Magnetic focusing in normal-superconductor hybrid systems: a semiclassical analysis

Abstract

We study a transverse electron-hole focusing effect in a normal-superconductor system. The spectrum of the quasiparticles is calculated both quantum mechanically and in semiclassical approximation, showing an excellent agreement. A semiclassical conductance formula is derived which takes into account the effect of electron-like as well as hole-like quasiparticles. At low magnetic field the semiclassical conductance shows characteristic oscillations due to the Andreev reflection, while at higher fields it goes to zero. These findigs are in line with the results of previous quantum calculations and with the expectations based on the classical dynamics of the quasiparticles.