  Epitaxy forms the basis of modern electronics and optoelectronics. We report
coherent atomically-thin superlattices, in which different transition metal
dichalcogenide monolayers--despite large lattice mismatches--are repeated and
integrated without dislocations. Grown by a novel omnidirectional epitaxy,
these superlattices display fully-matched lattice constants across
heterointerfaces while maintaining a surprisingly isotropic lattice structure
and triangular symmetry. This strong epitaxial strain is precisely engineered
via the nanoscale supercell dimensions, thereby enabling broad tuning of the
optical properties and producing photoluminescence peak shifts as large as 250
meV. We present theoretical models to explain this coherent growth as well as
the energetic interplay governing the flat-rippled configuration space in these
strained monolayers. Such coherent superlattices provide novel building blocks
with targeted functionalities at the atomically-thin monolayer limit.
