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... Show moreWe 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 . pound = (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 oc h over bar. Show less
We identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a one-dimensional (1D) quantum walk, where one spatial dimension plays the role of... Show moreWe identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a one-dimensional (1D) quantum walk, where one spatial dimension plays the role of time. In this mapping, a magnetic field B perpendicular to the bilayer maps onto an electric field. Bloch oscillations due to the periodic motion in a 1D Bloch band can then be observed in purely DC transport as magnetoconductance oscillations with periodicity set by the Bloch frequency. Show less
