Moiré and making superlattices

One of the biggest condensed matter trends in recent years has been the stacking of 2D materials and the development of moiré lattices.  The idea is, take a layer of 2D material and stack it either (1) on itself but with a twist angle, or (2) on another material with a slightly different lattice constant.  Because of interactions between the layers, the electrons in the material have an effective potential energy that has a spatial periodicity associated with the moiré pattern that results.  Twisted stacking hexagonal lattice materials (like graphene or many of the transition metal dichalcogenides) results in a triangular moiré lattice with a moiré lattice constant that depends on twist angle.  Some of the most interesting physics in these systems seems to pop out when the moiré lattice constant is on the order of a few nm to 10 nm or so.  The upside of the moiré approach is that it can produce such an effective lattice over large areas with really good precision and uniformity (provided that the twist angle can really be controlled - see here and here, for example.)  You might imagine using lithography to make designer superlattices, but getting the kind of cleanliness and homogeneity at these very small length scales is very challenging.

It's not surprising, then, that people are interested in somehow applying superlattice potentials to nearby monolayer systems.  Earlier this year, Nature Materials ran three papers published sequentially in one issue on this topic, and this is the accompanying News and Views article.

• In one approach, a MoSe2/WS2 bilayer is made and the charge in the bilayer is tuned so that the bilayer system is a Mott insulator, with charges localized in exactly the moiré lattice sites.  That results in an electrostatic potential that varies on the moiré lattice scale that can then influence a nearby monolayer, which then shows cool moiré/flat band physics itself.
• Closely related, investigators used a small-angle twisted bilayer of graphene.  That provides a moiré periodic dielectric environment for a nearby single layer of WSe2.  They can optically excite Rydberg excitons in the WSe2, excitons that are comparatively big and puffy and thus quite sensitive to their dielectric environment.  
• Similarly, twisted bilayer WS2 can be used to apply a periodic Coulomb potential to a nearby bilayer of graphene, resulting in correlated insulating states in the graphene that otherwise wouldn't be there.

Clearly this is a growth industry.  Clever, creative ways to introduce highly ordered superlattice potentials on very small lengthscales with other symmetries besides triangular lattices would be very interesting.