H). For infinite lattices, finite-order truncation in this scheme produces good agreement with other calculations and experiments.

A Theoretical study of 13C NMR chemical shifts in a series of rigid bicyclo[ m.n.o.] alkanes

The INDO-FPT calculated 13C NMR shielding constants, using GIAO's and at the London approximation, were analysed in a series of rigid bicyclo[ m.n.o.] alkanes ( m = 2, 3, 4; n = 2, 3; o = 1, 2), and adamantane. The trends in the experimental 13C chemical shifts values in this series of compounds are reasonably reproduced, and improved upon by the correction of the < r −3> integrals with the use of Mulliken populations. The discrepancy observed between the experimental and calculated 13C chemical shifts of the C(2) carbon atoms in bicyclo[2.2.1]heptane and bicyclo[3.2.1]octane, and the C(7) carbon atom in bicyclo[4.2.1]nonane, can be explained on the basis of a changed charge distribution resulting from nonbonded interactions in these highly strained five-membered rings, which, in turn, affect the one-center paramagnetic contribution to the shielding constant. The problem can be circumvented for C(2) in bicyclo[2.2.1]heptane and bicyclo[3.2.1]octane by regarding a more rigorous method for calculating charge distributions within molecules than the Mulliken population analysis.

Magnetic moments of neutron stars composed of a real baryon gas

A study is made in the London approximation of the thermodynamics of a rotating superfluid solution in the npe phase of a spherical neutron star composed of a real baryon gas. The drag of the superfluid protons by the rotating superfluid neutrons leads to the formation of a system of rectilinear neutron vortices parallel to the rotation axis. The inhomogeneous magnetic field /sup mm/ H(r) produced by this system leads when H > H /sub c1/ to the appearance of a nonuniform vortex lattice of unentrained protons with fluxes /phi//sub 0/. It is shown that the magnetic field of this lattice has a dipole nature. Integrated characteristics of the neutron star - the mass, radius, and total magnetic moment - are obtained as functions of the central density /rho//sub 0/. The magnetic moment of the star varies from 2 . 10/sup 27/ G . cm/sup 3/ to 10/sup 30/ G . cm/sup 3/. The conditions of occurrence of neutron and proton vortex filaments are considered with allowance for the spherical geometry of the star.

Nuclear magnetic shielding calculations in the finite perturbation method involving GIAO's at the INDO level and London's approximation. II. Carbon-13 and nitrogen-15

Magnetic shielding constants, calculated for C-13 and N-15 nuclei in the finite perturbation method using INDO and London's approximations, are analyzed in terms of mono-, di-, and tricentric contributions, thus permitting an assessment of the relative importance of local vs. nonlocal contributions. For both C-13 and N-15, it appears that the changes in total shielding are almost entirely dictated by those of the local paramagnetic contribution, i.e., [Formula: see text].

Integrals Irs and Jrs used in the computation of magnetic quantities by means of the McWeeny coupled perturbation method

AbstractWe have shown that integrals Irs and Jrs which occur in coupled Hartree–Fock perturbation, on a basis of gauge invariant atomic orbitals with the London approximation and neglect differential overlap, can be reduced, by appropriate transformations, to the overlap integral type. The computational program of Srs, Irs, and Jrs integrals is elaborated for Slater‐type atomic orbitals. The process proposed presents a double advantage: it is extended over the entire Periodical Table and does not use the analytical formulas of Mulliken.

π-Electron ring currents and magnetic properties of porphyrin molecules in the MO LCAO SCF method

The coupled variant of double-parameter perturbation theory in the MO LCAO SCF method in the London approximation has been used for the calculation of π-electron current distributions in the molecules of porphin and its derivatives. The chemical shifts of1H-NMR have been computed on the basis of calculations of ring currents and charge distributions. It is shown that π-electron ring currents are responsible for the dominant contribution to the shielding of protons. The theoretical and experimental values of proton chemical shifts are in a good agreement. Chemical shifts of the13C and15N nuclei have also been estimated. Two aromaticity scales are proposed for the compounds under study based on the calculations of the π-electron contribution to the diamagnetic susceptibility and of π-electron currents, respectively.

London approach to anisotropic type-II superconductors

The London equations with a phenomenlogical mass tensor are used to analyze the vortex structure near the lower critical field. The anisotropy results in a transverse magnetic field in the Abrikosov vortex. This field attenuates exponentially at large distances from the vortex axis. The strongly anisotropic attenuation length is evaluated. The line energy is found in the London approximation.

CNDO calculation of the diamagnetic susceptibilities of cyclic conjugated molecules

AbstractWe present the results obtained within the CNDO/2 method for the diamagnetic susceptibilities of a series of conjugated molecules including benzene, fulvene, pyridine, pyrrole, and furan. The calculations have been carried out, according to Bley's method, in the framework of coupled Hartree–Fock perturbation theory, using gauge invariant atomic orbitals and the London approximation. The two usual CNDO parametrizations, due respectively to Pople, Santry, and Segal and to Del Bene and Jaffe, did not enable one to obtain the principal susceptibilities of the molecules under consideration. We investigated the effect of the CNDO parametrizations on the different contributions to the susceptibility, and gave a first improvement to Bley's method, which permits the calculation of the mean susceptibility of conjugated molecules with less than 9% error.

The london approximation and the calculation of dispersion interactions as a sum of atom-atom terms

A London approximation utilizing atomic valence state ionization potentials and static polarizabilities yields C6 results in good agreement with accurate values for a number of systems. Generally there is considerable improvement over the results obtained using the London approximation in conjunction with molecular parameters and reasons for this are discussed.

Improved formalism for Abelian magnetic monopoles

Euclidean lattice methods are used to derive an improved version of the Schwinger-Zwanziger Lagrangian for magnetic monopoles. The formalism involves a nondynamical string variable ${x}_{\ensuremath{\mu}}(\ensuremath{\sigma},\ensuremath{\tau})$. When the monopoles are coupled to a charged scalar field, ${x}_{\ensuremath{\mu}}$ can be utilized to absorb the dynamics of discontinuities in the angular part of the scalar field. In the Higgs phase where such discontinuities have finite action, ${x}_{\ensuremath{\mu}}$ becomes a dynamical variable and the Lagrangian becomes manifestly covariant. We derive the heuristic string-monopole equations of Nambu as the classical limit of the Higgs model in the London approximation.