Valley-dependent tunneling through electrostatically created quantum dots in heterostructures of graphene with hexagonal boron nitride

Kelvin probe force microscopy (KPFM) has been employed to probe charge carriers in a graphene/hexagonal boron nitride (hBN) heterostructure [Nano Lett. 21, 5013 (2021)]. We propose an approach for operating valley filtering based on the KPFM-induced potential ${U}₀$ instead of using external or induced pseudomagnetic fields in strained graphene. Employing a tight-binding model, we investigate the parameters and rules leading to valley filtering in the presence of a graphene quantum dot (GQD) created by the KPFM tip. This model leads to a resolution of different transport channels in reciprocal space, where the electron transmission probability at each Dirac cone (${\mathbf{K}}_{\mathbf{1}}=\ensuremath{-}\mathbf{K}$ and ${\mathbf{K}}_{\mathbf{2}}=+\mathbf{K}$) is evaluated separately. The results show that ${U}₀$ and the Fermi energy ${E}_F$ control (or invert) the valley polarization, if electrons are allowed to flow through a given valley. The resulting valley filtering is allowed only if the signs of ${E}_F$ and ${U}₀$ are the same. If they are different, the valley filtering is destroyed and might occur only at some resonant states affected by ${U}₀$. Additionally, there are independent valley modes characterizing the conductance oscillations near the vicinity of the resonances, whose strength increases with ${U}₀$ and are similar to those occurring in resonant tunneling in quantum antidots and to the Fabry-Perot oscillations. Using KPFM, to probe the charge carriers, and graphene-based structures to control valley transport, provides an efficient way for attaining valley filtering without involving external or pseudomagnetic fields as in previous proposals.