When a magnetic field is applied to a type II superconductor, the field penetrates in the form of vortices wherein the superconducting order parameter vanishes over a length scale of 100 Å or so. Each vortex supports localized electronic states. Above the upper critical field H c2, the normal state is recovered and the electronic states are fully delocalized. A basic question is to ask how the electronic states evolve from being localized to delocalized as the intervortex distance is reduced (i.e. as the magnetic field is increased).; For that purpose, we have performed systematic studies of the electronic thermal conductivity κe/T through the vortex state at temperatures as low as 50 mK and fields as high as 13 Tesla. This was done in a variety of systems: V3Si, LuNi 2B2C, NbSe2 and Tl2Ba2CuO 6+δ.; The work performed on the phonon-mediated V3Si, LuNi 2B2C and NbSe2 led to many surprises. V3 Si is an archetypal type-II superconductor and displays the expected activated behavior. It provides a solid basis for comparison. However, we found that the borocarbide superconductor LuNi2B2C has a highly anisotropic gap of unprecedented magnitude (a factor of 10), while the layered compound NbSe2 is found to display multi-band superconductivity.; We also studied the overdoped cuprate superconductor Tl2Ba 2CuO6+δ where the upper critical field was low enough for us to reach the normal state. The Wiedemann-Franz law was tested and found to be satisfied with a 1% experimental accuracy. This represents the first unambiguous evidence that the overdoped side of the phase diagram is a Fermi liquid and displays no sign of spin-charge separation and thus provides a solid basis for a comprehensive theory of the phase diagram of cuprate superconductors. In the superconducting state, we find that Tl2Ba2CuO 6+δ is the textbook example of a d-wave superconductor as it shows quantitative agreement with theory.; In summary we obtained a range of behaviors in several different types of superconductors, from the test case of the conventional V3 Si to the highly unconventional cuprates and through highly anisotropic and multi-band superconductors. |