  In this paper we construct and analyze a two-well Hamiltonian on a 2D atomic
lattice. The two wells of the Hamiltonian are prescribed by two rank-one
connected martensitic twins, respectively. By constraining the deformed
configurations to special 1D atomic chains with position-dependent elongation
vectors for the vertical direction, we show that the structure of ground states
under appropriate boundary conditions is close to the macroscopically expected
twinned configurations with additional boundary layers localized near the
twinning interfaces. In addition, we proceed to a continuum limit, show
asymptotic piecewise rigidity of minimizing sequences and rigorously derive the
corresponding limiting form of the surface energy.
