  In this paper, we prove the convergence from the atomistic model to the
Peierls--Nabarro (PN) model of two-dimensional bilayer system with complex
lattice. We show that the displacement field of the dislocation solution of the
PN model converges to the dislocation solution of the atomistic model with
second-order accuracy. The consistency of PN model and the stability of
atomistic model are essential in our proof. The main idea of our approach is to
use several low-degree polynomials to approximate the energy due to atomistic
interactions of different groups of atoms of the complex lattice.
