2024 / Topological quantum states of matter are a central focus in modern condensed matter physics and quantum information science. The study of topological order in quantum spin systems is closely linked to the concept of gauge symmetries. In this dissertation, we conduct detailed studies of two quantum spin systems with local gauge symmetries. Specifically, we numerically investigate a recently proposed theoretical model that realizes local Z2 gauge symmetry with only two-body interactions.We confirm the existence of topological order and explore other physical properties within the model in depth. In the study of the U(1) toric code, we enhance the conventional Kitaev’s toric code by introducing global U(1) symmetry. The study emphasizes the interplay between local Z2 gauge symmetry and constraints arising from global U(1) symmetry. This examination uncovers the presence of topological degeneracy and reveals an unconventional UV/IR mixing phenomenon within the system. We explore possible implementations of the U (1) toric code in superconducting wires and discuss potential future research directions based on the insights gained from our investigations of these two models.

One of the most important and interesting unsolved problems of science is the nature of glassy dynamics and the glass transition. It is quite an old problem, and starting from the early20th century there have been many efforts towards a sound understanding of the phenomenon. As a result, there are a number of theories in the field, which do not entirely contradict each other, but between which the connection is not entirely clear. In the last couple of decades or so, there has been significant progress and currently we do understand many facets of the problem. But a unified theoretical framework for the varied phenomena associated with glassiness is still lacking. Mode-coupling theory, an extreaordinarily popular approach, came from Götze and co-workers in the early eighties. The theory was originally developed to describe the two¬ step decay of the time-dependent correlation functions in a glassy fluid observed near the glass transition temperature(Tg). The theory went beyond that and made a number of quantitative predictions that can be tested in experiments and simulations. However, one of the drawback of the theory is its prediction of a strong ergodic to non-ergodic transition at a temperature TMCT; no such transition exists in real systems at the temperatures at which MCT predicts it. Consequently, the predictions of the theory like the power-law divergences of the transport quantities (e.g., viscosity and relaxation time) fail at low enough temperature and the theory can not be used below TMCT. It is well understood now that MCT is some sort of a mean-field theory of the real phenomenon, and in real systems the transition predicted by MCT is at best avoided due to finite dimensions and activated processes, neither of which is taken into account in standard MCT. Despite its draw backs, even the most severe critic of the theory will be impressed by its power and the predictions in a regime where it works. Even though the non-ergodic transition predicted by the theory is averted, the MCT mechanism for the increase of viscosity and relaxation time is actually at work in real systems. The status of MCT for glass transition is ,perhaps, similar to the Curie-Weiss theory of magnetic phase transition and it will require hard work and perhaps a conceptual breakthrough to go beyond this mean-field picture. Discussion of such a theoretical framework and its possible directions are, however, beyond the scope of this thesis. In the first part of this work, we have extended the mode coupling theory to three important physical situations: the properties of fluids under strong confinement, a sheared fluid and for the growth kinetics of glassy domains. In the second part, we have studied a different class of non equilibrium phenomenon in arrested systems, the fluctuation relations for yielding. In the first chapter, we talk about some general phenomenology of the glass transition problem and a few important concepts in the field. Then we briefly discuss the physical problems to be addressed in detail later on in the thesis followed by a brief account of some of the important existing theories in the field. This list is by no means exhaustive but is intended to give a general idea of the theoretical status of the problem. We conclude this chapter with a detailed derivation of MCT and its successes and failures. This derivation is supposed to serve as a reference for the details of the calculations in later chapters. The second chapter deals with a simple theory of an important problem of lubrication and dynamics of fluid at nanoscopic scales. When a fluid is confined between two smooth surfaces down to a few molecular layers and an normal force is applied on the upper surface, it is found that one layer of fluid gets squeezed out of the geometry at a time. The theory to explain this phenomenon came from Persson and Tosatti. However, due to a mathematical error, the in-plane viscosity term played no role in the original calculation. We re-do this calculation and show that the theory is actually more powerful than was suggested originally by its proponents. In the third chapter, we work out a detailed theory for the dynamics of fluid under strong planar confinement. This theory is based on mode-coupling theory. The walls in our theory enter in terms of an external potential that impose a static inhomogeneous background density. The interaction of the density fluctuation with this static background density makes the fluid sluggish. The theory explains how the fluid under strong confinement can undergo a glassy transition at a higher temperature or lower density than the corresponding bulk fluid as has been found in experiments and simulations. One of the interesting findings of the theory is the three-step relaxation that has also been found in a variety of other cases. The fourth chapter consists of a mode-coupling calculation of a sheared fluid through the microscopic approach first suggested by Zaccarelli et al[J. Phys.: Condens. Matter 14,2413(2002)]. The various assumptions of the theory are quite clear in this approach. The main aim of this calculation is to understand how FDR enters with in the theory. The only new result is the modified form of Yvon-Born-Green(YBG) equations for a sheared fluid. Then we extend the theory for the case of a confined fluid under steady shear and show that a confined fluid will show shear thinning at a much lower shear rate than the bulk fluid. When a system is quenched past a phase transition point, phase ordering kinetics begins. The properties of the system show “aging” with time, and the characteristic length scale of the quenched system grows as one waits. The analogous question for glasses has also been asked in the contexts of various numerical and experimental works. We formulate a theory in chapter five for rationalizing these findings. We find that MCT, surprisingly, offers an answer to this key question in glass forming liquids. The challenge of this theory is that care must be taken in using some equilibrium relations like the fluctuation-dissipation relation(FDR), which is one of the key steps in most of the derivations of MCT. We find that the qualitative, and some times even the quantitative, picture is in agreement with numerical findings. A similar calculation for the spin-glass case also predicts increase of the correlation volume with the waiting time, but with a smaller exponent than the structural glass case. We extended this theory to the case of shear and find that shear cuts off the growth of the length-scale of glassy correlations when the waiting time becomes of the order of the inverse shear rate. For the case of sheared fluid, if we take the limit of the infinite waiting time, the system will reach a steady state. Then, the resulting theory will describe a fluid in sheared steady state. The advantage of this theory over the existing mode-coupling theories for a sheared fluid is that FDR has not been used in any stage. This is an important development since the sheared steady state is driven away from equilibrium. Interestingly, the theory captures a suitably-defined effective temperature and gives results that are consistent with numerical experiments of steady state fluids(both glass and granular materials). We give the details of a theoretical model for jamming and large deviations in micellar gel in the sixth chapter. This theory is motivated by experiments. Through the main ingredient of the attachment-detachment kinetics and some simple rules for the dynamics, the theory is capable of capturing all the experimental findings. The novel prediction of this work is that in a certain parameter range, the fluctuation relations may be violated although the large deviation function exists. We argue that a wider class of physical systems can be understood in terms of the present theory. In the final chapter, we summarize the problems studied in this thesis and point out some future directions.

This dissertation attempts to understand how energy transfer in a molecular wire and a spherical organic assembly are affected by molecular structure. The molecular wire is a DNA-hybrid structure composed of a strand of thymine bases appended by a cyanine dye. Hydrogen bonded to each base is a naphthalene-derivative molecule. Using time-integrated photoluminescence and time-correlated single photon counting measurements, energy transfer from the naphthalene donors to the cyanine acceptors was confirmed, and its dependence on temperature and DNA-template length investigated. Donor-thymine bonding was disrupted at temperatures above about 25 degrees Celcius resulting in poor donor template decoration and low rates of energy transfer. Increasing numbers of donors attach to the scaffold, forming an orderly array, as the template length increases due to the stabilising effects of the donor-donor pi-stacking interactions. Conversely, modelled energy transfer rates fall as the scaffold length increases because of the longer donor-acceptor distances involved. Therefore, the energy transfer rate was greatest for a template built from 30 thymines. The spherical organic assemblies (nanoparticles) are formed by fast injection of a small volume of molecularly dissolved fluorene-derivative amphiphilic molecules into a polar solvent. The amphiphilic molecules contained either a naphthalene (donor) or a benzothiadiazole (acceptor) core. The donor-acceptor mixed nanoparticles resemble an amorphous polymer film and were modelled as such using the Foerster resonance energy transfer theory. The Foerster radii extracted from the measurements depends intricately on the donor-acceptor spectral overlap and distance. The latter effect was controlled by the stacking interactions between the molecules. Altering the morphology of the structural units is the key to optimising energy transfer in molecular structures. To achieve efficient organic molecule-based devices, the importance of this property needs to be fully appreciated and effectively exploited.

Through our whole work we study the XY model with all its entirety, a particular spin model where spins are confined in a plane. We try to bring out a good understanding of this model with all different types of phases and phase transition, it undergoes in critical situations. We conceive of these external conditions from very different physical models like High Tc Superconductor, Ultracold atoms in optical lattice which are in focus of recent research. Firstly we model high Tc Superconductors with very simple 2D XY model to get an idea about the diamagnetic response exhibited by these materials when kept in a external magnetic field. This modeling is reasonable because most of the physics of cuprate High Tc Superconductors are governed by their 2D copper oxide planes which insists us to consider 2D models. Later we shifted to a more realistic 3D anisotropic XY model , as the coupling between cuprates plane may have a considerable role in devising physics of those materials. We particularly focus on the 2D to 3D crossover effect on magnetisation showed by these models, with keeping an eye on how all these can be relate to the experimentally acquired magnetisation profile of High Tc Supercondutors. On the second project we investigate on the phase diagram of a fully frustrated 2-leg ladder Bose Hubbard model. After mapping it properly to a classical model, a bi-layer Fully Frustrated XY model on square lattice, we found that the frustration leads to the emergence of a new phase "Chiral Mott insulator(CMI)" sandwiched between "Chiral Superfluid(CSF)" and "regular Mott insulator(MI)" phase. We divide the whole report into four parts. The first chapter is basically contain-ing introductory part comprising the motivation. In the second chapter we discuss various types of phases and phase transitions of the 2D & 3D XY models. We try to address their critical behaviors. In the third chapter and onwards we consider our model in external magnetic field and observe magnetisation in these systems. Here we specially focus on 2D to 3D crossover effect on magtisation measurement. Lastly in the fourth chapter we bring out a correspondence of XY model with the 2 leg ladder fully frustrated Bose Hubbard Model. There we report the emergence of a new phase, Chiral Mott Insulator(CMI) due to frustration in system.

The main goal of this thesis was to simulate a solar cell with the symbolic manipulation tool Maple and discuss the strength and weaknesses of using Maple instead of the already known simulation program PC1D. This was done mainly by solving the three essential differential equations governing the current density and excess electron and hole densities in the solar cell. This could be done easily by using known simplifications especially the low injection assumption. However it was also a success without using this particular simplification but the solutions had to be achieved using a numerical method instead of direct methods. The results were confirmed by setting up the same solar cell with PC1D. The conclusion is that Maple gives the user increased freedom when setting up the solar cell, however PC1D is easier to use if this freedom is not needed. At the end of this thesis a brief introduction is also made on the possibility of using Maple with a tandem cell setup instead of single junction.

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<p>A new electron cyclotron plasma enhanced chemical vapour deposition (ECR-PECVD) reactor has been installed and tested at McMaster University. The focus of this project was the installation of the reactor and the growth of silicon oxide, silicon oxynitride, cerium doped silicon oxynitride and aluminium doped silicon oxide films to test the capabilities of the reactor. Silicon oxide films were prepared with near-stoichiometric compositions and silicon rich compositions. Good repeatability of the growths was seen. An increase in deposition temperature showed stable refractive index and a decrease in the growth rates. Silicon oxynitride films of varying compositions were prepared, and showed a non-uniformity of ~1% and growth rates of ~3.5 nm/min. Films prepared with a low oxygen flow were seen to be nitrogen rich. Although the depositions using Ce(TMHD)4 showed significant cerium incorporation, there was also high carbon contamination. One likely cause of this is the high sublimator temperature used during depositions or a thermal shock to the precursor during initial system calibration. A definitive cause of the carbon contamination has not been established. The cerium films showed strong blue luminescence after post-deposition annealing in N2 above 900° C. A drop in the luminescence was observed at 1100° C and a return of the luminescence at 1200° C. Generally, high cerium incorporation was associated with higher total luminescence. Al(THMD)3 was evaluated as an aluminium precursor for Al-doped silicon oxide films. The films showed aluminium content up to 6% demonstrating the viability of using Al(THMD)3 as a Al doping precursor.</p> / Master of Applied Science (MASc)

Master of Science / Department of Physics / Robert Szoszkiewicz / Proteins are involved in many of the essential cellular processes, such as cell adhesion, muscle function, enzymatic activity or signaling. It has been observed that the biological function of many proteins is critically connected to their folded conformation. Thus, the studies of the process of protein folding have become one of the central questions at the intersection of biophysics and biochemistry. We propose to use the changes of the nanomechanical properties of these biomolecules as a proxy to study how the single proteins fold. In the first steps towards this goal, the work presented in this thesis is concentrated on studies of unfolding forces and pathways of one particular multidomain protein, as well as on development of the novel method to study elastic spring constant and mechanical energy dissipation factors of simple proteins and peptides. In the first part of this thesis we present the results of the mean unfolding forces of the NRR region of the Notch1 protein. Those results are obtained using force spectroscopy techniques with the atomic force microscope (AFM) on a single molecule level. We study force-induced protein unfolding patterns and relate those to the conformational transitions within the protein using available crystal structure of the Notch protein and molecular dynamics simulations. Notch is an important protein, involved in triggering leukemia and breast cancers in metazoans, i.e., animals and humans. In the second part of this thesis we develop a model to obtain quantitative measurements of the molecular stiffness and mechanical energy dissipation factors for selected simple proteins and polypeptides from the AFM force spectroscopy measurements. We have developed this model by measuring the shifts of several thermally excited resonance frequencies of atomic force microscopy cantilevers in contact with the biomolecules. Next, we provided partial experimental validation of this model using peptide films. Ultimately, our results are expected to contribute in the future to the developments of medical sciences, which are advancing at a level, where human health and disease can be traced down to molecular scale.

This thesis details the development of a novel photovoltaic device based on organometal halide perovskites. The initial focus of this thesis begins with the study of lighttrapping strategies in solid-state dye-sensitised solar cells (detailed in chapter 3). While I report enhancement in device performance through the application of near and far-field light-trapping techniques, I find that improvements remain step-wise due to fundamental limitations currently employed in dye-sensitised solar cell technology— notably, the available light-sensitising materials. I found a promising yet under researched family of materials in the methyl ammonium tri-halide plumbate perovskite (detailed in chapter 4). The perovskite light-sensitiser was applied to the traditional mesoscopic sensitised solar cell device architecture as a replacement to conventional dye yielding world-record breaking photo-conversion e!ciencies for solid-state sensitised solar cells as high as 8.5%. The system was further developed leading to the conception of a novel device architecture, termed the mesoporous superstructured solar cell (MSSC), this new architecture replaces the conventional mesoporous titanium dioxide semiconductor with a porous insulating oxide in aluminium oxide, resulting in very low fundamental losses evidenced through high photo-generated open-circuit voltages of over 1.1 V. This development has delivered striking photo-conversion ef- ficiencies of 10.9% (detailed in chapter 6).