PLANAR SUPERCONDUCTIVE PAIRING AND THE GAP IN HIGH MAGNETIC-FIELDS

We demonstrate some unusual features of superconductivity in high magnetic fields by analytically diagonalizing the microscopic Bogoliubov-de Gennes Hamiltonian in the presence of a quantizing magnetic field and in the limit of pairing occurring within a single Landau level. Pairing is shown to occur between states of opposite reduced momenta, with periodicity established by the magnetic field. The exact form of the gap in real space is a generalization of the Abrikosov-Gorkov solution. The quasiparticle excitation spectrum bears the signature of the high magnetic field. A nonzero electronic g factor has a significant effect on singlet superconductivity in this limit.