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.