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

Valley-dependent transmission is one of the key physical characteristics for valleytronics. In this work, we focus upon the valley-dependent nature of the quantum transport through a time-modulated-potential region in graphene, when the incident flow is collimated, with a given group velocity direction. Of particular interest is the interplay between the resonant sideband process and the trigonal-warping. The former causes transmission dip-structures which condition of occurrence is determined by sideband processes to a relevant band edge. The latter causes the relevant band-edge energy to become valley-dependent. The relevant band is a fixed-$k_{y}$ projection of the graphene energy band, where $k_{y}$ (along the time-modulate region interface) is conserved in the transmission. The valley polarization$ P$ in the transmission, for valley-unpolarized incident collimated beam, is calculated. Based on our understanding on the above valley-dependent nature, ways to optimize $P$ will be discussed.