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Two-dimensional confinement of lattices produces a variety of order anddisorder phenomena. When the confining walls have atomic granularity, uniquestructural phases are expected, of relevance in nanotribology, porous materialsor intercalation compounds where \textit{e.g.} electronic states can emergeaccordingly. The interlayer's own order is frustrated by the competinginteractions exerted by the two confining surfaces. We revisit the concept oforientational ordering, introduced by Novaco and McTague to describe the twistof incommensurate monolayers on crystalline surfaces. We predict a two-waytwist of the monolayer as its density increases. We discover such a behavior inalkali atom monolayers (sodium, cesium) confined between graphene and aniridium surface, using scanning tunneling microscopy and electron diffraction.

Two-way twisting of a confined monolayer: orientational ordering within the van der Waals gap between graphene and its crystalline substrate