All-electrical scheme for valley polarization in graphene

We propose an all-electrical setup to generate valley polarization in graphene. A finite graphene sheet is connected to two normal metal electrodes each with two terminals along its zigzag edges, while the armchair edges remain free. When a bias is applied to one terminal and the others are grounded, valley polarization emerges due to transverse momentum matching between the graphene and the metal electrodes. Significant valley polarization is achieved when the Fermi wavevector in the metal exceeds half the separation between the \( K \) and \( K' \) valleys in graphene. We analyze how conductance and valley polarization depend on geometric and electronic parameters. While increasing the width enhances both conductance and polarization, increasing the length introduces Fabry--Pérot oscillations and suppresses valley polarization due to enhanced intervalley mixing. We also examine the effects of disorder: on-site disorder in graphene increases conductance near the Dirac point but reduces valley polarization. Finally, we study the impact of imperfect armchair edges and interface roughness, finding that moderate deviations from ideal conditions still yield substantial valley polarization. Our results demonstrate a viable route to electrically controlling valley degrees of freedom in graphene-based devices.