Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals.

Paul J. Ackerman,Ivan I. Smalyukh,Jao van de Lagemaat

doi:10.1038/ncomms7012

Abstract

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains that exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields.

Highlights

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state
Control and generation of defects in liquid crystals (LCs) by colloids and vortex laser beams allowed for obtaining individual stable line and point defects as well as twisted solitons such as torons and localized structures resembling the mathematical Hopf fibration[5,6,7,8,13,14,15,16,17,18,19] and even patterning of two-dimensional (2D) crystalline and quasicrystalline arrays of such defects and solitons when pinned to confining substrates during the laser generation process[13,14]
In a chiral nematic LC (CNLC), the groundstate director is twisting at a constant rate along a ‘helical axis’, with the distance over which n(r) rotates by a 2p-dubbed ‘pitch’ p

Summary

Introduction

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Control and generation of defects in LCs by colloids and vortex laser beams allowed for obtaining individual stable line and point defects as well as twisted solitons such as torons and localized structures resembling the mathematical Hopf fibration[5,6,7,8,13,14,15,16,17,18,19] and even patterning of two-dimensional (2D) crystalline and quasicrystalline arrays of such defects and solitons when pinned to confining substrates during the laser generation process[13,14] To bridge these rather distinct regimes of observation of defects and topological solitons in condensed matter, we explore their field-controlled self-assembly. The exquisite control of topologically nontrivial structures is achieved at voltages of the order of 1 V, potentially enabling mesostructured soft-matter composites with tunable optical properties and a host of new technological applications

Methods

Results

Conclusion