Breathing mode in open-orbit magnetotransport: A magnetic lens with a quantum mechanical focal length

We consider the propagation of electrons in a lattice with an anisotropic dispersion in the x-y plane (lattice constant a), such that it supports open orbits along the x axis in an out-of-plane magnetic field B. We show that a point source excites a "breathing mode,"a state that periodically spreads out and refocuses after having propagated over a distance ?=(eaB/h)-1 in the x direction. Unlike known magnetic focusing effects, governed by the classical cyclotron radius, this is an intrinsically quantum mechanical effect with a focal length.