Electronic Bloch oscillation in a pristine monolayer graphene

In a pristine monolayer graphene subjected to a constant electric field along the layer, the Bloch oscillation of an electron is studied in a simple and efficient way. By using the electronic dispersion relation, the formula of a semi-classical velocity is derived analytically, and then many aspects of Bloch oscillation, such as its frequency, amplitude, as well as the direction of the oscillation, are investigated. It is interesting to find that the electric field affects the component of motion, which is non-collinear with electric field, and leads the particle to be accelerated or oscillated in another component.