Superconductivity in a high magnetic field: Excitation spectrum and tunneling properties

The tunneling current between the metallic tip of a scanning microscope and s-wave and p-wave superconductors in a quantizing magnetic field is investigated. The differential conductance is calculated both as a function of bias voltage at the centre of the vortex line and for varying position of the scanning tunneling microscope tip at a stable voltage.

The Landau quantization effects are considered in low carrier concentration unconventional spin triplet p-wave superconductors in a high magnetic field region. The field dependence of the superconducting order parameter and the vortex lattice states for intra Landau level pairing are analyzed. The gap functions are calculated within mean field approximation.

We show that gapless superconductivity of a strongly type-II superconductor in a high magnetic field prevails in the presence of disorder, suggesting a topological nature. We calculate the density of states of the Bogoliubov-de Gennes quasi-particles for a two-dimensional inhomogeneous system in both cases of weak and strong disorder. In the limit of very weak disorder, the effect is very small and the density of states is not appreciably changed. As the disorder increases, the density of states at low energies increases and the ratio of the low energy density of states to its maximum increases significantly.The interplay between superconductivity and a magnetic field has attracted interest for a long time. For sufficiently strong fields the Meissner phase is destroyed and a mixed state appears in the form of a quantized vortex lattice 1 . The superconductor order parameter has zeros at the vortex locations, through which the external magnetic field penetrates in the sample. Contrarily to previous understanding, the increase of the magnetic field intensity, and its associated diamagnetic pair breaking, is counteracted at high magnetic fields by the Landau level structure of the electrons 2 . This leads to interesting properties such as enhancement of the superconducting transition temperature at very high magnetic fields where the electrons are confined to the lowest Landau level 2 . Associated with the zeros of the order parameter in real space are gapless points in the magnetic Brillouin zone 3 , which lead to qualitatively different behavior at low temperatures and high magnetic fields 4 .It has been argued that the gapless behavior is restricted to high fields very close to the upper critical line where the so-called diagonal approximation (where the coupling between Landau levels is neglected) is valid. It has been shown, however, that the presence of offdiagonal terms does not destroy this behavior 4 and that a perturbation scheme on the off-diagonal terms is possible, as long as there are no band-crossings 5 . It was shown analytically to all orders in the perturbation theory on the off-diagonal terms that there is always a discrete set of points which are gapless that are associated with coherent propagation of the quasiparticles (so-called Eilenberger points). These nodes are associated with the center of mass coordinates of the Cooper pairs and not to some internal structure like in d-wave superconductors. Lowering the magnetic field, a quantum levelcrossing transition has been found that eventually leads to a gapped regime and to states localized in the vortex cores 6,7 .On the other hand, the effect of disorder on superconductivity has also attracted interest for a long time. In the case of non-magnetic impurities and s-wave pairing Anderson's theorem states that, at least for low concentrations, they have little effect since the impurities are not pair-breaking 8 . In d-wave superconductors however, non-magnetic impurities cause a strong pair breaking effect 9 . In the limit of strong scattering it ...