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

The quasiparticle excitation spectrum of a type-II superconductor placed in high magnetic field near ${\mathit{H}}_{\mathit{c}2}$(T) is shown to be gapless. The gap turns to zero at the points in the magnetic Brillouin zone that are in correspondence with the vortex lattice in real space. When the field decreases below a certain critical value, branch crossings occur and gaps start opening up at the Fermi surface. The strong dispersion around the gapless points leads to an algebraic temperature dependence in the thermodynamic functions and the algebraic voltage dependence in the tunneling conductance between the microscope tip and superconductor in a scanning tunneling microscope experiment. The crossover from the localized midgap states at the core of an isolated vortex to the coherent quasiparticle band at high fields is reflected in a qualitative change of differential conductance.