doktorska disertacija
Saša Harkai (Author), Samo Kralj (Mentor)

Abstract

V delu obravnavamo kompleksne strukture linijskih defektov v enoosni nematski fazi, ograjeni v planparalelno geometrijo, in različne načine njihovega prevezovanja. Nematske strukture opisujemo na mezoskopski skali s tenzorskim nematskim ureditvenim parametrom. Ravnovesna stanja določimo z numerično minimizacijo pripadajoče proste energije sistema. Različne defektne strukture vsiljujemo topološko z robnimi pogoji na ograjujočih ploščah. Preko slednjih vsiljujemo dvodimenzionalne (2D) površinske defekte, karakterizirane z ovojnim številom m. Te robne pogoje lahko eksperimentalno realiziramo, npr. z vtisno metodo z uporabo mikroskopa na atomsko silo. Pozornost posvečamo predvsem t. i. topološko "nenabitim" disklinacijam z |m| = 1/2, katerih 3D topološki naboj je enak 0. Najprej preučimo strukturno raznovrstnost, ki jo omogoča površinsko vsiljen topološki defekt z m = 1. V odvisnosti od razmerja debeline celice glede na dvoosno korelacijsko dolžino in začetnih pogojev se v celici realizira bodisi linijski defekt z m = 1, razcepljeni defekt, ki ga sestavljata dve medsebojno odbijajoči liniji z m = 1/2, ali pa brezdefektna pobegla struktura. Stabilnosti ravnovesnih nematskih struktur in preklapljanje med njimi z uporabo zunanjega električnega polja preverimo tudi eksperimentalno. Pretežno antiparalelne "nenabite" linije v dovolj debelih celicah, ki so lokalizirane ob ograjujočih površinah, stabiliziramo s kvadratno mrežo 2 × 2 alternirajočih m = ±1/2 površinskih defektov. Pokažemo, da se takšni antiparalelni disklinaciji obnašata kot defekt in antidefekt s težnjo medsebojne anihilacije. Demonstriramo možno prevezavo med različnimi defektnimi nematskimi strukturami z uporabo zunanjega električnega polja. Z vsiljevanjem 4 × 4 vzorca alternirajočih defektov z m = ±1 na komandni površini v dovolj debelih celicah ustvarimo multistabilen sistem z 18 kvantitativno in 7 kvalitativno različnimi (meta)stabilnimi konfiguracijami. Na izbranih konfiguracijah demonstriramo, da jih lahko reverzibilno prevezujemo z zunanjim električnim poljem, kar kvalitativno tudi eksperimentalno reproduciramo. Pokažemo, da lahko "nenabite" disklinacije stabiliziramo tudi preko koloidov toroidne topologije. Topološko "nenabite" disklinacije izkazujejo lastnosti, podobne Majoranovim delcem. Rezultati so zanimivi zaradi fundamentalnih in aplikativnih razlogov. Različne konfiguracije defektov, ki jih vsilimo preko regularnih vzorcev 2D vtisnjenih defektov, potencialno tvorijo zanke periodičnih 3D struktur, ki so lahko uporabne za različne fotonske ali elektro-optične aplikacije.

Keywords

tekoči kristali;nematiki;topološki defekti;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [S. Harkai]
UDC: 538.9(043.3)
COBISS: 87958531 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Reconfigurable networks of nematic topological defects
Secondary abstract: The thesis covers complex line defect structures in a uniaxial nematic phase, bound by a planparallel geometry, and the different methods of reconfiguring them. We describe the nematic structures on a mesoscopic scale with a tensor nematic order parameter. Equilibrium states are determined through numerical minization of the corresponding free energy. We enforce different defect structures topologically using boundary conditions on enclosing surfaces, through which we enforce two-dimensional (2D) surface defects, characterized with a winding number m. The boundary conditions are experimentally reproducible with methods such as AFM scribing. We pay special attention to the so-called topologically "chargeless" |m| = 1/2 disclinations, whose 3D topological charge is equal to 0. First we study the structural diversity enabled by an m = 1 defect enforced by the surface. Depending on the ratio between the cell thickness and biaxial correlation length or the starting conditions, either an m = 1 line defect, a split defect, comprised of two mutually repulsive m = 1/2 lines, or a defect-less escaped structure is realized. We investigate the stability of equilibrium nematic structures and switching between them using an external electric field, which we verify experimentally. We stabilize the mostly antiparallel "chargeless" lines using a 2×2 pattern of alternating m = ±1/2 surface defects in thick enough cells. We show that such antiparallel disclinations behave like a defect and antidefect with a tendency to mutually annihilate. We demonstrate the possibility of rewiring between different defect structures using an external electric field. By enforcing a 4 × 4 pattern of m = ±1 alternating defects on the master surface, creating a multistable system with 18 quantitatively and 7 qualitatively (meta)stable configurations in thick enough cells. We demonstrate the ability to reversibly switch in select cases using an external electric field, which we qualitatively reproduce experimentally. We show the possibility of stabilizing "chargeless" disclinations using colloids with toroidal topology. Topologically "chargeless" disclinations exhibit properties, similar to Majorana particles. The results are interesting for fundamental and applicative reasons. The different defect configurations that we enforce using the regular patterns of 2D imprinted defects can potentially form loops of periodic 3D structures, which can be useful for various photonic or electro-optic applications.
Secondary keywords: liquid crystals;nematics;topological defects;Tekoči kristali;Disertacije;
Type (COBISS): Doctoral dissertation
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za fiziko
Pages: 85 str.
ID: 14047838