Moire patterns result from setting a 2D material such as graphene on another
2D material with a small twist angle or from the lattice mismatch of 2D
heterostructures. We present a continuum model for the elastic energy of these
bilayer moire structures that includes an intralayer elastic energy and an
interlayer misfit energy that is minimized at two stackings (disregistries). We
show by theory and computation that the displacement field that minimizes the
global elastic energy subject to a global boundary constraint gives large
alternating regions of one of the two energy-minimizing stackings separated by
domain walls.
We derive a model for the domain wall structure from the continuum bilayer
energy and give a rigorous asymptotic estimate for the structure. We also give
an improved estimate for the L2-norm of the gradient on the moire unit cell for
twisted bilayers that scales at most inversely linearly with the twist angle, a
result which is consistent with the formation of one-dimensional domain walls
with a fixed width around triangular domains at very small twist angles.Comment: 20 pages, 14 figure