Single-electron transport through the vortex core levels in clean superconductors

We develop a microscopic theory of single-electron low-energy transport in normal-metal-superconductor-normal-metal hybrid structures in the presence of applied magnetic field introducing vortex lines in a superconductor layer. We show that vortex cores in a thick and clean superconducting layer are similar to mesoscopic conducting channels where the bound core states play the role of transverse modes. The transport through not very thick layers is governed by another mechanism, namely by tunneling via vortex core levels. We apply our method to calculation of the thermal conductance along the magnetic field.