Measurements of partial discharges are commonly used to diagnose the insulation system in high voltage components. Traditionally a single xed frequency of the applied voltage is used for such measurements as in the Phase Resolved Partial Discharge Analysis (PRPDA) technique. With the Variable Frequency Phase Resolved Partial Discharge Analysis (VF-PRPDA) technique the frequency of the applied voltage is instead variable. This technique provides more information about the condition of the insulation than the PRPDA technique. To extract the extra information a physical understanding of the frequency dependence of partial discharges is necessary. In this thesis partial discharges in cylindrical cavities in polycarbonate are measured using the VF-PRPDA technique in the frequency range 10 mHz { 100 Hz. It is studied how the cavity diameter and height inuence the frequency dependence of partial discharges. Insulated cavities are compared with cavities bounded by an electrode. It is shown that from measurements at variable applied frequency it is possible to distinguish between cavities of di erent dimensions and between insulated and metal bounded cavities. A two-dimensional eld model of partial discharges in a cylindrical cavity is developed. The sequence of discharges in the cavity is simulated by use of the eld computation program FEMLABR. Discharges are modeled with a voltage and current dependent streamer conductivity and are simulated dynamically to obtain charge and current consistency. It is shown that the frequency dependence of partial discharges is signi - cantly inuenced by the statistical time lag and by the two dielectric time constants related to charge movements on the cavity surface and in the bulk insulation. Simulation results are used to interpret the frequency dependent partial discharge activity in a cylindrical cavity. / QC 20101129

High-entropy alloys (HEAs) are composed of multi-principal elements with equal or near-equal concentrations, which open up a vast compositional space for alloy design. Based on first-principle theory, we focus on the fundamental characteristics of the reported HEAs, as well as on the optimization and prediction of alternative HEAs with promising technological applications. The ab initio calculations presented in the thesis confirm and predict the relatively structural stability of different HEAs, and discuss the composition and temperature-induced phase transformations. The elastic behavior of several HEAs are evaluated through the single-crystal and polycrystalline elastic moduli by making use of a series of phenomenological models. The competition between dislocation full slip, twinning, and martensitic transformation during plastic deformation of HEAs with face-centered cubic phase are analyzed by studying the generalized stacking fault energy. The magnetic moments and magnetic exchange interactions for selected HEAs are calculated, and then applied in the Heisenberg Hamiltonian model in connection with Monte-Carlo simulations to get further insight into the magnetic characteristics including Curie point. The Debye-Grüneisen model is used to estimate the temperature variation of the thermal expansion coefficient. This work provides specific theoretical points of view to try to understand the intrinsic physical mechanisms behind the observed complex behavior in multi-component systems, and reveals some opportunities for designing and optimizing the properties of materials / <p>QC 20171127</p>

<p>QC 20171219</p>

In this thesis, we aim to display characteristics of symmetry protected topological phases within quantum mechanics (QM). Building on well known aspects of QM, we relate the formalism to basic group representation theory, and review the connection between projective symmetries and protected vacuum degeneracies. Symmetries acting projectively on the Hilbert space, corresponding to non-trivial equivalence classes in group cohomology, guarantee degenerate vacua. Furthermore, considering QM in the framework of path integrals, we see that an SPT phase for the system consisting of a particle on a circle maps to a so-called "anomaly theory" in one dimension higher. / Uppsatsens ändamål är att presentera en grundläggande introduktion till symmetri bevarade topologiska faser (SPT) inom kvantmekanik. Med en genomgång av Kvantmekanikens formalism, påvisas ett samband mellan representationer av symmetrier och degenererade grundtillstånd. Mer specifikt, anmärker vi att G-symmetriska SPT faser har den besynnerliga egenskapen att parametriseras av ekvivalensklasser i G:s grupp kohomologi. Bevarade symmetrier med en icke-trivial projektiv fas, garanterar degenerarat vakuum. Vi undersöker även ett specifikt kvantmekaniskt system som består av en partikel på en ring. Under vägintegral-formalismen, uppenbaras då SPT fasen som en anomali för teorin.

The III-nitride semiconductors family includes gallium nitride (GaN), aluminum nitride (AlN), indium nitride (InN), and related ternary and quaternary alloys. The research interest on this group of materials is sparked by the direct bandgaps, and excellent physical and chemical properties. Moreover, the ternary alloys (InGaN, InAlN and AlGaN) present the advantage of bandgap tuning, giving access to the whole visible spectrum, from near infrared into deep ultraviolet wavelengths. The intrinsic properties of III-nitride materials can be combined with characteristical features of nanodimension and geometry in nanorod structures. Moreover, nanorods offer the advantage of avoiding problems arising from the lack of native substrates, like lattice and thermal expansion, film – substrate mismatch. The growth and characterization of group III-nitride semiconductos nanorods, namely InAlN and GaN nanorods, is presented in this thesis. All the nanostructures were grown by employing direct-current reactive magnetron sputter epitaxy. InxAl1−xN self-assembled, core-shell nanorods on Si(111) substrates were demonstrated. A comprehensive study of temperature effect upon the morphology and composition of the nanorods was realized. The radial nanorod heterostructure consists of In-rich cores surrounded by Al-rich shells with different thicknesses. The spontaneous formation of core-shell nanorods is suggested to originate from phase separation due to spinodal decomposition. As the growth temperature increase, In desorption is favored, resulting in thicker Al-rich shells and larger nanorod diameters. Both self-assembled and selective-area grown GaN nanorods are presented. Self-assembled growth of GaN nanorods on cost-effective substrates offers a cheaper alternative and simplifies device processing. Successful growth of high- quality GaN (exhibiting strong bandedge emission and high crystalline quality) on conductive templates/substrates such as Si, SiC, TiN/Si, ZrB2/Si, ZrB2/SiC, Mo, and Ti is supported by the possibility to be used as electrodes when integrated in optoelectronic devices. The self-assembled growth leads to mainly random nucleation, resulting in nanorods with large varieties of diameters, heights and densities within a single growth run. This translates into non-uniform properties and complicates device processing. These problems can be circumvented by employing selective-area growth. Pre-patterned substrates by nano-sphere lithography resulted in GaN nanorods with controlled length, diameter, shape, and density. Well-faceted c-axis oriented GaN nanorods were grown directly onto the native SiOx layer inside nano-opening areas, exhibiting strong bandedge emission at room- temperature and single-mode lasing. Our studies on the growth mechanism revealed a different growth behavior when compared with selective-area grown GaN nanorods by MBE and MOCVD. The time-dependent growth series helped define a comprehensive growth mechanism from the initial thin wetting layer formed inside the openings, to the well-defined, uniform, hexagonal NRs resulted from the coalescence of multiple initial nuclei.

In this thesis we have thermodynamically characterized finite time processes performed on a colloidal particle, kept in contact with thermal reservoir(s). Thermodynamic processes are implemented on the colloidal particle by systematically changing the confining potential in a time dependent way, according to an external driving protocol or by controlling the environmental conditions over a finite duration. First, we study two externally driven systems: one in which the driving is deterministic, and another where the driving is stochastic. These models have appeared in the literature as the building blocks of microscopic machines such as Brownian heat engines and are hence of interest to analyze. In particular, it is of interest to understand the distribution of work done by the colloidal particle as well as the distribution of heat dissipated. These distributions are known in all generality only in a very few cases. In the work we present here, we determine exactly the asymptotic forms of the work distributions (for a finite time duration of the process), which is shown to have non-Gaussian fluctuations. We also find a method to obtain the exact moment generating function of the work distribution, using which we can explicitly calculate aspects of a recently discovered relation for non-equilibrium systems, namely the thermodynamic uncertainty relation. To our knowledge, our model provides the only non-trivial example of a system where the uncertainty relation can be investigated exactly for all times. We have studied the system in various temporal regimes, and have found interesting features such as a time of minimum uncertainty, which may be relevant for the functioning of microscopic machines. Finally, we discuss, an experimentally realized colloidal heat engine model which consists of a single colloidal particle as the working substance. Exact finite time statistics can be obtained for this model using the methods we discuss in the thesis. We present our preliminary results illustrating this.

It is well known that in conventional three dimensional (3D) Hermitian two band models, the intersections between the energy bands are generically given by points. The typical example are Weyl semimetals, where these singular points can be effectively described as Weyl fermions in the low energy regime. By explicitly imposing discrete symmetries or fine-tuning, the intersection can form higher- dimensional nodal structures, e.g. nodal lines. By instead considering dissipative contributions to such a system, the degeneracies will generically take the form of closed 1D curves, consisting of exceptional points, i.e. points where the Hamiltonian becomes defective. By constructing the Hamiltonian in a particular way, the 1D exceptional curves can host non-trivial topology, i.e. they can form links or knots in the Brillouin zone. In stark contrast to line nodes occurring in Hermitian systems, which inevitably rely on discrete symmetries or fine tuning, the exceptional knots are generically stable towards any small perturbation. In further contrast to point singularities and unknotted circles, the topology of knots cannot be characterized by usual integer valued invariants. Instead, the complexity of the knottedness is captured by polynomial type invariants, making the physical classification and interpretation of these system challenging. To this end, the study of knotted nodal band structures naturally brings two different aspects of topology together – mathematical knot theory on the one hand, and the physical theory of topological phases on the other hand. This licentiate thesis focuses on providing the necessary theoretical background to understand the two accompanying publications entitled Knotted non-Hermitian metals, written by Johan Carlström, together with the author of this thesis, Jan Carl Budich and Emil J. Bergholtz, published in Physical Review B on April 24 2019, and Hyperbolic nodal band structures and knot invariants, written by the author of this thesis, together with Lukas Rødland, Gregory Arone, Jan Carl Budich and Emil J. Bergholtz, published in SciPost Physics August 8 2019. An introduction to gapless topological phases in the Hermitian regime, focusing on Weyl semimetals, their classification and surface states, is provided. Then, the light is brought to non-Hermitian operators and the differences from their conventional Hermitian counterpart, such as the two different set of eigenvectors bi-orthogonal to each other, exceptional eigenvalue degeneracies and some of their consequences, are explained. Afterwards, these operators are applied to dissipative physical system, and some of the striking differences from the conventional Hermitian systems are highlighted, the main focus being the possibly non-trivial topology of the 1D exceptional eigenvalue degeneracies. In order to be somewhat self contained, a brief conceptual introduction to the utilized concepts of knot theory is given, and lastly, further research directions and possible experimental realization of the considered systems are discussed.

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The study of the properties of magnetic materials is of primary importance in the development of newtechnologies. In this project, we aim to investigate the symmetries of some of the relevant properties ofa cobalt and platinum alloy that emerge from the symmetry of the crystal structure of the alloy. Morespecifically, our goal is to calculate the magnetocrystalline anisotropy energy (MAE) for various orientations of the magnetization. The MAE is computed through the implementation of density functionaltheory (DFT) via the open-source package OpenMX.The project consists of three main parts: Study on the convergence of the total energy of the systemas a function of some relevant parameters, computation of the energy, the spin magnetic moment andthe orbital magnetic moment as a function of the orientation of the magnetization, and a calculation ofthe magnetocrystalline anisotropy energy of the studied alloy.The studied system is an ordered compound of cobalt and platinum, with a tetragonal crystal structure.The easy axis of magnetization was found to be along the c-axis of the crystal, and defined accordinglytowards the z-axis in cartesian coordinates. The compound exhibits angular symmetry for the energy,the spin and orbital magnetic moments and the MAE, with a minimum energy along the easy axis ofmagnetization and a maximum at spherical angles θ=90◦ and ϕ=45◦. Looking at the plots for the MAE,this maximum can be interpreted as an energy barrier that must be surpassed in order to invert thedirection of the magnetization. Using an expression of the MAE in spherical angles, theoretical valuesfor the anisotropy constants K1, K2 and K3 are determined. / Computational Study of the Magnetocrystalline Anisotropy Energy of Ordered CoPt

This thesis aims to study the nonlinear electrical transport response of monolayer and bilayer graphene systems under the influence of different lattice deformations (strain). Broken inversion and rotation symmetries can generate a second-order transverse current response called the nonlinear Hall effect in the presence of time-reversal symmetry. The nonlinear Hall currents are proportional to the Berry curvature dipole (BCD), a quantity proportional to an intrinsic topological quantity known as the Berry curvature. We investigate homo-strain and hetero-strain in bilayer graphene, in which the two carbon layers are deformed symmetrically and asymmetrically respectively. Our numerical results show that bilayer graphene systems give a larger BCD, up to an order of magnitude using homo-strain and up to two orders of magnitude using heterostrain, when compared to monolayer graphene for the same strain due to larger Berry curvature and density of states. Furthermore, we obtain a large BCD in bilayer graphene under hetero-strain, which breaks both the inversion and three-fold rotational symmetries. Based on an effective k · p analysis, it is necessary to consider higher-order corrections, that are linear in momentum qj and strain uij, in the velocity renormalization of the Dirac fermions to obtain a finite Berry curvature induced by hetero-strain. Larger BCD and the implication of hetero-strain make bilayer graphene a better candidate for practical applications such as detecting terahertz radiation. The result of this thesis motivates the investigation of hetero-strain in twisted bilayer graphene, a hot topic in condensed matter physics. In particular, the impact of strain-induced velocity renormalization is not explored systematically in the literature, which can be a subject of future study.