Accepted for publication in Physical Review B.
We introduce configuration space as a natural representation for calculating
the mechanical relaxation patterns of incommensurate two-dimensional (2D) bilayers, bypassing
supercell approximations to encompass aperiodic relaxation patterns. The approach can be
applied to a wide variety of 2D materials through the use of a continuum model in combination
with a generalized stacking fault energy for interlayer interactions. We present computational
results for small-angle twisted bilayer graphene and molybdenum disulfide (MoS2), a representative
material of the transition metal dichalcogenide (TMDC) family of 2D semiconductors. We calculate
accurate relaxations for MoS2 even at small twist-angle values, enabled by the fact that our
approach does not rely on empirical atomistic potentials for interlayer coupling. The results
demonstrate the efficiency of the configuration space method by computing relaxations with
minimal computational cost for twist angles down to 0.05º, which is smaller than what can be
explored by any available real space techniques. We also outline a general explanation of domain
formation in 2D bilayers with nearly-aligned lattices, taking advantage of the relationship
between real space and configuration space.