Curvature-Controlled Band Alignment Transitions in 1D van der Waals Heterostructures

One-dimensional (1D) van der Waals (vdW) heterostructures, formed between coaxial nanotubes of transition metal dichalcogenides (TMDCs), have emerged as a new area of endeavor in nanoscience. A key to designing and engineering the properties of such 1D vdW heterostructures lies on understanding the band alignment of coaxial nanotubes in the heterostructures. However, how curvature, tube diameters, and intertube coupling affect the band-edge levels and band alignment of TMDC nanotubes in 1D vdW heterostructures remains unknown. Here, through comprehensive first-principles calculations and analyses, we establish a complete framework of band alignment in 1D vdW heterostructures of TMDC nanotubes. We reveal that, as the diameter of a TMDC nanotube decreases, the combined effects of curvature-induced flexoelectricity and intrinsic circumferential tensile strain cause a rapid and continuous lowering of the conduction band minimum (CBM), whereas the valence band maximum (VBM) exhibits an initial lowering before rising, which originates from a change in the orbital character of the VBM. The transition in the orbital character of VBM also leads to direct-to-indirect bandgap transition in small-diameter armchair and chiral nanotubes, as well as photoluminescence quenching in zigzag nanotubes. As individual TMDC nanotubes form coaxial 1D vdW heterostructures, the effect of intertube coupling via flexovoltage effect can result in a transition of intertube band alignment from Type II to Type I in multiple heterostructural systems, including large-diameter MoSe$_2$@WS$_2$, MoTe$_2$@MoSe$_2$, and MoTe$_2$@WS$_2$ heterostructures. These results lay down a foundation for the rational design of 1D vdW heterostructures.