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  • 1QCD Labs, QTF Centre of Excellence, Department of Applied Physics, <a href="https://ror.org/020hwjq30">Aalto University</a>, P.O. Box 13500, FI-00076 Aalto, Finland.

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We discovered topologically protected knots in ordered media, specifically non-Abelian vortices in tetrahedral order. These knots are stable against decay, offering new possibilities for defect structures in physical systems.

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Area of Science:

  • Condensed matter physics
  • Liquid crystals
  • Bose-Einstein condensates

Background:

  • Ordered media can exhibit complex vortex structures with unique topological characteristics.
  • Tetrahedral order is a specific type of ordering found in certain physical systems.
  • Non-Abelian vortices are a class of topological defects with non-commutative properties.

Purpose of the Study:

  • To investigate non-Abelian vortices within a tetrahedral order.
  • To explore the construction of topologically protected knots using these vortices.
  • To demonstrate the applicability of these findings to experimental systems.

Main Methods:

  • Utilized the mathematical formalism of colored links to analyze vortex structures.
  • Investigated systems exhibiting tetrahedral order, including spin-2 Bose-Einstein condensates and nematic liquid crystals.
  • Examined the stability of constructed knots against defect crossings and reconnections.

Main Results:

  • Successfully constructed knots from non-Abelian vortices in tetrahedral order.
  • Demonstrated that these knots possess topological protection, preventing decay into simpler loop defects.
  • Identified the first examples of such protected knots in experimentally realizable systems.

Conclusions:

  • Non-Abelian vortices in tetrahedral order provide a mechanism for creating topologically protected knots.
  • These findings have implications for understanding defect structures in various condensed matter systems.
  • The discovered knots represent a significant advance in the study of topological defects and knot theory in physics.