Valley-dependent resonant inelastic transmission through a time-modulated region in graphene

We investigate resonant sideband processes in the transmission through a time-modulated-potential region in graphene. Valley-dependent features in the time-dependent transmission due to trigonal-warping effects in the electronic structures are explored within a tight-binding model. Three main results obtained are dip structures in the transmission, valley dependence of the dip structures, and nontypical-Fabry-Pérot behavior in the dip-structure amplitudes. Dip structures in the transmission are obtained when a relevant band edge is available for the sideband processes. The relevant band edges are shown to become valley dependent, when the incident flow is formed from states of the same group-velocity direction. This is a consequence of the trigonal-warping effects, and it leads to the valley dependence in the dip structures. The dip-structure amplitudes, on the other hand, are found to exhibit a nontypical Fabry-Pérot oscillatory behavior, in their dependence on the width of the time-modulated region. This is shown, in our multiple sideband scattering analysis, to result from resonant sideband processes to a relevant band edge. As such, the nontypical Fabry-Pérot oscillatory behavior serves as another evidence for the key role the relevant band edges play in the transmission dip structures.