First-principles methods based on Density functional theory (DFT) are now adopted routinely to calculate the properties of materials. However, one of the biggest challenges of DFT is to describe the electronic behaviors of random alloys. One of the aims of this thesis is to study binary alloys, e.g. Ti-Al, Cu-Au, and multi-component alloys by using two models for chemically random structures: the special quasi-random structure (SQS) and coherent potential approximation (CPA). I investigate these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. Within the SQS approach, the LLD effect can be modeled in a straightforward manner by relaxing the positions of atoms in the supercell. However, within this approach, it is difficult to model the random multi-components alloys due to the large size of the supercells. On the other hand, the CPA approach uses single-site approximation and thus it is not limited by the number of alloy components. But CPA suffers from the neglect of the local lattice relaxation effect, which in some systems and for some properties could be of significant importance. In my studies, the SQS and CPA approaches are combined with the pseudopotential method as implemented in the Vienna Ab-initio Simulation Package (VASP) and the Exact Muffin-Tin Orbitals (EMTO) methods, respectively. The mixing energies or formation enthalpies and elastic parameters of fcc Ti1-xAlx and Cu1-xAux (0 =&lt; x =&lt; 1) random solid solutions and high-entropy multicomponent TiZrVNb, TiZrNbMo and TiZrVNbMo alloys are calculated as a function of concentration. By comparing the results with and without local lattice relaxations, we find that the LLD effect is negligible for the elastic constants C11, C12, and C44. In general, the uncertainties in the elastic parameters associated with the symmetry lowering in supercell studies turn out to be superior to the differences between the two alloy techniques including the effect of LLD. However, the LLD effect on the mixing energies or formation enthalpies is significant and depends on the degree of size mismatch between alloy constituents. In the cases of random Cu-Au and high-entropy alloys, the formation enthalpies and mixing energies are significantly decreased when the LLD effect is considered. This finding sets the limitations of CPA for the mixing energies or formation enthalpies of alloys with large atomic size differences. The other goal of the thesis is to study the effect of exchange-correlation functionals on the formation energies of ordered alloys. For this investigation, we select the Cu-Au binary system which has for many years been in the focus of DFT and beyond DFT schemes. The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation term in DFT is a mature approach and have been adopted routinely to investigate the properties of metallic alloys. In most cases, PBE provides theoretical results in good agreement with experiments. However, the ordered Cu-Au system turned out to be a special case where large deviations between the PBE predictions and observations occur. In this work, we make use of a recently developed exchange-correlation functional, the so-called quasi-nonuniform exchange-correlation approximation (QNA), to calculate the lattice constants and formation energies for ordered Cu-Au alloys as a function of composition. The calculations are performed using the EMTO method and verified by a full-potential method. We find that the QNA functional leads to an excellent agreement between theory and experiment. The PBE strongly overestimates the lattice constants for ordered Cu3Au, CuAu, CuAu3 compounds and also for the pure metals which are nicely corrected by the QNA approach. The errors in the formation energies of Cu3Au, CuAu, CuAu3 relative to the experimental data decrease from 38-45% obtained with PBE to 5-9% calculated for QNA. This excellent result demonstrates that one can reach superior accuracy within DFT for the formation energies and there is no need to go beyond DFT. Furthermore, it shows that error cancellation can be very effective for the formation energies as well and that the main DFT errors obtained at PBE or LDA levels originate from the core-valence overlap region, which is correctly captured by QNA due to its particular construction. Our findings are now extended to disordered alloys, which is briefly discussed already in one of my published papers. / <p>Qc 20170630</p>

With the discovery of the quantum Hall effect more than thirty years ago, a whole new field emerged—that of topological quantum matter. This field is now a very mature one, and many different aspects are covered in the literature. The main text of this thesis introduces the field and gives a background to topological quantum matter, as well as topological aspects of superconductivity and the Abelian fractional quantum Hall (FQH) states.  Together with the main text there are five articles that address five different questions, all connected to topological quantum matter. In the first article, representative wave functions for the Abelian FQH states are calculated using conformal field theory methods. Before this paper was published, similar constructions had been restricted to flat geometries, but in this paper we generalize the analysis to the simplest curved geometry, namely the sphere. On top of being of interest for numerical studies (which usually are performed on a sphere), the response of the FQH liquids to curvature can be used to detect a topological quantity, the shift, which is the average orbital spin of the constituent electrons. In the second article, we construct an effective field theory for the two-dimensional spinless, chiral p-wave superconductor that faithfully describes the topological properties of the bulk state, and also provides a model for the subgap states at vortex cores and edges. In particular, it captures the topologically protected zero-modes and has the correct ground state degeneracy on the torus. In the third paper, tools for a hydrodynamic theory for insulators in three dimensions are derived. Specifically, we use functional bosonization to write insulators as a condensation phase of the U(1) gauge theory obtained in the functional bosonization language. In the fourth paper, we investigate the edge Majorana modes in the two-dimensional chiral p-wave superconductor. We define the model on surfaces with different geometries—the annulus, the cylinder, the Möbius band, and a cone—and with different configurations of magnetic flux threading holes in these surfaces. In particular, we address the following question: Given that, in the absence of magnetic flux, the ground state on the annulus does not support Majorana modes, while the one on the cylinder does, how is it possible that the conical geometry can interpolate smoothly between the two? In the fifth and last article, we demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. We propose this geo-Meissner effect as an unequivocal signature of chiral superconductivity that could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of Majorana modes. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 5: Manuscript.</p>

To investigate the existence  of  molecular heterogeneties in mixtures of DMSO-water, the dynamics were measured with the method of dynamic light scattering (DLS). Three different compositions (20 mol %, 33 mol% and 60 mol%) were included in the study and measured at room temperature (295 K) and for one composition (33 mol %) also a temperature dependence (from 295 K down to 263 K) was measured. Measurements were done on samples both with and without nanoparticles acting as tracers for the DLS. The diffusion coefficients of DMSO in water was extracted from the analysis and the results from samples without nanoparticles are consistent with diffusion of DMSO molecules reported previously, except for the highest concentration,  and showed a clear Arrhenius behaviour with an activation energy of 26±1kJ/mol. The viscosity was extracted from the diffusioncoefficient of the nanoparticles in the solutions and followed an expected trend regarding the concentration as well as for the higher temperatures, but deviated for lower temperatures due to an unexpected drastic change in the diffusion coefficient around the temperature T= 273 K. The reason for the drastic change could be connected to a possible liquid-liquid phase separation in the DMSO-water  mixture. The hydrodynamical radii was estimated using Stokes-Einsteins equation and had a small but unsure concentration dependence so the size could only be confirmed to be around 0.43 nm at T= 295 K and increased with temperature up to 1.6 nm atT= 263 K, indicating clustering effects and supporting the theory of molecular heterogeneity in DMSO-water mixtures. This was a pilot study to aproposed x-ray experiment at NanoMax at MaxIV to capture the nanoscale fluctuations present in binary solutions.

This thesis presents results from large scale Monte Carlo simulations of systems subject to a superfluid phase transition in the presence of disorder. The simulations are performed by state-of-the-art, collective Monte Carlo algorithms treating phase degrees of freedom in effective models with amplitude fluctuations integrated out. In Paper I a model system for the possible solid to supersolid transition in 4He is presented.The Wolff cluster algorithm is used to study how the presence of linearly correlated random defects is able to alter the universality class of the 3-dimensional XY-model. In the pure case the superfluid density and heat capacity have singular onsets, which are not seen in the supersolid experiments where instead a smooth onset is obtained. Using finite size scaling of Monte Carlo data, we find a similar smooth onset in our simulations, governed by exponents  ν=1 for the superfluid density and α=-1 for the heat capacity. These results are in qualitative agreement with experiments for the observed transition in solid 4He. In Paper II a systematic investigation of the scaling result z=d for the dynamic critical exponentat the Bose glass to superfluid quantum phase transition is performed. The result z=d has been believed to be exact for about 20 years, but although it has been questioned lately no accurate estimate of z has been available. An effective link current model of quantum bosons at T=0 with disorder in 2D is simulated using highly effective worm Monte Carlo simulations.The data analysis is based on a finite size scaling approach todetermine the quantum correlation time from simulationdata for boson world lines without any a priori assumption on the critical parameters. The resulting critical exponents are z=1.8 \pm 0.05, ν=1.15 \pm 0.03, and η=-0.3 \pm 0.1. This suggests that z=d is not satisfied. / <p>QC 20111206</p>

QC 20110309

Special quasi-random structure (SQS) and coherent potential approximation (CPA) are techniques widely employed in the first-principles calculations of random alloys. The aim of the thesis is to study these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. We compare the elastic parameters obtained from SQS and CPA calculations. For the CPA and SQS calculations, we employ the Exact Muffin-Tin Orbitals (EMTO) method and the pseudopotential method as implemented in the Vienna Ab initio Simulation Package (VASP), respectively. We compare the predicted trends of the VASP-SQS and EMTO-CPA parameters against composition. As a first case study, we investigate the elastic parameters of face centered cubic (fcc) Ti1−xAlx(0≤x≤100at.%) random solid solutions as a function of Al content (x). The EMTO-CPA and VASP-SQS results are in good agreement with each other. Comparing the lattice constants from SQS calculations with and without local lattice relaxations, we find that in Ti-rich (Al-rich) side the lattice constants remain almost unchanged (slightly increase) upon atomic relaxations. Taking local lattice distortions into consideration decreases the C11 and C44 elastic parameters, but their trends are not significantly affected. The C12 elastic constant, on the other hand, is almost unchanged when atomic relaxations are included. In general, the uncertainties in the elastic parameters associated with the symmetry lowering in supercell studies turn out to be superior to the differences between the two alloy techniques including the effect of LLD. We also investigate the elastic properties of random fcc Cu1−xAux(0≤x≤100 at.%) alloys as a function of Au content employing the CPA and SQS approaches. It is found that the CPA and SQS values forC11andC12 are consistent with each other no matter whether the atomic relaxations are taken into account or not. On the other hand, the EMTO-CPA values for C44 are slightly larger than those from SQS calculations especially for Cu-rich alloys which we ascribe to the differences in the DFT solvers rather than the differences between CPA and SQS. The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation term in density functional theory (DFT) is a mature approach and have been adopted routinely to investigate the properties of metallic alloys. In most of the cases, PBE provides theoretical results in good agreement with experiments. However, the ordered Cu-Au system turned out to be a special case where large deviations between the PBE predictions and observations occur. In this work, we make use of a recently developed exchange-correlation functional, the so-called quasi-non-uniform exchange-correlation approximation (QNA), to calculate the lattice constants and formation energies for ordered Cu-Au alloys as a function of composition. The calculations are performed using the EMTO method. We find that the QNA functional leads to excellent agreement betweent heory and experiment. The PBE strongly overestimates the lattice constants for ordered Cu3Au, CuAu, CuAu3 compounds and also for the pure metals which is nicely corrected by the QNA approach. The errors in the formation energies of Cu3Au, CuAu, CuAu3relative to the experimental data decrease from 38-45% obtained with PBE to 5-9% calculated for QNA. / <p>QC 20151216</p>

Ab initiocalculation based on density function theory (DFT) is an accu-rate and efficient method for modelling material properties. It is performedby solving the Shrödinger equations with a few assumptions to obtain thephysical properties of the system. It is very computational demanding whendealing with large systems or long-time simulations. Developing empiricalpotentials on the basis ofab initiocalculations on smaller systems is a possi-ble way to solve this problem. The empirical potentials will benefit from theaccuracy ofab initiosimulations and can facilitate applications to large sys-tems and long-time simulations. In this thesis, we have performed two studiesregarding fitting empirical potentials: one is fitting an empirical Sutton-Chenpotential based onab initiosimulations for iron under extreme conditionsand the other one is fitting an improved Finnis-Sinclair potential for ternaryV-Ti-Cr alloy.In the first part, we focus on fitting a Sutton-Chen potential for solid Feunder the Earth’s inner core condition. Based onab initiomolecular dynam-ics (MD) simulation results, the Sutton-Chen potential is fitted to energies ofthe configurations obtained fromab initioMD simulations at the pressure of360 GPa and temperature of 6000 K. The method applied for the fitting isthe Particle Swarm Optimization (PSO) algorithm. The Sutton-Chen poten-tial can reproduce theab initioenergies with an error of 6.2 meV/atom. Setas the same withab initioMD simulations, classical MD using Sutton-Chenpotential can obtain the consistent results with those fromab initioMD sim-ulations at the pressure of 360 GPa and temperature of 6000 K. In order toexplore the size effect on the results, we extend the classical MD to large-sizesystems (from 1024 atoms to 65536 atoms). We also extend the temperaturerange to see the temperature effect on the results.In the second part, we develop an improved Finnis-Sinclair (IFS) potentialfor ternary V-Ti-Cr alloys. The interaction parameters of V-V, Ti-Ti andCr-Cr are fitted to the experimental lattice constants, cohesive energies andelastic constants. The binary alloy potential parameters are obtained byconstructing 3 binary alloy models (V15Ti, V15Cr, V8Ti8) and fitting to theirtheoretical lattice constants, cohesive energies and elastic constants. Finally,the IFS potential is successfully used to calculate mechanical properties andthe monovacancy formation energy in V-Ti-Cr alloy. It is also applied toinvestigate the composition effect on the mechanical properties of ternaryV-Ti-Cr alloys. / <p>QC 20160815</p>

This licentiate thesis deals with the electronic and geometrical properties of metal-semiconductor and organic-semiconductor interfaces investigated by photoelectron spectroscopy and scanning tunneling microscopy. First in line is the Co-InAs interface (metal-semiconductor) where it is found that Co is reactive and upon adsorption and thermal treatment it alloys with the indium of the substrate to form metallic islands, about 20 nm in diameter. The resulting broken bonds causes As entities to form which are loosely bond to the surface and evaporate upon thermal treatment. Thus, the adsorption of Co results in a rough interface. Secondly the metal-free phthalocyanine (H2PC) - titanium dioxide interface (organic-semiconductor) is investigated. Here it is found that the organic molecules arrange themselves along the substrate rows upon thermal treatment. The interaction with the TiO2 is mainly with the valence Π-electrons in the molecule causing a relatively strong bond, but this interaction is short range as the second layer of molecules retains their molecular character. This results in an ordered adsorption but limited mobility of the molecules on the surface prohibiting well ordered close packed layers. Furthermore, the hydrogen atoms inside the cyclic molecule leave the central void upon thermal treatment. The third case is the H2PC-InAs/InSb interface (organic-semiconductor). Here ordered overlayer growth is found on both substrates where the molecules are preferentially adsorbed on the In rows in the [110] direction forming one-dimensional chains. The InSb-H2PC interface is found to be weakly interacting and the bulk-like molecular character is retained upon both adsorption and thermal treatment. On the InAs-H2PC interface, however, the interaction is stronger. The molecules are more affected by the surface bond and this effect stretches up a few monolayers in the film after annealing. / QC 20101122

This thesis is dealing with simulation of polycrystalline materials underthe conditions of anisotropic pressure and temperature. Work has been carriedout in three steps:ˆ Research of the inuence of point defects and grain boundaries on theprocess of melting. The inuence of defects' concentration, grain sizeand lattice direction mismatch on the superheating temperature wasstudied.ˆ Investigation of the boundaries of application of the metadynamics methodto the simple atomic model with Buckingham interaction. The solidsolidphase transition, where one of the phases has temperature inducedstability was conrmed. We found the optimal size of simulation boxto study the solid-solid phase transitions using the metadynamics technique.ˆ A model of polycrystalline materials based on macroscopic approximationwas formulated. This model was applied to the model of the polycrystallinematerial using cellular automata. Using this approximationthe eect of anisotropic stress caused by anisotropic heating was studied. / <p>QC 20140611</p>

The Scanning Tunneling Microscope (STM) was invented by Gerd Binnig and Heinrich Rohrer and gave them the Nobel Prize in Physics 1986. STM can give us atomic resolution of a surface by applying a voltage between a very sharp tip (STM-tip) and the surface of a material that we want to examine. The STM-tip is moving over the surface and a computer is collecting the tunnel current in every single point to create a digital image. This diploma work is focused on the preparation of the STM-tip. The preparation method that is used is electrochemical etching of a tungsten wire. The sharper the STM-tip is the better resolution in the STM images we can get. With the purpose to get as sharp tip as possible and with a well-defined geometry, we prepared several tips by systematically varying the etching parameters such as voltage, current, concentration and wire length. A new method has been tested to minimize the oxidation on the surface and finally the tips were characterized with scanning electron microscope (SEM).