Andreev edge channels and magnetic focusing in normal-superconductor systems: A semiclassical analysis

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 electronlike as well as holelike quasiparticles. At weak magnetic fields, the semiclassical conductance shows characteristic oscillations due to the Andreev reflection, while for stronger fields it goes to zero. These findings are in line with the results of previous quantum calculations and with the expectations based on the classical dynamics of the quasiparticles.