Generation and Detection of Valley Current in Single and Double Layered Graphene through the Electron-Phonon Interaction

We report a possible method to generate and detect the valley current carried by quasi-particles in both single and double layered graphene. We observe that the term in the collision integral originated from mixing the scalar and vector gauge-field-like vertices in the electron-phonon interaction turns current carriers of two different valleys in opposite directions. As a result, the electron-phonon collision produces a valley current. Finally, we show that the valley current carried by quasi-particles could be not only generated but also detected in a non-local resistance measurement through the inverse version of this mechanism. Our study proposes a new approach to manipulate the valley degrees of freedom in a pristine graphene or bilayer graphene sample without breaking the spatial inversion symmetry. The effect increases with temperature owing to a higher rate of collisions with phonons at higher temperatures.