As crystals are classified by space groups, nematic liquid crystals should be in principle classified by point groups. Conventionally, the study of nematic liquid crystals has mainly been focused... Show moreAs crystals are classified by space groups, nematic liquid crystals should be in principle classified by point groups. Conventionally, the study of nematic liquid crystals has mainly been focused on a very small subset of the whole nematic family, partly because of limitations of traditional methods. In this thesis, we introduce a non-Abelian gauge theory that can treat nematic phases with arbitrary point group symmetries in a unified framework in an efficient way. The proposed gauge theory allows us to compare nematic phases against a common reference. We are therefore able to quantify the orientational fluctuations of nematic orders with different symmetries and identify a novel chiral liquid phase. Moreover, this gauge theory can act as an order-parameter generator, and we thus achieve a full classification of nematic-order-parameter tensors, which has never been done before. Finally, we show that the gauge theory provides a convenient way to access the anisotropy of axial orders, by which we generalize the extensively studied biaxial-uniaxial transition of D2h nematics to a much broader class. Show less
This thesis deals with two different models in two different contexts. The first part deals with dynamical Gibbs-non-Gibbs transitions. Gibbs measures describe the equilibrium states of a system... Show moreThis thesis deals with two different models in two different contexts. The first part deals with dynamical Gibbs-non-Gibbs transitions. Gibbs measures describe the equilibrium states of a system consisting of a large number of components that interact with each other. Due to the large number of particles, it is natural to assume that the state of the system is random. Gibbs measures capture this randomness. This description involves some particular ``regularity'' conditions for the conditional probabilities. The question of interest is whether this condition remains valid after the system is subjected to a stochastic dynamic. Is it still possible to describe the evolved measure as a Gibbs measure? The second part deals with stochastic geometry. The relevant information about the particles is their position. Particles may be placed at random in any region of the space. Subsequently, each particle is displaced independently of each other according to a d-dimensional Brownian Motion during t time, and the trace produced by that motion is recorded. The question of interest is whether the final set obtained from all the traces has an infinite connected component or not. If so, then is it unique? Show less
This thesis is devoted to the effects of disorder on two-dimensional systems of Dirac fermions. Disorder localizes the usual electron system governed by the Schroedinger equation. The influence of... Show moreThis thesis is devoted to the effects of disorder on two-dimensional systems of Dirac fermions. Disorder localizes the usual electron system governed by the Schroedinger equation. The influence of disorder on Dirac fermions is qualitevely different. We concentrate on a random mass term in the Dirac equation. We have discovered that Dirac fermions in graphene are localized by a random mass, without any transition into metallic state. The situation is entirely different for Dirac fermions in a p-wave superconductor. There electrostatic disorder appears in the Dirac equation as a random mass, which localizes the excitation, but only if the disorder is relatively weak. For large mass fluctuations a transition into metallic state appears. This qualitatively different response to disorder in graphene and in p-wave superconductors is explained by the appearance of Majorana bound states, which allow for resonant tunneling and metallic state. Electrostatic disorder in a d-wave superconductor represented as random vector potential in the Dirac equation. We look at the transmission of Dirac fermions for electrostatic potential with long- and short-range fluctuations. We study the interplay of electrical and mechanical properties of suspended graphene by calculating the correction to the conductivity due to its deformation by a gate electrode. Show less
This thesis concerns the symmetry, phase, and order parameter of the superfluid helium-3 in restricted geometries in combination with a magnetic field. Two cylindrical containers are constructed... Show moreThis thesis concerns the symmetry, phase, and order parameter of the superfluid helium-3 in restricted geometries in combination with a magnetic field. Two cylindrical containers are constructed for which the axis is aligned with the magnetic field. The first cell has a diameter (540 nm) of only a few times the size of the Cooper pairs, designed to find a new superfluid phase, namely the polar has. The second container has a diameter of 1 mm, which is the ideal size to create a potential (in the B-phase) for spin waves. To probe any superfluid phase, or spin waves, we use Nuclear Magnetic Resonance (NMR) Techniques. As the superfluids have an anisotropic susceptibility, it is an excellent tool to distinguish the different phases. However, as our samples are relatively small in volume, and the experiments needs to be performed in low magnetic field to prevent additional symmetry breaking, a very sensitive read-out magnetic resonance detection system needs to be developed, which is accomplish by creating an LC-circuit which maintains an ultra-high quality factor as it is combined with a weakly coupled transformer. Show less
Doped manganese oxides such as La0.67Ca0.33MnO3 (LCMO) are strongly correlated electron systems which display an insulator to metal transition upon cooling at a temperature T_MI. At low temperature... Show moreDoped manganese oxides such as La0.67Ca0.33MnO3 (LCMO) are strongly correlated electron systems which display an insulator to metal transition upon cooling at a temperature T_MI. At low temperature the material is ferromagnetic. Above the transition the material is a paramagnetic insulator in which conduction is governed by activated polaron hopping. As yet, the fundamental question of conductance on micrometer length scales (the scale on which electronic phase separation can occur) has been little studied. We investigate this question of electrical transport in LCMO, which requires the fabrication of micron sized structures in LCMO thin films. We measure current-voltage (I-V) characteristics as function of temperature, in high magnetic fields, in electric fields and with varying film thickness. In warming from the metallic to the insulating state we find strong non-linear effects in the steep part of the transition. The differential resistance is largest at zero bias, then drops with increasing current, and saturates at a current density which is the same for different samples. Resistance drops of up to 80 % are observed upon increasing the applied current. We propose that the nonlinear behavior is a direct signature of an intervening phase involving the formation of short range polaron correlations (electron-glass). The nonlinear behavior occurs when the homogeneous glass phase which now encompasses the entire microstructure is melted by the applied electrical current. We also associate the formation of inhomogeneities in the microstructure with the appearance of a strong electric field effect. Show less
This thesis describes the work performed on crystals with a phase transition to a Charge-Density Wave (CDW). The electrical transport properties change when crystal sizes are smaller than... Show moreThis thesis describes the work performed on crystals with a phase transition to a Charge-Density Wave (CDW). The electrical transport properties change when crystal sizes are smaller than characteristic length scales for CDWs, typically 1 micrometer. In contrast to metals, semiconductors and superconductors, reduction of sizes is relatively unexplored in the case of CDWs. The development of methods to reduce sizes of CDW crystals are described in this thesis. Numerous finite-size transport effects are found as a result of the development of these new fabrication methods. These finite-size effects have led to the development of models to describe the microscopic aspects of CDWs. Show less
