Abstract

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 U₀ 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 (K₁ = −K and K₂ = +K) is evaluated separately. The results show that U₀ and the Fermi energy EF 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 EF and U₀ are the same. If they are different, the valley filtering is destroyed and might occur only at some resonant states affected by U0. Additionally, there are independent valley modes characterizing the conductance oscillations near the vicinity of the resonances, whose strength increases with U₀ 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.

Abstract

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 U₀ 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 (K₁ = −K and K₂ = +K) is evaluated separately. The results show that U₀ and the Fermi energy EF 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 EF and U₀ are the same. If they are different, the valley filtering is destroyed and might occur only at some resonant states affected by U0. Additionally, there are independent valley modes characterizing the conductance oscillations near the vicinity of the resonances, whose strength increases with U₀ 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.

Abstract

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 U₀ 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 (K₁ = −K and K₂ = +K) is evaluated separately. The results show that U₀ and the Fermi energy EF 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 EF and U₀ are the same. If they are different, the valley filtering is destroyed and might occur only at some resonant states affected by U0. Additionally, there are independent valley modes characterizing the conductance oscillations near the vicinity of the resonances, whose strength increases with U₀ 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.

Abstract

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 U₀ 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 (K₁ = −K and K₂ = +K) is evaluated separately. The results show that U₀ and the Fermi energy EF 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 EF and U₀ are the same. If they are different, the valley filtering is destroyed and might occur only at some resonant states affected by U0. Additionally, there are independent valley modes characterizing the conductance oscillations near the vicinity of the resonances, whose strength increases with U₀ 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.