  Sliding and twisting van der Waals layers with respect to each other gives
rise to moir\'e structures with emergent electronic properties. Electrons in
these moir\'e structures feel weak potentials that are typically in the tens of
millielectronvolt range when the moir\'e structures are smooth at the atomic
scale. Here we report a facile technique to achieve deep, deterministic
trapping potentials via strain-based moir\'e engineering in van der Waals
bilayers. We use elasto-scanning tunneling microscopy to show that uniaxial
strain drives a commensurate-incommensurate lattice transition in a multilayer
MoSe$_2$ system. In the incommensurate state, the top monolayer is partially
detached from the bulk through the spontaneous formation of topological
solitons where stress is relieved. Intersecting solitons form a honeycomb-like
network resulting from the three-fold symmetry of the adhesion potential
between layers. The vertices of the honeycomb network occur in bound pairs with
different interlayer stacking arrangements. One vertex of the pair is found to
be an efficient trap for electrons, displaying two states that are deeply
confined within the semiconductor gap and have a spatial extent of 2 nm.
Honeycomb soliton networks thus provide a unique path to engineer an array of
identical deeply confined states with a strain-dependent tunable spatial
separation, without the necessity of introducing chemical defects into the host
materials.
