Funneling and spin-orbit coupling in transition-metal dichalcogenide nanotubes and wrinkles

Strain engineering provides a powerful means to tune the properties of two-dimensional materials. Accordingly, numerous studies have investigated the effect of bi- and uniaxial strain. Yet, the strain fields in many systems such as nanotubes and nanoscale wrinkles are intrinsically inhomogeneous and the consequences of this symmetry breaking are much less studied. Understanding how this affects the electronic properties is crucial especially since wrinkling is a powerful method to apply strain to two-dimensional materials in a controlled manner. In this paper, we employ density functional theory to understand the correlation between the atomic and the electronic structure in nanoscale wrinkles and nanotubes of the prototypical transition metal dichalcogenide $\mathrm{WSe}_2$. Our research shows that the symmetry breaking in these structures leads to strong Rashba-like splitting of the bands at the $\Gamma$ point and they thus may be utilized in future tunable spintronic devices. The inhomogeneous strain reduces the band gap and leads to a localization of the band edges in the highest-curvature region, thus funneling excitons there. Moreover, we show how wrinkles can be modeled as nanotubes with the same curvature and when this comparison breaks down and further inhomogenities have to be taken into account.