Spontaneous flexoelectricity and band engineering in MS₂ (M = Mo, W) nanotubes

Spontaneous flexoelectricity in transition metal dichalcogenide (TMD) nanotubes is critical to the design of new energy devices. However, the electronic properties adjusted by the flexoelectric effect in TMD nanotubes remain vague. In this work, we investigate the effect of flexoelectricity on band engineering in single- and double-wall MS₂ (M = Mo, W) nanotubes with different diameters based on first-principles calculations and an atomic-bond-relaxation method. We find that the energy bandgap reduces and the polarization and flexoelectric voltage increase with decreasing diameter of single-wall MS₂ nanotubes. The polarization charges promoted by the flexoelectric effect can lead to a straddling-to-staggered bandgap transition in the double-wall MS₂ nanotubes. The critical diameters for bandgap transition are about 3.1 and 3.6 nm for double-wall MoS₂ and WS₂ nanotubes, respectively, which is independent of chirality. Our results provide guidance for the design of new energy devices based on spontaneous flexoelectricity.