Kink-antikink asymmetry and impurity interactions in topological mechanical chains

Area of Science:

• Condensed matter physics
• Nonlinear dynamics
• Materials science

Background:

• Periodic chains of rotors exhibit complex dynamics.
• Spatial inversion symmetry breaking is crucial in condensed matter systems.
• Topological excitations like kinks can arise in nonlinear systems.

Purpose of the Study:

• To analyze the dynamical response of a diatomic periodic chain of rotors.
• To investigate the role of a topological boundary term in symmetry breaking.
• To understand the propagation dynamics of topological kinks and antikinks.

Main Methods:

• Derivation of a nonlinear field theory from a discrete model.
• Fixed-point analysis using cobweb plots for kink motion.
• Application of continuum elasticity theory and tangent stiffness matrix approach.
• Introduction of impurities (disorder) in spring stiffness and length.

Main Results:

• A topological boundary term energetically favors kinks over antikinks.
• Kinks propagate without the Peierls-Nabarro potential energy barrier.
• Energy degeneracy between kink and antikink configurations is broken.
• Kink-antikink asymmetry affects interactions with impurities.

Conclusions:

• The topological boundary term dictates the asymmetric dynamics of kinks and antikinks.
• The absence of the Peierls-Nabarro barrier is linked to this asymmetry.
• Impurities further highlight the kink-antikink asymmetry in nonlinear excitations.
• Experimental prototypes validate the theoretical predictions.