Static and dynamic properties of half-skyrmions in thin layers of chiral liquid crystals

Pišljar, Jaka (author), Muševič, Igor (mentor)

Skyrmions are nonsingular, vortex-like formations, emerging in some continuous fields, that are topologically protected by their twisted structure, which also offers them energetic stability. They have been observed in a number of condensed matter systems including liquid crystals (LCs). In highly chiral variants of nematic (N) LCs complex phases called blue phases (BPs) are formed. The 3D structure of BPs may be described as three dimensional stacking of fractional-skyrmion filaments, accompanied by a dual lattice of line-like defects with isotropic core. The stacking is regular in cubic BPs (BPI/II) and amorphous in BPIII. We deal in this work with three distinct phenomena related to BPs and their confined variants. In the first part we show experimentally and numerically, that the structure of amorphous BPIII is a highly dynamic liquid of fractional-skyrmion filaments, which like the cubic BPI, transforms into a quasi-2D lattice of half-skyrmions (HS) when confined to dimensions below the material pitch. Two distinct branches of observed BPIII dynamics are attributed to slow rearrangements within the 2D/3D skyrmion liquid and fast fluctuations of the N director structure within the filaments. In the second part we deal with fluctuating appearance of HS at the transition from the high temperature isotropic phase (I) in sub-100~nm layers of a highly-chiral system. The observed fluctuations are slow with relaxation rates of 1-1000~Hz and consist of spontaneous and stochastic formation, reshaping and decay of HS and their parts. We approach the dynamic analysis in two ways: (i) feature tracking software on real-space videos and (ii) differential dynamic microscopy, operating in the reciprocal spatial domain. We show that analogous fluctuating behaviour takes place at the transition of a confined achiral nematic. There it appears for confinement thicknesses in a narrow range above the critical thickness. Below it, capillary condensation of N phase takes place and the transition becomes gradual. Using simple energetic arguments, based on Landau-de Gennes N-I phase transition theory in confinement, we show a probable mechanism behind these fluctuations is formation, disappearance and movement of capillary bridges between the surfaces. In the third part we focus on dense HS structures, formed below the transition. We show analysis of ordering of the hexagonal structures, formed between two different types of substrates, softer and stronger, both imposing planar degenerate anchoring. We find the degree of ordering to depend mainly on substrate type, confinement, thickness and temperature. For both substrate types we show, there is an order-disorder transition with thickness and that the transition region is significantly narrower in case of softer substrates. We describe the dynamics of lattice HS at different thicknesses and types of substrates. We observe that dynamics becomes unconstrained in case of softer substrates and drastically increases with decreasing thickness below 100~nm. In summary, the goal of this thesis is description of static and dynamic properties of novel skyrmion-based chiral phases, found in nematic liquid crystals, close to, and below the phase transition from the isotropic phase.

• Language: English
• Keywords: skyrmions, half-skyrmions, blue phases, BPIII, chirality
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-147163
• COBISS.SI-ID: 156665603
• Publication date in RUL: 24.06.2023

Secondary language

• Language: Slovenian
• Title: Statične in dinamične lastnosti pol-skirmionov v tankih plasteh kiralnih tekočih kristalov

Abstract

Skirmioni so nesingularne vrtinčaste strukture zveznih vektorskih polj, ki jim struktura nudi topološko zaščito in zagotavlja energijsko stabilnost. Najti jih je mogoče v raznolikih fizikalnih sistemih, med katerimi so tudi nematski tekoči kristali. Modre faze (BP) kiralnih nematskih tekočih kristalov tvorijo valjasti filamenti s skirmionskim profilom, zloženi v 3D kubično (BPI/BPII) ali amorfno strukturo (BPIII). V obeh primerih so obdani z mrežo defektnih linij, v katerih ni ureditve. V tem doktorskem delu obravnavamo tri pojave, povezane z modrimi fazami ter strukturami, ki jih tvorijo ob ograditvi v tanko plast. V prvem delu eksperimentalno in s pomočjo numeričnih simulacij pokažemo, da je modra faza tipa III 3D dinamična tekočina skirmionov z delnim nabojem. Podobno kot v primeru BPI tudi tu opazimo, da se ob ograditvi v plast debeline manjše od kiralne periode struktura pretvori v 2D mrežo polskirmionov. Strukture, ki jih vidimo pod mikroskopom v veliki meri poustvarimo z optičnimi simulacijami na izračunanih strukturah. V meritvah BPIII opazimo dva hitrostno razmaknjena dinamična načina. Počasnejši način razumemo kot posledico gibanja in preurejanja skirmionskih filamentov ter defektnih linij, hitrejšega pa kot posledico fluktuacij povprečne ureditve znotraj filamentov. V drugem delu obravnavamo strukturne fluktuacije, ki se pojavijo ob ograditvi kiralnega nematika v plasteh z debelinami, manjšimi od 100~nm, na prehodu med izotropno in skirmionsko fazo. Fluktuacije sestojijo iz stohastičnega nastajanja, izginjanja in dinamičnega spreminjanja polskirmionov ter njihovih delov. Opazne so v območju soobstoja faz in so dovolj počasne, da jih je mogoče opazovati v realnem času. Dinamika postaja vse hitrejša z naraščajočo temperaturo, kar potrdimo na dva načina: (i) s sledenjem migetajočim strukturam zajetih na videu, in (ii) s pomočjo metode diferenčne dinamične mikroskopije. Podobno dinamiko opazimo tudi blizu prehoda v ograjeni nematski fazi akiralnega kristala blizu kritične debeline. Pod slednjo je mehanizem nastanka nematske faze kapilarna kondenzacija, ki poteka zvezno s temperaturo. V ozkem območju debelin nad njo pa zaradi termičnih fluktuacij potekata tvorba in razpad kapilarnih mostičkov nematske faze. Da je tak mehanizem faznega prehajanja mogoč le v tankih plasteh, pokažemo s preprostimi energijskimi argumenti, ki slonijo na Landau-de Gennesovi teoriji faznega prehoda. Tretji del je posvečen obravnavi prehoda med urejeno in neurejeno mrežo polskirmionov v ograjeni BPI, ki ga opazimo z manjšanjem debeline pri konstantni temperaturi. Pokažemo, da poleg debeline stopnjo ureditve določata tudi temperatura ter interakcija s površinami. V primeru, ko se polskirmioni tvorijo med površinama, prevlečenima s polimerom PMMA, je prehod med neurejeno in urejeno polskirmionsko fazo z večanjem debeline vidno ostrejši kot v primeru navadnega stekla. Opišemo mehanizem dinamike mrežnih polskirmionov in njeno aktivnost pri različnih debelinah in temperaturah. Ta se v primeru PMMA površin sprosti in z manjšanjem debeline pod 100~nm izrazito poveča. Če povzamem, je cilj doktorskega dela predstavitev statičnih in dinamičnih lastnosti skirmionskih faz kiralnih tekočih kristalov v ograditvi v bližini faznega prehoda in pod njim.

• Keywords: skirmioni, pol-skirmioni, modre faze, BPIII, kiralnost