Berry curvature induced valley Hall effect in non-encapsulated hBN/Bilayer graphene heterostructure aligned with near-zero twist angle

Valley Hall effect has been observed in asymmetric single-layer graphene and bilayer graphene systems. In single-layer graphene systems, asymmetry is introduced by aligning graphene with hexagonal boron nitride (hBN) with a near-zero twist angle, thereby breaking the sub-lattice symmetry. Although a similar approach has been used in bilayer graphene to break the layer symmetry and thereby observe the valley Hall effect, the bilayer graphene was sandwiched with hBN on both sides in those studies. It has been shown theoretically that having hBN on one side and both sides affect the symmetry of the system differently. Thus, here we show the valley Hall effect through non-local resistance measurement ($R_{\rm{NL}}$) in non-encapsulated hBN/bilayer graphene heterostructure where the hBN and bilayer graphene crystallographic axes are aligned. We also show that the $R_{\rm{NL}}$ can be controlled by applying a displacement field across the heterostructure. Furthermore, the electronic band structure and Berry curvature calculations validate the experimental observations.