  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.
