Enhanced asymmetric valley scattering by scalar fields in nonuniform out-of-plane deformations in graphene

Abstract

We study the electron scattering produced by local out-of-plane strain deformations in the form of Gaussian bumps in graphene. Of special interest is taking into account the scalar field associated with the redistribution of charge due to deformations on the same footing as the pseudomagnetic field. Working with the Born approximation approach, we show analytically that even when a relatively small scalar field is considered, strong backscattering and enhancement of the valley-splitting effect could arise as a function of the energy and angle of incidence. In addition, we find that the valley polarization can reverse its sign as the incident energy is increased. These behaviors are totally absent if the scalar field is neglected or screened. Interestingly, we find that there is a further possibility of controlling the valley scattering polarization purely by electrical means through the presence of external scalar fields in combination with strain fields. These results are supported by quantum dynamical simulations of electron wave packets. Results for the average trajectories of wave packets in locally strained graphene clearly show focusing and beam-splitting effects enhanced by the presence of the scalar field that could be of interest in the implementation of valleytronic devices.