One effective tool to probe a system revealing topological order is to biparti- tion the system in some way and look at the properties of the reduced density operator corresponding to one part of the system. In this thesis we focus on a bipartition scheme known as the particle cut in which the particles in the system are divided into two groups and we look at the rank of the re- duced density operator. In the context of fractional quantum Hall physics it is conjectured that the rank of the reduced density operator for a model Hamiltonian describing the system is equal to the number of quasi-hole states. Here we consider the Laughlin wave function as the model state for the system and try to put this conjecture on a firmer ground by trying to determine the rank of the reduced density operator and calculating the number of quasi-hole states. This is done by relating this conjecture to the mathematical properties of symmetric polynomials and proving a theorem that enables us to find the lowest total degree of symmetric polynomials that vanish under some specific transformation referred to as clustering transformation.

<p>Ytterligare forskningsfinansiärer: Knut and Alice WallenbergFoundation for a Fellowship Grant and Project funding (KAW 2015.0043), Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO MatLiUNo. 2009 00971), Swedish Research Council VR-RFI (#2017-00646_9), Swedish Foundation for Strategic Research(contract RIF14-0053)</p>

Despite the weak interaction between electrons and atomic vibrations (phonons) in the one-atom thick crystal of carbon called graphene, the scattering of electrons off phonons limits coherent electron transport in pristine devices over mesoscopic length scales. The future of graphene as a replacement to silicon and other materials in advanced electronic devices will depend on the success of controlling and optimizing electronic transport. In this dissertation, we explore the electron-phonon interaction via Raman scattering, elucidating the effects of filling and emptying charge states on the phonons in both the metallic state and when levels are quantized by an applied perpendicular magnetic field. In zero magnetic field, the phonon energy shifts due to electronic screening by charge carriers. Previously, a logarithmic divergence of the phonon energy was predicted as a function of the charge carrier density. For the first time, we observe signatures of this logarithmic divergence at liquid He temperatures after vacuum annealing on single layers. We also measure the electron-phonon coupling strength, Fermi velocity, and broadening of electronic quantum levels from Raman scattering and correlate these parameters to electronic transport. In a strong perpendicular magnetic field, the energy bands split into discrete Landau levels. Here, we observe kinks and splitting of the optical phonon energy, even when the Landau level transitions are far from resonant with the phonons. We discover that the kinks are attributed to charge filling of Landau levels, as understood from a linearized model based on electron-phonon interactions. Moreover, we show that material parameters determined without magnetic fields also describe phonon behavior in high magnetic fields.

The recent decades of research in molecular biology have resulted in break-throughs concerning our knowledge of the genetic code, protein structures and functions of the different cellular components. With this new information follows an increased interest in constructing computational models of the biological systems. A computational model can range from a description of one specific protein to a complete cell or organism. The aim of a computational model is often to complement the experimental studies and help identify essential mechanisms of a system. All processes taking place in our cells, from general metabolic processes to cell specific actions, originates from information encoded in our DNA. The first step in transferring the genetic information to a functional protein or RNA, is through the transcription of a gene. The transcription process is controlled by cellular proteins binding to DNA regions called promoters. The term "genetic switch", used in the title of this thesis, refers to a specific change in transcription activity, where one or several promoters get activated or silenced. In this thesis, I present studies of the regulation mechanisms in two different genetic switches. The first is a switch between two central promoters in the Epstein- Barr virus. This human virus is mostly known for causing the ’kissing disease’, but is also coupled to several cancer types. Infected cells can change between a resting and a proliferating phenotype, depending on which viral promoter is active. In order to understand what causes uncontrolled proliferation in tumors, it is important to understand the regulation of these viral promoters. The other switch is present in the phage λ, a bacterial virus. This virus has one specific promoter region, controlling expression of two proteins that determine if the phage will remain silent (lysogenic) in the host cell, or start producing new viral particles (go lytic). For the Epstein- Barr virus we tested, and confirmed, the hypothesis that the regulation of the two central promoters can be obtained by only one viral and one human protein. Further, we studied the cooperative effects on one of the promoters, showing that steric hindrance at the promoter region results in a more effective switching than with only cooperative binding present. For the bacteriophage λ we studied the genetically altered λ- Lac mutants, presented by Little &amp; Atsumi in 2006. We demonstrate that the experimental results cannot, in terms of its equilibria, be explained by the mechanisms generally believed to be in control of the lysogenic/ lytic switch. / QC 20101119

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.

<p>Nitride semiconductors are promising for applications in opto-electronic devices due to their wide band gap that is adjustable by appropriate choice of alloy composition. To date, many III-nitride devices have been demonstrated, such as light-emitting diodes, lasers, etc. Most opto-electronic devices make use of the optical transition from conduction band to valence band. Moreover, the large conduction band offset achieved by III-nitrides makes it possible to take advantage of transitions inside the conduction band or valence band, which provide much more freedom for band engineering. Although many III-nitrides based opto-electronic devices have been invented and implemented in commercial use, there is still a need for more compact, rugged, higher efficiency devices with lower cost. Many challenges of III-nitride semiconductors are related to material defects, lattice mismatch and internal polarization fields. Photoluminescence is a convenient technique to characterize sample quality and optical properties. It does not destroy the samples or need any electrical contacts. Therefore, it is commonly used in qualitative analysis of III-nitrides. This thesis focuses on non-polar m-plane III-nitrides structures, because this crystal orientation eliminates internal polarization fields in heterostructures. We first performed a photoluminescence study of a series of m-plane InGaN thin films with In compositions up to 24.5%. Evidence of large In composition fluctuations was observed. This inhomogeneity of In composition contributes to the non-monotonic temperature dependence of photoluminescence peak energy and linewidth. A large drop of internal quantum efficiency when temperature increases to room temperature was observed, which indicates the presence of a large number of non-radiative recombination centers. This is due to low temperature growth of InGaN by plasma assisted molecular beam epitaxy. The InGaN film with 11% has a linewidth close to theoretical calculations for InGaN with random In distribution, and much smaller than many reported polar c-plane InGaN films with comparable In compositions, which suggests improved material quality. This In composition was selected for the design of InGaN/AlGaN superlattices.</p> <p>In order to avoid the disadvantage of strain buildup, we designed nearly strain-balanced non-polar m-plane InGaN/AlGaN structures with In composition of about 9%. Steady-state photoluminescence and time-resolved photoluminescence were performed on these structures. A significant discrepancy between measured and calculated PL peak positions was observed. This is likely due to the In composition fluctuations and quantum confinement in quantum wells. The broadening mechanism of the PL in the superlattices was investigated. The low-temperature linewidth of undoped superlattices is comparable to many previously reported values for m-plane InGaN/GaN quantum wells. Similar to InGaN films, the internal quantum efficiency drops dramatically when temperature reaches room temperature. Regions with high In compositions act as localization centers for excitons. An average localization potential depth of 21 meV was estimated for undoped superlattices. This small potential depth does not reduce the degree of polarization of emitted light, and contributes to the narrow linewidth. A fast decay time of 0.3 ns at 2 K was observed for both doped and undoped superlattices. This value is much smaller than that for polar c-plane InGaN/GaN superlattices. The localization of excitons was found to be strong and not affected by magnetic field at low temperatures. Compared with undoped superlattices, the doping sheets reduce decay pathways of excitons in doped superlattices.</p> <p> </p>