Field-Programmable Topological Torons in Chiral Nematic Liquid Crystals

Abstract

Torons are three-dimensional double-twist solitons in chiral nematic liquid crystals that form localised director configurations protected by topology and bounded by closed defect loops. They behave as particle-like entities while retaining a fully reconfigurable optical response. Here it is shown experimentally that individual torons can be created, steered and parked on demand using tailored alternating-current electric fields in planar cells, enabling deterministic control of both position and trajectory. By tuning the ratio of cell thickness to cholesteric pitch and systematically adjusting waveform parameters, including amplitude, modulation frequency, duty-cycle asymmetry and small DC offsets, robust toron nucleation is achieved and programmable translation is realised along arbitrary in-plane directions with submicrometre placement accuracy. Directional transport is controlled within a defined frequency and temperature window and can be reversed by changing modulation conditions even at zero offset. A dedicated graphical interface enables real-time switching between waveform presets so that torons follow scripted paths and draw user-defined shapes. Quantitative Landau-de Gennes Q-tensor simulations reproduce toron nucleation and the ensuing translational dynamics, supporting an interpretation in which waveform-controlled director reorientation, reorientation-driven flow and rectified polarity-sensitive coupling jointly bias the drift. Finally, three proof-of-concept functions are demonstrated: a software-defined liquid-crystal racetrack memory analogue with optical readout, deterministic path writing for reconfigurable patterning, and toron-mediated pick-and-place transport of microparticles for micromanipulation.

Figures (4)

• Figure 1: Voltage-induced formation and pitch-dependent scaling of torons in a confined chiral nematic cell. (a) POM micrographs at 0, 12, 20 and 24 V showing the transition from a Grandjean stripe texture to isolated torons. Polariser (P) and analyser (A) directions indicated. Scale bars, 15 $\mu$m. (b) Numerical reconstruction of a toron: director field with coloured preimage surfaces (top) and simulation geometry, $H = 5\,\mu$m, under applied voltage (bottom). (c) Experimental (top) and simulated (bottom) POM textures for varying pitch $p$. Scale bars, 1 $\mu$m (left) and 3 $\mu$m (right). (d) DHM amplitude map showing the optical path-length modulation. (e) Toron lateral diameter versus pitch.
• Figure 2: Field-stabilised persistence and relaxation dynamics of an isolated toron. (a) Polarising optical micrographs showing long-term stability under continuous driving, with no observable change after 7 days. (b) Relaxation following field removal. Top: applied voltage protocol ($\pm6$ V$_{\mathrm{pp}}$ square-wave drive followed by a zero-field interval). Middle: experimental POM time sequence showing the toron core persisting while the surrounding background destabilises. Bottom: corresponding $Q$-tensor simulations and director profiles reproducing the same relaxation pathway. Scale bars, 5 $\mu$m.
• Figure 3: Programmable directional transport of torons using burst-modulated electric fields and temperature-controlled reversal. (a) Position versus time for a representative toron driven along the four cardinal directions ($\Delta x(t)$ top, $\Delta y(t)$ bottom). (b) Waveform library enabling eight-direction control. (c) Per-second mean speed over a 12 s interval for the north-east trajectory; dashed line indicates the trimmed mean. (d) Mean velocities for all eight programmed directions. Error bars denote the standard error of per-second means from 12 one-second bins. (e) Temperature-controlled reversal of transport under a fixed electrical drive; images acquired in 1 $^{\circ}$C steps. All measurements used a 1 kHz carrier; "north" is defined perpendicular to the rubbing direction.
• Figure 4: Proof-of-concept applications. (a) Centroid-tracked trajectory of a single toron steered to trace the letters "SMP" under GUI-controlled waveform presets. (b) Liquid-crystal racetrack memory analogue: torons written, shifted and erased along a reconfigurable virtual track with optical readout. (c) Toron-mediated microparticle pick-and-place: a silica bead cluster captured by the toron elastic field is transported and released at a target site. Scale bars, 10 $\mu$m.