Type-II superconductors in high magnetic fields
Superconductivity in high magnetic fields has attracted considerable atten- tion in recent years. The topic is important both for our fundamental un- derstanding of superfluids and for numerous practical applications. In this thesis, we consider several effects originating from the interplay between the Landau level structure of the normal state quasiparticle spectrum, and the tendency of the quasiparticles to form Cooper pairs below the critical tem- perature. A formalism designed to describe extreme type-II superconductors close to the upper critical field Hc2 is developed. The theory which utilizes the selection rules coming from the symmetry properties of the vortex lattice, simplifies the algebra describing a superconductor in the mixed state signifi- cantly. We are, on the mean field level, able to include the quantizing effects of the magnetic field on the electron motion exactly. A main achievement is the exact calculation of the expansion coefficients giving the grand canonical potential of a superconductor in terms of a power series in the size of the or- der parameter. The result is an expression for the grand canonical potential in terms of a polynomial in a finite set of variables close to Hc2. Using this formalism, a theory for the experimentally observed damped de Haas-van Alphen (dHvA) oscillations in the mixed state of a 2-dimensional (2D) superconductor is presented. The theory is compared with numerical results and the agreement is found to be good. A simple physical interpreta- tion of the damping is provided. The dependence of the damping on a finite Zeeman term, temperature, and the magnetic field is considered. A compar- ison of the theory with experimental data for the quasi-2D superconductor K-(ET)2Cu(NCS)2 yields good agreement. The attenuation of a longitudinal sound wave in the mixed state is then calculated. In analogy with the dHvA effect, we predict that there should be damped oscillations in the sound attenuation in the mixed state as the exter- nal magnetic field is varied. Furthermore, the dependence of the oscillations on the sound frequency and temperature is shown to yield information on the low lying quasiparticle spectrum. Especially, the presense of gapless excita- tions due to the magnetic field makes the attenuation qualitatively different as compared to the attenuation in the Meissner state. Some formal convergence properties of the Gor'kov theory for type-II su- perconductors close to Hc2 are derived. We show that the theory is essentially a high temperature expansion; the convergence radius of the Gor'kov series is proportional to kBT when there is a Landau level at the chemical potential.