Interference effects and Huygens principle in transverse magnetic focusing of electrons and holes

Interference effects form a fundamental pillar of quantum mechanics. In this paper, we examine the interference in spin-orbit-coupled transverse magnetic focusing, where a weak magnetic field is used to focus charge carries over mesoscopic scales. We determine a semiclassical form for the Green's function in a weak magnetic field, for the case of both spinless and spin-orbit-coupled charge carriers. The obtained forms for the Greens' function are independent of particle dispersion and are thus applicable to a wide variety of systems.