<p>The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing.</p><p>This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory.</p><p>The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2<i>n</i>^-1, pertinent to nonabelian statistics, in the presence of 2<i>n</i> quasiholes in the Moore-Read state and generalise this result to 2<i>n</i>-<i>k</i> quasiholes and <i>k </i>quasielectrons.</p><p>In the third approach, we study the topological nature of the degeneracy 2<i>n</i>^-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-<i>T</i>c superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2<i>n</i>^-1 for 2<i>n</i> vortices.</p>

Materials at extreme conditions exhibit properties that differ substantially from ambient conditions. High pressure and high temperature expose anharmonic, non-linear behavior, and can provoke phase transitions among other effects. Experimental setups to study that sort of effects are typically costly and experiments themselves are laborious. It is common to apply theoretical techniques in order to provide a road-map for experimental research. In this thesis I cover computational algorithms based on first-principles calculations for high-temperature and high-pressure conditions. The two thoroughly described algorithms are: 1) the free energy studies using temperature-dependent effective potential method (TDEP), and 2) a higher-order elastic constants calculation procedure. The algorithms are described in an easy to follow manner with motivation for every step covered. The Free energy calculation algorithm is demonstrated with applications to hexagonal close-packed Iron at the conditions close to the inner Earth Core’s. The algorithm of elastic constants calculation is demonstrated with application to Molybdenum, Tantalum, and Niobium. Other projects included in the thesis are the study of effects of van der Waals corrections on the graphite and diamond equations of state. / Material vid extrema förhållanden uppvisar egenskaper som skiljer sig avsevärt från omgivningsförhållanden. Högt tryck och hög temperatur exponera anharmonicity, icke-linjärt beteende, och kan framkalla fasövergångar bland andra effekter. Experimentella uppställningar för att studera denna typ av effekter är vanligtvis dyra och experiment själva är mödosam. Det är vanligt att tillämpa teoretiska metoder för att ge en färdplan för experimentell forskning. I denna avhandling täcker jag beräkningsalgoritmer baserat på första principer beräkningar för hög temperatur och högt tryck. De två grundligt beskrivna algoritmer är: 1) den fria energin studier med temperaturberoende effektiv potentiell metod (TDEP), och 2) en högre ordning elastiska konstantberäkningsproceduren. Algoritmerna beskrivs i en lätt att följa sätt med motivation för varje steg som omfattas. Den fria energiberäkningsalgoritm visas med program till hexagonal tätpackad järn på villkoren nära jordens inre kärna. Algoritmen av elastiska konstanter beräkning demonstreras med tillämpning till molybden, tantal, och niob. Andra projekt som ingår i avhandlingen är effekterna av van der Waals-korrigeringar på tillståndsekvation och elastiska konstanter i grafit och diamant.

Salt is a common substance of which the structure has been investigated in this study. Molecular dynamics simulations has been performed of a solution of Caesium Chloride in water for four different concentrations. Radial distribution functions show a change in the structure of oxygen-oxygen with increasing concentration, especially for the second solvent shell. Contributions of the ions increases the separation between the water molecules and a long range peak of approximately 0.9 nm appears for higher concentrations. The results can be compared with experimental results performed at Swedish University of Agricultural Sciences. These distances are much longer (around 3.4 Å) and shows signs of cluster formation.

Thermoelectrics is the reversible process which transforms a temperature gradient across a material into an external voltage through a phenomenon known as the Seebeck effect. This has resulted in niche applications such as solid-state cooling for electronic and optoelectronic devices which exclude the need for a coolant or any moving parts and long-lasting, maintenance-free radioisotope thermoelectric generators used for deep-space exploration. However, the high price and low efficiency of thermoelectric generators have prompted scientists to search for new materials and/or methods to improve the efficiency of the already existing ones. Thermoelectric efficiency is governed by the dimensionless figure of merit 𝑧𝑇, which depends on the electrical conductivity, thermal conductivity and Seebeck coefficient value of the material and has rarely surpassed unity. In order to address these issues, research conducted on early transition metal nitrides spearheaded by cubic scandium nitride (ScN) thin films showed promising results with high power factors close to 3000 μWm−1K−2 at 500 °C. In this thesis, rock-salt cubic chromium nitride (CrN) deposited in the form of thin films by reactive magnetron sputtering was chosen for its large Seebeck coefficient of approximately -200 μV/K and low thermal conductivity between 2 and 4 Wm−1K−1. The results show that CrN in single crystal form has a low electrical resistivity below 1 mΩcm, a Seebeck coefficient value of -230 μV/K and a power factor close to 5000 μWm−1K−2 at room temperature. These promising results could lead to CrN based thermoelectric modules which are cheaper and more stable compared to traditional thermoelectric material such as bismuth telluride (Bi2Te3) and lead telluride (PbTe). In addition, the project resulting this thesis was prompted to investigate prospective ternary nitrides equivalent to ScN with (hopefully) better thermoelectric properties. Scandium nitride has a relatively high thermal conductivity value (close to 10 Wm−1K−1), resulting in a low 𝑧𝑇. A hypothetical ternary equivalent to ScN may have a similar electronic band structure and large power factor, but with a lower thermal conductivity value leading to better thermoelectric properties. Thus the elements magnesium, titanium, zirconium and hafnium were chosen for this purpose. DFT calculations were used to simulate TiMgN2, ZrMgN2 and HfMgN2. The results show the MeMgN2 stoichiometry to be stable, with two rivaling crystal structures: trigonal NaCrS2 and monoclinic LiUN2. / <p>The series name <em>Linköping Studies in Science and Technology Licentiate Thesis</em> is incorrect. The correct series name is <em>Linköping Studies in Science and Technology Thesis</em>.</p>

<p>A screened GPM approach in an EMTO-CPA framework was investigated in order to study its ability of describing transition temperatures in phase separating systems, i. e. systems giving either a random or a cluster structure depending on the temperature and the relative concentration of the ingoing atoms of the binary alloy used for the study. A motivation for the study is that the method works well for ordering systems, i. e. systems giving either a random or ordered structure dependent on the temperature and the relative concentration of the components in the binary alloy. Thereby is it of interest to find out the methods capacity in phase separating systems. The so called GPM potentials derived in the approach were applied in statistical Monte Carlo simulations for this purpose. The systems chosen for the investigation were the RhPd and the AlZn binary alloy systems. For both systems the method showed acceptable accuracy when properties as lattice parameter and mixing enthalpy were calculated. The quality of the derived GPM potentials has also been checked by calculating ordering energy for different ordered structures; directly from first principles calculations and from the GPM approach. The results were in acceptable agreement and thereby indicating that the GPM potentials were reliable. The transition temperatures in the RhPd phase diagram, derived by the statistical Monte Carlo simulations showed anyway deviation from experimental results. The error in the predictions might be due to the existing concentration dependencies in the GPM potentials.The conclusion from this study is that the Monte Carlo scheme might be inconvenient in order to handle the concentration dependencies seen in the GPM potentials.</p>

<p>Idag används guld som kontaktmaterial på elektriska kontakter för lågströmstillämpningar. Guldhar emellertid låg nötningsbeständighet, är dyrt och miljömässigt påfrestande att utvinna. Ettalternativt kontaktmaterial till guld är nanokomposit Ti-Si-C-Ag belagt medlikströmsmagnetronsputtring. Nanokomposit Ti-Si-C-Ag har hittills belagts med sammansatt Ti-Si-C sputterkälla och separat silverkälla.</p><p>I detta arbete har filmer belagts från tre olika sammansatta Ti-Si-C-Ag-källor med tre olikakolhalter. Filmerna har belagts i två olika beläggningssystem: Ett konventionellt batchladdat ochett sekventiellt med sluss.</p><p>Filmernas fas- och ämnessammansättning har studerats med XRD och EDX. Tjocklek ochmikrostruktur har analyserats med SEM. Vidhäftning och resistivitet har analyserats medRockwellindentation och ytresistansmätning med fyrpunktsprob. Kontaktresistansen har ävenstuderats i begränsad mån.</p><p>Arbetet visar att ökat kolinnehåll i källan ger kolrikare filmer med större titankarbidkorn.Resistiviteten ökar p.g.a. tilltagen amorf fas mellan kornen men kontaktresistansen sjunker givetduktilare film.</p> / <p>Today gold is used as contact material on electric contacts for low current applications. Gold, however,has low wear resistance, is expensive and environmentally stressful to produce. An alternative contactmaterial to gold is nano composite Ti-Si-C-Ag deposited with DC-magnetron sputtering. Nanocomposite Ti-Si-C-Ag has so far been deposited by a compound Ti-Si-C sputter source with a separateAg source.</p><p>In this work films have been deposited by three different compound Ti-Si-C-Ag sources with threedifferent carbon contents. The films have been deposited in two separate PVD systems: Oneconventional batch loaded and one sequential with a load-lock.</p><p>The phase- and elemental composition of the films has been studied with XRD and EDX respectively.Thickness and microstructure have been analysed with SEM. Adhesion and resistivity has beenanalysed with Rockwell indentation and surface resistivity measurement with four point probe. Contactresistance has also been studied to a limited extent.</p><p>The work shows that the increment of carbon content in the source yields more carbon rich films withlarger titanium carbide crystallites. The resistivity is increasing due to an increased amorphous phasebetween the crystallites but the contact resistance is decreasing due to a more ductile film.</p>

In this thesis I have studied some problems of condensed matter at high pressures and temperatures by means of numerical simulations based on Density Functional Theory (DFT). The stability of MgCO3 and CaCO3 carbonates at the Earth's mantle conditions may play an important role in the global carbon cycle through the subduction of the oceanic crust. By performing ab initio electronic structure calculations, we observed a new high-pressure phase transition within the Pmcn structure of CaCO3. This transformation is characterized by the change of the sp-hybridization state of carbon atom and indicates a change to a new crystal-chemical regime. By performing ab initio Molecular Dynamics simulations we show the new phase to be stable at 250 GPa and 1000K. Thus, the formation of sp3 hybridized bonds in carbonates can explain the stability of MaCO3 and CaCO3 at pressures corresponding to the Earth's lower mantle conditions. We have also calculated phase transition sequence in CaCO3, SrCO3 and BaCO3, and have found that, despite the fact that these carbonates are isostructural and undergo the same type of aragonite to post-aragonite transition, their phase transformation sequences are different at high pressures. The continuous improvement of the high-pressure technique led to the discovery of new composite structures at high pressures and complex phases of many elements in the periodic table have been determined as composite host-guest incommensurate structures. We propose a procedure to accurately describe the structural parameters of an incommensurate phase using ab initio methods by approximating it with a set of analogous commensurate supercells and exploiting the fact that the total energy of the system is a function of structural parameters. By applying this method to the Sc-II phase, we have determined the incommensurate ratio, lattice parameters and Wyckoff positions of Sc-II in excellent agreement with the available experimental data. Moreover, we predict the occurrence of an incommensurate high-pressure phase in Ca from first-principle calculations within this approach. The implementation of DFT in modern electronic structure calculation methods proved to be very successful in predicting the physical properties of a solid at low temperature. One can rigorously describe the thermodynamics of a crystal via the collective excitation of the ionic lattice, and the ab initio calculations give an accurate phonon spectra in the quasi-harmonic approximation. Recently an elegant method to calculate phonon spectra at finite temperature in a self-consistent way by using first principles methods has been developed. Within the framework of self-consistent ab initio lattice dynamics approach (SCAILD) it is possible to reproduce the observed stable phonon spectra of high-temperature bcc phase of Ti, Zr and Hf with a good accuracy. We show that this method gives also a good description of the thermodynamics of hcp and bcc phases of Ti, Zr and Hf at high temperatures, and we provide a procedure for the correct estimation of the hcp to bcc phase transition temperature.

The understanding of complex condensed matter systems is an area of intense study. In this thesis, some properties of simple liquids with strong preference for tetrahedral local ordering are explored. These liquids are amenable to supercooling, and give complex crystalline structures on eventual crystallisation. All liquids studied are simple, monatomic and are similar to real metallic liquids. The vibrational density of states of a glass created in simulation is calculated. We show a correspondence between the vibrational properties of the crystal and the glass, indicating that the vibrational spectra of crystals can be used to understand the more complex vibrational spectra of the glass of the same substance. The dynamics of supercooled liquids is investigated using a previously not implemented comprehensive measure of structural relaxation. This new measure decays more slowly in the deeply supercooled domain than the commonly used measure. A new atomic model for octagonal quasicrystals is presented. The model is based on findings from a molecular dynamics simulation that resulted in 45˚ twinned β-Mn. A decoration is derived from the β-Mn unit cell and the unit cell of the intermediate structure found at the twinning interface. Extensive simulations are used to explore the phase diagram of a liquid at low densities. The resulting phase diagram shows a spinodal line and a phase coexistence region between a liquid and a crystalline phase ending in a critical point. This contradicts the old conclusion of the Landau theory -- that continuous transitions between liquids and crystals cannot exist The same liquid is explored at higher densities. Upon cooling the liquid performs a first order liquid-liquid phase transition. The low temperature liquid is shown to be strong and to have very good glass forming abilities. This result offers new insights into fragile to strong transitions and suggests the possibility of a good metallic glass former. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Paper 3: In progress.

Nanomaterials because of their small size, may have special properties unlikely to be seen in ordinary types of materials. Nanomaterials like nanotubes,nanowires and nanoparticles are best studied at the nanoscale, vital but also problematic. In this thesis we use a transmission electron microscope (TEM)combined with a scanning tunneling microscope probe. This system allows TEM images to be captured and recorded into a movie together with recordedelectrical data for real time analysis. Using this method we found that the electrical conductivity of molybdenumbased nanowires Mo6S3I6 can be improved by current induced transformation. This might be a general method of improving nanowires which is of high valueif the wires are to be used in electrical circuits or field emission devices. The bending modulus for these nanowires were also determined, by an electromechanical resonance method, to 4.9 GPa. The sintering phase of silver nanoparticles, used in electrical conductive ink for printing electrical circuits, were studied by the in-situ TEM probing method. We observed that percolation path ways are formed and that the dispersive agent of the particles can be pyrolysed into a net of carbon with characteristics similar to graphite. We also developed a method for decorating nanowires and nanotubes with gold nanoparticles. Nanowire particle composites are often used in assembling more complex devices (electronic circuits) or for linking to organic molecules (biosensor applications) and existing particle decoration methods are either difficult or with low yield. By in situ TEM probing we found that carbon nanocages can be grown onto these gold nanoparticles. The size of the gold nanoparticles is controllable an thus the size of the nanocages. These nanocages may be used in medicine- or hydrogen storage-applications. / Nanomaterial har givits stort intresse under det senaste årtiondet, detta på grund av deras unika egenskaper som gör att de i många hänseenden överträffar traditionella material. Egenskaperna beror till största del på storlek och därför är det nödvändigt att studera dessa material på nanonivå, något som är problematiskt. För sådana studier krävs ett instrument med tillräckligt hög upplösning på nanonivå samt ett system med en prob som möjligör selektion och karakterisering utav individuella byggstenar. I denna avhandling används ett transmissionselektronmikroskop (TEM) tillsammans med ett sveptunnelmikroskop (STM) där det senare används som prob. Systemet medger studier på nanonivå och karakterisering av enskilda byggstenar under realtids avbildning (in situ). Metoden medger en bättre överblick och hanterbarhet vid nanomanipulering än vad till exempel atomkraftmikroskopi medger. Piezodrivna probar kan även användas i svepelektronmikroskop men dessa medger inte samma upplösning som transmissionselektronmikroskopet. Nanotrådar av Mo6S3I6 är ett alternativt material till kolnanorör och överträffar dessa i form av löslighet i båda organiska såväl som polära lösningsmedel. De är enkla att syntetisera men deras elektriska konduktivitet är låg. Mo6S3I6 nanotrådar studerades med in situ TEM probing. Vi fann att genom att driva en tillräckligt hög elektrisk ström genom nanotråden så resulterade detta i en omvandling till en solid metallisk molybden nanotråd med en konduktivitet nära värdet för bulkmaterialet. Resultat är intressant då nanotrådar kan användas i t.ex. fältemission, men resultatet visar också på att det kan vara en generell metod för att förbättra nanotrådar överlag. På dessa nanotrådar har även en elektromekanisk resonans studie utförts där böjmodulen för materialet bestämdes till 4.9 GPa. Med in situ-TEM-probing metoden har även silvernanobläck studerats under en sintringsprocess. Studien visade att vid sintringen så bildas perkulativa vägar genom bläckets silvernanopartiklar samt att vid hög sinteringstemperatur förkolnades det lösningsmedel som silvernanopartiklarna är lösta i. Förkolningen av lösningsmedlet resulterade i ett kolnät med liknande egenskaper som för grafit. Förståelse utav sinteringsprocessen är nödvändig eftersom vid tryckning av elektriskt ledande banor på papper används sintring för att höja ledningsförmågan. Genom att växa nanopartiklar på nanotrådar förändras deras egenskaper och tillämpningar. Existerande metoder är endera komplicerade eller ger dåligt ut- byte. Ett enkelt recept för att växa guldnanopartiklar på kolnanorör och Mo6S3I6 nanotrådar har därför tagits fram. Dessa kolnanorör och nanotrådar har sedan studerats med in-situ-TEM-probing metoden som visade att utanpå dessa guldnanopartiklar kan burar av kol skapas. Eftersom partiklarnas storlek kan kontrolleras kan även kolnanoburarnas storlek kontrolleras. Burarna har användningsområden t.ex. inom medicin och vid lagring av vätgas. / The thesis covers six scientific papers

The quantum Hall (QH) system---cold electrons in two dimensions in a perpendicular magnetic field---is a striking example of a system where unexpected phenomena emerge at low energies. The low-energy physics of this system is effectively one-dimensional due to the magnetic field. We identify an exactly solvable limit of this interacting many-body problem, and provide strong evidence that its solutions are adiabatically connected to the observed QH states in a similar manner as the free electron gas is related to real interacting fermions in a metal according to Landau's Fermi liquid theory. The solvable limit corresponds to the electron gas on a thin torus. Here the ground states are gapped periodic crystals and the fractionally charged excitations appear as domain walls between degenerate ground states. The fractal structure of the abelian Haldane-Halperin hierarchy is manifest for generic two-body interactions. By minimizing a local k+1-body interaction we obtain a representation of the non-abelian Read-Rezayi states, where the domain wall patterns encode the fusion rules of the underlying conformal field theory. We provide extensive analytical and numerical evidence that the Laughlin/Jain states are continuously connected to the exact solutions. For more general hierarchical states we exploit the intriguing connection to conformal field theory and construct wave functions that coincide with the exact ones in the solvable limit. If correct, this construction implies the adiabatic continuation of the pertinent states. We provide some numerical support for this scenario at the recently observed fraction 4/11. Non-QH phases are separated from the thin torus by a phase transition. At half-filling, this leads to a Luttinger liquid of neutral dipoles which provides an explicit microscopic example of how weakly interacting quasiparticles in a reduced (zero) magnetic field emerge at low energies. We argue that this is also smoothly connected to the bulk state.