van der Waals Epitaxy of Soft Twisted Bilayers: Lattice Relaxation and Mass Density Waves

Interfaces
comprising incommensurate or twisted hexagonal lattices
are ubiquitous and of great interest, from adsorbed organic/inorganic
interfaces in electronic devices, to superlubricants, and more recently
to van der Waals bilayer heterostructures (vdWHs) of graphene and
other 2D materials that demonstrate a range of properties such as
superconductivity and ferromagnetism. Here we show how growth of 2D
crystalline domains of soft block copolymers (BCPs) on patterned hard
hexagonal lattices provide fundamental insights into van der Waals
heteroepitaxy. At moderate registration forces, it is experimentally
found that these BCP-hard lattice vdWHs do not adopt a simple moiré
superstructure, but instead adopt local structural relaxations known
as mass density waves (MDWs). Simulations reveal that MDWs are a primary
mechanism of energy minimization and are the origin of the observed
preferential twist angle between the lattices.