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Kink-antikink asymmetry and impurity interactions in topological mechanical chains

Yujie Zhou (周宇杰), Bryan Gin-ge Chen*, Nitin Upadhyaya†, and Vincenzo Vitelli

  • Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands

  • *Current address: Department of Physics, University of Massachusetts, Amherst, MA, 01002, USA.
  • †Current address: Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
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Phys. Rev. E 95, 022202 – Published 1 February, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.022202

Abstract

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 prestressed 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.

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Phys. Rev. E 95, 022202– Published 1 February, 2017
  • Received 17 August 2016

©2017 American Physical Society

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