Influence of electrostatic field on the Weiss oscillations in graphene

• We explore the electrostatic field effect on the Weiss oscillations in graphene.
• The electric field could enhance the oscillation amplitude of Weiss oscillations.
• The electric field leads to an abrupt disappearance of the Weiss oscillations.
• The electric field increases the value of longitudinal magnetoconductivity.

Recent theoretical works have predicated the appearance of Weiss oscillations in the magnetoconductivity with a one-dimensional periodic electrical or magnetic modulation in graphene. This paper further explores the electrostatic field effect on the Weiss oscillations in the presence of crossed uniform in-plane electric field and perpendicular magnetic field that is weakly and periodically modulated along one direction. We find that the oscillation amplitude (OA) of Weiss oscillations and the value of conductivity are both shown to increase as the electric field E increases for a given magnetic field B  . More interestingly, the electric field leads to an abrupt disappearance of the Weiss oscillations, when the value of electric to magnetic field ratio approaches a threshold value, i.e., γe=EυFB=1. These phenomena, not known in the conventional 2D electron gas, are a consequence of the anomalous spectrum of electron in graphene.