Achieving epitaxy between incommensurate materials by quasicrystalline interlayers

Epitaxial interfaces of commensurate periodic materials can be characterized by a locking into registry of their atomic structure. This characteristic is identified as a natural framework to capture the essence of epitaxy also for systems including quasicrystalline materials. The resulting general definition for epitaxy requires a matching of reciprocal lattice points. The consequences for the real space structure of an epitaxial interface between quasiperiodic and periodic materials are explored and an experimental realization of such an interface is presented. It is demonstrated that due to their higher number of reciprocal lattice basis vectors (exceeding three), quasicrystals can provide interlayers epitaxially linking incommensurate materials.