H. Umezawa

Derivation and application of the boson method in superconductivity

Abstract This is a review article on the boson method in superconductivity. It covers derivations of the basic equations in the boson method and applications of these equations to the magnetic properties of type II superconductors and to the Josephson phenomena.

Thermo field dynamics

A quantum field theory at finite temperature is presented. The temperature dependent vacuum is defined such that the vacuum expectation value agrees with the statistical average. The vacuum states with different temperature are connected by a Bogoliubov transformation. Our formalism allows the use of the Feynman diagrams for the causal Green’s function and the Bethe-Salpeter technique for bound states at finite temperature, The entropy operator is introduced.

Dynamical rearrangement in the Anderson-Higgs-Kibble mechanism☆

The Anderson-Higgs-Kibble mechanism is investigated by functional methods in the Lorentz gauge, with particular emphasis on the particle structure. We find that a massless Goldstone boson and a massless ghost particle are present besides the massive vector meson and other massive particles. The two massless particles do not contribute to matrix elements of the S-matrix or any gauge invariant quantity, because their effects compensate each other, but their presence is essential as agents of the symmetry transformations. The modifications when the Coulomb gauge is employed are also discussed.

Magnetic properties of pure type-II superconductors

Abstract It is shown that the magnetic properties of type-II superconductors can be computed from a knowledge of the boson characteristic function which can be determined from experimental data for the scattering of neutrons by a vortex lattice. In this consideration surface effects are neglected.

Behavior of type-II superconductors around κcr

Abstract The calculation of the critical κ separating type II/1 superconductors from type II/2 is presented.

Computation of the boson characteristic function

Here ).L( T) is the temperature-dependent London penetration depth and Ho, the Meissner field, is the magnetic field induced solely by external effects. The role of the function c(x, T), which has been called the boson characteristic function, is not restricted to the description of the Meissner state, but is extended to the description of any physical situation occuring in superconducting systems. This is so because the c-function appears in the expression of every observable quantity (2.3). For example, we have shown (3.5) that alI the magnetic properties of the mixed state of type-1I superconductors can be expressed in terms of the boson characteristic function. The form factor F(k) for elastic scattering of neutrons by flux lines has the expression (3)

Computation of the magnetization curve for vanadium at T = 0°C

Abstract The magnetization of pure vanadium for H close to Hcl at T = 0°K is calculated by the boson method. The results are in very good agreement with experiment.

Temperature dependence of κc for type-II superconductors

Abstract The temperature dependence of the critical value κc of the Ginzburg-Landau parameter which separates type-II/1 from type-II/2 superconductors is theoretically computed by means of a microscopic calculation of the boson characteristic function at nonzero temperature, assuming that the temperature is not too close to Tc. Agreement with experimental data is satisfactory in the region 0⩽T T c ⩽0.6 .

Intrinsic hysteresis of type II/1 superconductors

Abstract We predict the existence of an intrinsic hysteresis at H c 1 for type II/1 superconductors, which is due to the mutual interaction between flux lines only.

Study of pure type-II superconductors at T = 0 K

In an earlier paper we presented a preliminary analysis of the magnetic properties of pure type-II superconductors near Hc1 at T = 0 K. In this paper, we present an improvement of the previous analysis by using the exact shape of the boson characteristics function, which is calculated by means of the computer. We also take the normal cores at the center of the vortices into consideration. Detailed analysis of the phase transition at Hc1 is presented. Numerical calculations of Hc1, Hc2, kc, kcr and the equilibrium lattice length, d0 are given. These results are in reasonable agreement with experimental data. Our results depend not only on k, but also mildly on VN(0).