  We study the dynamical response of a diatomic periodic chain of rotors
coupled by springs, whose unit cell breaks spatial inversion symmetry. In the
continuum description, we derive a nonlinear field theory which admits
topological kinks and antikinks as nonlinear excitations but where a
topological boundary term breaks the symmetry between the two and energetically
favors the kink configuration. Using a cobweb plot, we develop a fixed-point
analysis for the kink motion and demonstrate that kinks propagate without the
Peierls-Nabarro potential energy barrier typically associated with lattice
models. Using continuum elasticity theory, we trace the absence of the
Peierls-Nabarro barrier for the kink motion to the topological boundary term
which ensures that only the kink configuration, and not the antikink, costs
zero potential energy. Further, we study the eigenmodes around the kink and
antikink configurations using a tangent stiffness matrix approach appropriate
for pre-stressed structures to explicitly show how the usual energy degeneracy
between the two no longer holds. We show how the kink-antikink asymmetry also
manifests in the way these nonlinear excitations interact with impurities
introduced in the chain as disorder in the spring stiffness. Finally, we
discuss the effect of impurities in the (bond) spring length and build
prototypes based on simple linkages that verify our predictions.
