A new treatment is presented for the Landau domain structure that is realized when a magnetic field less than H~i s applied at a small angle to the large faces of a flat plate of a type-I superconductor.We work within the established framework of the Landau-Sharvin theory but attempt to take into account the nonlinear aspect of the magnetic interaction energy. The result is a new expression for the domain periodicity as a function of the fraction of the sample surface in the normal state, both of which quantities are direct experimental observables. Recent experimental work lends support to our result.

A complete set of charge-conserving, gauge-invariant, time-dependent Ginzburg-Landau equations is derived for a gapless, dirty, type-II superconductor using the method of Gor kov and Eliashberg. Pair breaking by magnetic impurities and by a static magnetic field is permitted in any ratio, in contrast to the equations of Hu and Thompson, where the magnetic impurities dominate. Our extension of the range of validity requires a sizable increase in complexity. The space and time derivatives of the order parameter and the dynamic electromagnetic fields must be included to one higher order than in previous work. The equations are solved for a plane geometry in perpendicular magnetic field to first order in a parallel time-independent electric field, including all screening or backflow effects. The nonlinear terms due to normal-state Joule heating found by Larkin and Ovchinnikov are also obtained, and a precise connection is made between the vertex functions appearing in our equations and the electron distribution function appearing in the Boltzmann equation in the normal state.

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We calculate the thermoelectric power of a metal by considering particularly the particle-hole transformation symmetry. If there is complete symmetry with respect to this transformation, the thermopower is absent. However, the electron-phonon and the electron-impurity interactions are intrinsically such that they change sign under this transformation. Thus a finite thermopower arises due to an interference between different orders in a perturbation expansion in these interactions.

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