THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical...

Flux vortices and transport currents in type II superconductors

http://cds.cern.ch/record/257993/files/9401310.pdf

QCD phenomenology based on a chiral effective Lagrangian

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

The fluctuation of the order parameter in a superconductor in the temperature slightly above the transition temperature is studied in the framework of the current microscopic theory. It is convenient to divide the temperature region where the fluctuation of the order parameter becomes important into two regions; the classical and the' critical region. In the classical region the spatial correlation of the fluctuation is of the Ornstein-Zernike type, while in the critical region it depends on the relative distance like r-3/2. We show that the elec­ trical resistivity, the nuclear spin lattice relaxation time and the ultrasonic attenuation co­ efficient decrease like 1-ai1li- 1I2 and 1-a'i1li- 1I3 in the classical and in the critical region . respectively, where 1l= (TITe) -1 and a and a' are constants of the order (Telp.) 1/2 (lPo)-3/2 and (Tel p.) 1/3 (lpo) -1 respectively. Here p. is the chemical potential, l is the electronic mean free path and Po is the fermi momentum. It is also shown that the thermal conductivity has no singular term at the transition temperature.

/pdf/critical-fluctuation-of-the-order-parameter-in-a-37k8c5mc64.pdf

Critical Fluctuation of the Order Parameter in a Superconductor. I

Quantum corrections to solitons in polyacetylene

We reexamine here microscopically the transport properties of the vortex state in a dirty type II superconductor in the high-field region We show that the previous theory by Caroli and Maki predicts the entropy carried by a single vortex line, which is consistent with recent experiments, provided the expression of the heat current is properly corrected Furthermore, we show that a large heat delivered by vortex lines together with the normal thermoelectric effect, which persists even in the vortex state, results in a large Hall current in the vortex state This may account for a large Hall effect observed by Niessenet al in Nb-Ta alloys

Motion of the vortex lattice in a dirty type II superconductor

/pdf/pinning-effect-due-to-periodic-variation-of-impurity-2v5v05ecyy.pdf

Pinning Effect due to Periodic Variation of Impurity Concentration in Type II Superconductors

/pdf/thermoelectric-power-in-dilute-magnetic-alloys-8zjp8lknbm.pdf

Kazumi Maki

Papers

Critical Fluctuation of the Order Parameter in a Superconductor. I

Quantum corrections to solitons in polyacetylene

Motion of the vortex lattice in a dirty type II superconductor

Pinning Effect due to Periodic Variation of Impurity Concentration in Type II Superconductors

Thermoelectric Power in Dilute Magnetic Alloys