  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
pseudo-magnetic 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 ($K_1$= -K and
$K_2$ = +K) is evaluated separately. The results show that U0 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 pseudo-magnetic fields as in
previous proposals.
