Pseudo Magnetic Faraday and Quantum Hall Effect In Oscillating Graphene*

When a graphene layer is stressed, the strain changes the phase between sites in a tight binding model of the system. This phase can be viewed as a pseudo-magnetic vector potential. The corresponding pseudo-magnetic field has been experimentally verified in static cases.\footnote{ N. Levy et al. {\it Science} {\bf 329}, 544 (2010)} We examine the case of oscillating graphene ribbons and explore two new effects. The first is to investigate an oscillating pseudo-magnetic field that produces a quantum Hall effect: we calculate the I-V characteristic of an oscillating graphene nanoribbon as a function of frequency, and amplitude in both the oscillations and the applied driving voltage. Second, the time dependent pseudo-magnetic field should produce a pseudo-Faraday effect driving electrons in different valleys in opposite directions. In both cases, we make explicit calculations for experiment.