In-Plane and Out-of-Plane\nElectronic and Tunnel Properties\nof Moire Homo- and Heterostructures

We study the in-plane electronic and the out-of-plane\ntunnel properties\nand their correlation for moiré homo- and heterostructures.\nFor the in-plane electronic properties, two-dimensional (2D) twisted\nhomobilayer moiré structures often exhibit a flattening of\nthe band edges. Using the moiré homobilayer of β-InSe,\nwe reveal the origin of the coexistence of dispersive and flat bands\nin moiré structures and find that the dispersion or flatness\nof energy bands is related not only to the energy difference of band\nedges in the different local-stacking regions but also to the dispersion\nor flatness of the involved bands in the component monolayer and show\nthe significance of interlayer interaction between valence and conduction\nbands for the formation of well-isolated flat band. Then, we uncover\nthe effect of in-plane local potential variation on the out-of-plane\ntunneling properties, which is important for electronic device performance.\nWe find that the significant variation of tunneling barriers in different\nlocal-stacking regions results in a “sieve” effect for\nelectron tunneling across the van der Waals (vdW) gap. The “sieve”\neffect for the moiré heterostructure of a 3D metal/2D MoS<sub>2</sub> vdW junction explains the inverted height profile in the\nscanning tunneling microscopy measurement reported in the literature.\nOur current study focuses on the coexistence of in-plane local and\nnonlocal properties and the “sieve” effect for electron\ntunneling in different in-plane local regions, which has important\nimplications for a broader family of moiré homo- and heterostructures\nof 2D semiconductor junctions and metal/2D semiconductor junctions.