Vortices induced by electric and magnetic field and topological transitions in out of equilibrium systems

Abstract

Electrically driven nematic liquid crystal layers are ideal platform for studying the interactions of local topological defects, called vortices or umbilical defects. This thesis is devoted to experimentally and theoretically study the behavior of vortices in nematic liquid crystal cells under the influence of external electric and magnetic field. This dissertation is composed of six chapters and appendixes that contain articles published and manuscripts submitted during this work. In the first chapter, we present a theoretical and experimental framework required to understand the present dissertation. In second chapter, we investigate the interaction of vortices in an inhomogeneous nematic liquid crystal cell. Experimentally, we characterize the coarsening dynamics in samples containing glass beads as spacers and show that the inclusion of such imperfections changes the critical exponent of the coarsening law. Moreover, we demonstrate that slightly deformed beads attract vortices of both topological charges, thus, presenting a mainly quadrupolar behavior. Theoretically, based on a model of diluted vortices in a dipolar medium, a 2/3 exponent is inferred, which is consistent with the experimental observations. In third chapter, we investigate an experiment involving a liquid crystal cell under the influence of a low frequency oscillatory electric field. Unexpectedly, we observe topological states of matter in systems with injection and dissipation of energy. An amplitude equation with oscillatory parameters allows us to characterize the topological transition. In fourth chapter, we study a nematic liquid crystal cell under the combined effect of the electric and the magnetic field of a magnetic ring which exhibits a stable vortex triplet. Theoretically, an amplitude equation with topological forcing allows us to reveal the origin of the vortex triplet. A lattice of vortices is observed when the frequency of the applied voltage is decreased. By adding an inertia term to the amplitude equation it is possible to reveal the origin of this phenomenon. In fifth chapter, we investigate how the inherent fluctuations affect the vortex nucleation. Experimentally, the number of vortices was studied as a function of voltage and temperature. Theoretically, a model was derived to describe the number of vortices as a function of different parameters. Numerically, the number of vortices was studied as a function of the bifurcation parameter, anisotropy, and noise, showing a quite fair agreement with the experimental observations. Finally, in chapter six, we summarize the conclusions of this thesis and related perspectives.