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Periodic boundary conditions alter topological defect interactions in liquid crystals. This study reveals anomalous, non-Coulombic interactions mediated by solitons, highlighting the importance of domain topology.

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Area of Science:

  • Condensed Matter Physics
  • Soft Matter Physics
  • Theoretical Physics

Background:

  • Periodic boundary conditions (PBCs) are widely used to simulate infinite systems.
  • Two-dimensional periodic domains possess distinct topology compared to an infinite plane.
  • The impact of PBCs on topological properties of matter remains an open question.

Purpose of the Study:

  • To investigate the effect of periodic boundary conditions on topological defects in two-dimensional p-atic liquid crystals.
  • To derive an analytical expression for the orientation field in such systems.
  • To understand the resulting defect interactions and their underlying mechanisms.

Main Methods:

  • Analytical derivation of orientation fields for p-atic liquid crystals under PBCs.
  • Continuum simulations of nematic liquid crystals (p=2) to validate analytical findings.
  • Analysis of defect interactions and the role of topological solitons.

Main Results:

  • An analytical expression for the orientation field in 2D p-atic liquid crystals with PBCs was derived.
  • An anomalous, non-Coulombic interaction between topological defects was identified.
  • Continuum simulations confirmed these anomalous interactions for nematic liquid crystals.
  • Non-singular topological solitons, stabilized by PBCs, mediate these interactions.

Conclusions:

  • Periodic boundary conditions significantly alter the interactions between topological defects.
  • Domain topology, not just geometry, is crucial for understanding defect interactions.
  • The findings have implications for theoretical and computational studies of topological systems.