An 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 along its zigzag edges, with armchair edges left free. When a bias is applied at one terminal and the others are grounded, valley polarization arises from transverse momentum matching between graphene and the normal metal. Significant polarization occurs when the Fermi wave vector in the metal exceeds half the \( K \)--\( K' \) valley separation. We analyze the dependence of conductance and valley polarization on geometric and electronic parameters, and show that while increased width enhances both, increased length leads to Fabry--P\'erot oscillations and suppresses polarization due to intervalley mixing. Disorder near the Dirac point enhances conductance but reduces polarization. Our findings offer a route to electrical control of valley degrees of freedom in graphene-based devices.