London Approximation Research Articles

Kondo tunneling through a biased double quantum dot

Electron tunneling through a system formed by two coupled quantum dots in a parallel geometry is considered within a generalized Anderson model. The dots are assumed to have nearly equal radii but different (and tunable) gate voltages. In the absence of tunneling to and from the leads, the isolated two-dot system (with two electrons in it) resembles an hydrogen molecule within the Heitler London approximation. In particular, it has a singlet ground state and low-lying excited triplet state. When tunneling is switched on, and when the gate voltages are properly tuned the ground state becomes a triplet and singlet and triplet states are intermixed. In the region, where charge fluctuations are suppressed, the pertinent antiferromagnetic exchange interaction has the form (J T S +J ST P )· s . It is written in terms of the electron spin s, the double dot spin 1 operator S and an additional vector operator P. The operators S and P generate the algebra o 4 of a spin rotator. The related Kondo effect is similar to that of a vertical quantum dot, discussed and analyzed recently.

Screw-dislocation-induced plasticization of a pinned vortex lattice

The energy of vortex-lattice screw dislocations is computed numerically on the basis of the isotropic London approximation. The results of computation are applied to the collective-pinning theory proposed by Larkin and Ovchinnikov. The present modified pinning model predicts that a vortex lattice is stabilized by possessing many screw dislocations for sufficiently strong pinning. Then the spacing between slip planes nearly equals the vortex-lattice constant, where the Burgers vectors of two adjacent slip planes are in the opposite direction. Penetration of the screw dislocations induces sudden vortex-lattice plasticization, which can be observed as a discontinuous jump of the critical current. This prediction is compared with the critical-current abrupt rises observed in amorphous ${\mathrm{Nb}}_{x}\mathrm{Ge}$ films and in neutron-irradiated ${\mathrm{V}}_{3}\mathrm{Si}$ bulks.

13C NMR chemical shift of single-wall carbon nanotubes.

We compute the magnetic shielding tensor within the London approximation and estimate the Knight shift of single-wall carbon nanotubes. Our results indicate that high resolution 13C NMR should be able to separate the metallic and insulator character of the nanotubes since a 11 ppm splitting is predicted from the respective resonances. As a model for disorder, bending, and defects in these structures, we investigate the magnetic response of nanotubes with finite size. We get a small line broadening coming from an intrinsic length dependent resonance effect. The nanotube packing is also studied and leads to a 20 ppm broadening which disappears under experimental high-resolution conditions.

Equilibrium magnetic characteristics of high-Tc superconductors with allowance for the spatial distribution of the order parameter in the vortex cores. II. Vibrational contribution to the dynamic magnetic permeability

The vibrational contribution μv(H) to the dynamic magnetic permeability μac′ is calculated with allowance for the spatial variation of the order parameter in the magnetic field region H≪Hc2, where the properties of type-II superconductors are usually described in the London approximation. The features of the behavior of the analytical relations μv(H) are analyzed for the case when the vortices execute small oscillations about their equilibrium positions corresponding to the thermodynamic-equilibrium vortex lattice. It is shown that taking into account the suppression of the order parameter in the vortex cores leads to substantial differences in the behavior of μv(H) in comparison with the analogous dependence obtained in the London approximation. It is found that the main factor responsible for these differences is a change in shape of the effective potential well in which the vibrational motion of the subsurface vortices takes place.

Dipolar interactions in superconductor-ferromagnet heterostructures

We consider a simple model for a superlattice composed of a thin magnetic film placed between two bulk superconductors. The magnetic film is modelled by a planar but otherwise arbitrary distribution of magnetic dipoles and the superconductors are treated in the London approximation. Due to the linearity of the problem, we are able to compute the magnetic energy of the film in the presence of the superconductors. We show that in the case of small wavenumbers compared to the inverse London penetration depth, the magnetic energy resembles the energy of a distribution of magnetisation in a two dimensional space. Possible experimental applications of these results are discussed.

Interaction between a vortex and a columnar defect in the London approximation

We calculate the interaction between a vortex and an insulating cylindrical cavity in a type-II superconductor using the London approximation, thus extending the result in an earlier work by Mkrtchyan and Shmidt (Zh. \'Eksp. Teor. Fiz. 61, 367 (1971) [Sov. Phys. JETP 34, 195 (1972)]) to an arbitrarily large cavity radius. In the limit of an infinitely large radius our result reduces to the well-known Bean-Livingston formula for the interaction between a vortex and an insulating wall.

Vortex-line-lattices in anisotropic superconductors in an applied field

We consider a uniaxial anisotropic superconductor placed in an external magnetic field of magnitude H and arbitrary orientation and determine the vortex-line-lattices (VLL) that minimize the Gibbs free energy in the London approximation. To do this, we develop a numerical method based on simulated annealing that assumes only straight vortex-lines and VLL with only one vortex-line per unit cell. We pally the method to low fields to estimate the lower critical field H c1 for each direction of H and the VLL shape as a function of H.

Vortex patterns in mesoscopic superconducting ellipses and strips

Vortex patterns inside a superconducting elliptic sample are considered. In the London approximation, the energy of a given configuration is calculated analytically by the method of Fourier series, in terms of the positions of the vortices. These positions are determined by numerical minimization of the energy, for given applied field and shape of the ellipse. Vortices appear to arrange themselves in particuliar classes of geometrical structures and the magnetic fields responsible for the transitions, from one geometry to the other, are found to be roughly independent of the shape of the ellipse. For a superconducting strip, we find vortex-line transitions which are clearly seen in the magnetization curves. A paramagnetic effect is observed in the case of small samples.

Magnetization of type-ii superconductors in the range of fields H c 1 ≤ H ≤ H c 2Variational Method

A variational method is proposed to find the magnetic field dependence of the magnetization of type-II superconductors in the mixed state by a self-consistent technique. This model allows for suppression of the order parameter to zero at the centers of Abrikosov vortices and also for the magnetic field dependence of the order parameter. The results can be applied to the entire range of fields H c 1 ≤ H ≤ H c 2 for any values of the Ginzburg-Landau parameter $$\kappa > 1/\sqrt 2$$ . It is shown that in weak fields where κ ≫ 1 the behavior of the magnetization can be described exactly in the London approximation provided that the correct value of H c 1 is used. Near the second critical field this dependence shows good agreement with the well-known Abrikosov result. It is also shown that using the concept of isolated vortices and applying the principle of superposition of the fields and currents generated by these vortices to calculate the magnetization gives inaccurate quantitative results even in fairly weak fields. By going beyond these concepts, it was possible to allow more accurately for the influence of the vortex cores on the magnetization behavior in the intermediate range of fields H c 1 ≪H ≪ H c 2 and to identify the range of validity of various approximations used widely in the literature.

Frenkel excitons beyond the Heitler–London approximation

We consider Frenkel excitons in molecular crystals beyond the Heitler–London approximation (HLA). Beyond the HLA the wave function of the molecular crystal with one exciton contains states with several excited molecules. In this case the statistics of the molecular excitations becomes important. Thus, the boson approximation, frequently used to go beyond the HLA, needs to be corrected. We calculate the corrections to the HLA for Frenkel exciton energy and oscillator strength taking into account the exact statistics of molecular excitations. In these calculations we consider the crystals of general structure and beyond the two-level model, thus taking into account also the mixing of molecular configurations. For the model of a one-dimensional chain of two-level molecules and in the nearest-neighbor approximation our results coincide with the results found earlier by Bakalis and Knoester who used the Jordan–Wigner transformation from paulions to fermions. We show that for multilevel molecules the crystal Hamiltonian contains additional terms that give important contributions to the corrections for the Frenkel exciton energy.

Transitions between different superconducting states in mesoscopic disks

Using a linear analysis, we studied the stability of giant-vortex states in very thin disks. The vortex expulsion and penetration fields are obtained for finite thickness disks from a numerical solution of the nonlinear Ginzburg–Landau (GL) equations. Using an extension of the London approximation, in which the phase distribution of the order parameter is prescribed and the superconducting electron density is found numerically, we consider the free energy behavior for transitions between different superconducting states.

NMR chemical shift of single-wall carbon nanotubes

AbstractWe report calculation of the NMR chemical shift anisotropy (CSA) tensor →μ of single-wall carbon nanotubes, within the London approximation (ring currents contribution). Our results indicate that the isotropic line as measured by high resoultion experiments is splited about 11ppm between metallic and semiconductor nanotubes. We carefully check that this result remains vaild and observable when the bundle packing is taken into account. The resulting broadening is aroune 20ppm, but reduces onto a sharp lorentzian (<1ppm) when averaging by high resoultion NMR measurements.

Numerical method for zero-temperature vortex-line phase diagrams

A numerical method to calculate equilibrium vortex-line configurations in bulk anisotropic type-II superconductors, at zero temperature, placed in an external magnetic field is introduced and applied to two physical problems. The method is designed to search for the minimum of the Gibbs free-energy in the London approximation and assumes only that the vortex lines are straight and arranged in a periodic lattice. Based on these assumptions a simulated annealing algorithm is developed to find the vortex-line-lattice unit cell shape, and vortex-line positions within it. This algorithm is made fast and accurate by the use of a rapidly converging series to calculate the lattice sums entering the vortex–vortex interaction energy. The method's accuracy is illustrated by calculating the magnetic induction versus applied field curve for an isotropic superconductor. The method is applied to a superconductor with a square lattice of columnar defects to study selected regions of the zero-temperature-phase diagram where vortex-line-lattices commensurate with the columnar defect lattice exist.

Effects of excited state mixing on transient absorption spectra in dimers: Application to photosynthetic light-harvesting complex II

The excited state mixing effect is taken into account considering the difference spectra of dimers. Both the degenerate (homo) dimer as well as the nondegenerate (hetero) dimer are considered. Due to the higher excited state mixing with the two-exciton states in the homodimer, the excited state absorption (or the difference spectrum) can be strongly affected in comparison with the results obtained in the Heitler–London approximation. The difference spectrum of the heterodimer is influenced by two resonance effects (i) mixing of the ground state optical transitions of both monomers in the dimer and (ii) mixing of the excited state absorption of the excited monomer with the ground state optical transition in the nonexcited monomer. These effects have been tested by simulating the difference absorption spectra of the light-harvesting complex of photosystem II (LHC II) experimentally obtained with the 60 fs excitation pulses at zero delay times and various excitation wavelengths. The pairs of coupled chlorophylls a and b for simulations have been taken from the best LHC II assignment model obtained by simulating the steady-state spectra and the transient absorption at various excitation wavelengths. Qualitatively the spectral peculiarities of the difference spectra are explained by means of the resonance interpigment interactions, which are responsible for the excited state mixing.

Expanding vortex rings in a current-carrying superconducting cylinder

Generation of Abrikosov vortex rings and half-rings by an external current in a type-II superconducting cylinder of arbitrary radius is considered. The energy barrier preventing nucleation of the vortices is calculated in the London approximation. Dependence of the barrier height on both the current density and the cylinder radius is studied. The critical current required for development of vortex instability in a pinning-free superconducting cylinder is found. It is shown that the average density of the critical current grows monotonically when the radius of the cylinder is decreased.

London Approximation with the Finite Core Size for the Mixed State of Type II Superconductor

The mixed state of type II superconductor was studied by means of the Wigner-Seitz approximation at κ ≫ 1 for the entire range of magnetic fields between Hc1 < H0 < Hc2. The vortex structure was described in the framework of the improved London model with finite core radius by the introduction of the order parameter in form of a constant function at ρ > ρm and a variational function at ρ < ρm, where ρm is the core radius. The dependencies of magnetic induction, core radius, vortex amplitude upon the external magnetic field at Hc1 < H < Hc2 were derived, the values of the first and the second critical fields as well as the critical vortex radius were calculated. The obtained results are in a good agreement with the results received by Abrikosov and Brandt. Der gemischte Zustand von Supraleitern II. Art wird im Grenzfall κ ≫ 1 und für das ganze Intervall des Magnetfelds zwischen Hc1 < H0 < Hc2 mit Hilfe der Wigner-Seitz-Näherung behandelt. Die Struktur der Flußlinie wird beschrieben im Rahmen des verbesserten Modells von London mit endlichem Vortex-Kern bei Einführung des Ordnungsparameters in Form einer konstanten Funktion für ρ > ρm und einem Variationsansatz für ρ < ρm, wobei ρm der Radius des Kerns ist. Abhängigkeiten der magnetischen Induktion, des Kernradius und der Amplitude der Flusslinie vom äußeren Magnetfeld bei Hc1 < H < Hc2 wurden erhalten. Die Werte des ersten und zweiten kritischen Magnetfelds und des kritischen Radius der Flusslinie wurden berechnet. Die erhaltenen Resultate stimmen gut mit den Resultaten von Abrikosov und von Brandt überein.

Thermodynamics of the first-order vortex lattice melting transition inYBa2Cu3O7−δ

Using the London approximation within the high-field scaling regime, we calculate the jump in the specific heat $\ensuremath{\Delta}c$ at the first-order melting transition of the vortex lattice in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ This has recently been measured [A. Schilling et al., Phys. Rev. Lett. 78, 4833 (1997)] and reported to be at least 100 times higher than expected from the fluctuations of field-induced vortices alone. We demonstrate how the correct treatment of the temperature dependence of the model parameters, which are singular at the mean-field ${B}_{c2}$ line, leads to good agreement between the predictions of the London model and the size of the experimental jump. In addition, we consider the changes in the slopes of the magnetization $\ensuremath{\Delta}(\ensuremath{\partial}M/\ensuremath{\partial}T)$ and $\ensuremath{\Delta}(\ensuremath{\partial}M/\ensuremath{\partial}H)$ at the transition. Using continuum anisotropic scaling theory we demonstrate the consistency of measurements at different angles of the magnetic field with respect to the crystal c axis.

Magnetic self-field entry into a current-carrying type-II superconductor. III. General criterion of penetration for an external field of arbitrary direction

The first magnetic-flux penetration into a current-carrying cylindrical type-II superconductor subjected to an external magnetic field is considered in the frame of the London approximation. The lower transverse critical field as well as critical field of the first vortex nucleation at the surface are evaluated on the basis of an exact solution for a vortex of arbitrary flat configuration. Taken together with the previous consideration of the parallel magnetic-field penetration in a current-carrying superconductor [Phys. Rev. B 49, 6950 (1994) and B 51, 3686 (1995)] the above results allow us to formulate the general criterium for the first flux entry in the current-carrying samples of arbitrary transverse size subjected to an external field of arbitrary direction.

Abrikosov vortex loop near the surface of superconductor

Properties of the Abrikosov vortex loop in the form of a half-ring of arbitrary radius near the flat surface of type-II superconductor are theoretically studied in the London approximation.

Electromagnetic binding of a vortex line to a spherical cavity in a superconductor

We calculate in London approximation the magnetic field distribution of a linear vortex centered on a spherical cavity of radius R. The electromagnetic energy of such a configuration turns out to be smaller than that of an isolated vortex line for all values of R.