<p>A complex system is a system for which the statement "the whole is greater than the sum of its parts" holds. A network can be viewed as a backbone of a complex system. Combining the knowledge about the entities constituting the complex system with the properties of the interaction patterns we can get a better understanding of why the whole is greater than the sum. One of the purposes of network studies, is to relate the particular structural and dynamical properties of the network to the function it is designed to perform. In the present work I am briefly presenting some of the advances that have been achieved in the field of the complex networks together with the contributions which I have been involved in.</p>

An important, but also difficult, research field in condensed matter physics is that of strongly correlated systems. This thesis considers two topics in this field. The first topic is disorder and frustration in spin models. The introduction of disorder into quantum spin chains creates a complex problem. The ground state of the random-bond spin-1 Heisenberg chain is studied by means of stochastic series expansion quantum Monte Carlo simulation, applying the concept of directed loops. It is found that this system undergoes a phase transition to the random-singlet phase if the bond disorder is strong enough. Further a frustrated spin system is investigated. The frustration is introduced by having spins positioned on a triangular lattice. Performing a quantum Monte Carlo simulation for such a frustrated lattice leads to the occurrence of the infamous sign problem. This problem is investigated and it is shown that it is possible to use a meron cluster approach to reduce its effect for some specific models. The second topic concerns atomic condensates in optical lattices. A system of trapped bosonic atoms in such a lattice is described by a Bose-Hubbard model with an external confining potential. Using quantum Monte Carlo simulations it is demonstrated that the local density approximation that relates the observables of the unconfined and the confined models yields quantitatively correct results in most of the interesting parameter range of the model. Further, the same model with the addition that the atoms carry spin-1 is analyzed using density matrix renormalization group calculations. The anticipated phase diagram, with Mott insulating regions of dimerized spin-1 chains for odd particle density, and on-site singlets for even density is confirmed. Also an ultracold gas of bosonic atoms in an anisotropic two dimensional optical lattice is studied. It is found that if the system is finite in one direction it exhibits a quantum phase transition. The Monte Carlo simulations performed show that the transition is of Kosterlitz-Thouless type. / QC 20100628

A complex system is a system for which the statement "the whole is greater than the sum of its parts" holds. A network can be viewed as a backbone of a complex system. Combining the knowledge about the entities constituting the complex system with the properties of the interaction patterns we can get a better understanding of why the whole is greater than the sum. One of the purposes of network studies, is to relate the particular structural and dynamical properties of the network to the function it is designed to perform. In the present work I am briefly presenting some of the advances that have been achieved in the field of the complex networks together with the contributions which I have been involved in.

This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.

Multislice HAADF - STEM image simulations of SrTiO 3 are performed at 300 K.The procedure of these simulations and the used techniques are briefly ex-plained and reasoned. The results are presented and discussed in a conciseway and in an attached paper a comparison to experimental images is made.The paper proofs that the electron optical setup developed in Dresden is indeed capable of producing atomic-sized EVBs, a precondition for measuring EMCD with atomic resolution.

Molybdenum disulfide (MoS2) has been demonstrated to be a potential catalyst in the hydrogen evolution reaction (HER). Due to its highly active edge site, abundance, and low cost, it rivals Pt. However, the potential activity of the MoS2 basal plane has largely been ignored. The physical characteristics of MoS2 and its corresponding band structure change significantly with decreasing thickness, especially at the monolayer limit. Thus, an investigation on the thickness dependence may provide important insights into the MoS2 basal plane activity. In this thesis, the layer dependent electrocatalytic performance is investigated with mono-, bi- and multilayer MoS2 based individual nanodevices. Three conclusions were reached. (1) Monolayers showed exchange current densities more than one order of magnitude higher than that of the multilayers, 0.12 mA/cm2 and 8.7 mA/cm2, respectively. Furthermore, the onset potential of the monolayer was several hundred millivolts lower than that of the multilayer, about 0.2 V vs RHE for the monolayer versus 0.5 V vs RHE for the multilayer. The Tafel slope of 100-200 mV/dec revealed that the rate limiting step was the adsorption of hydrogen. (2) Interestingly, the bilayer sample exhibited an increase in its exchange current density from 0.3 mA/cm2 to 8 mA/cm2 when cycled extensively. This is suspected to be caused by intercalation of hydrogen between the atomic layers. (3) Additionally, the back-gate voltage is applied to tune the Fermi level of the material and the catalytic performance. It was found that the back-gate voltage induces an irreversible change in all samples, increasing the exchange current density by an order of magnitude. The superior basal plane performance of the monolayers to that of the multilayers reveals a new way to optimize the performance of MoS2 as a HER catalyst. In addition, the results above illuminate the yellow brick road to potential improvements in other layered materials as well.

The possibility to change magnetic anisotropy of amorphous TbCo films from out-of-plane to in-plane has been investigated. The effects of TbCo film's thickness and composition on the magnetic anisotropy were investigated together with the effects of growing the TbCo films on a SmCo seed layer. This was studied by sputtering TbCo films of composition Tb_xCo_(100-x) x=16,18,20,22 and 24, with thickness ranging between 2-20 nm, with and without the presence of a 20 nmSm_15Co_85 seed layer. All films were grown in a 130 mT magnetic in-plain field to imprint an in-plane anisotropy. The structure and composition of the films were examined with Rutherford backscattering spectrometry, X-ray reflectivity, and Grazing incidence X-ray diffraction. The magnetic properties of the films were studied with magneto-optic Kerr effect measurement, vibrating sample magnetometer, Kerr microscopy and magnetic force microscopy. The magneto-optic Kerr effect measurement showed that it was possible to change TbCo film's preferred magnetization direction from out-of-plane to in-plane by reducing the film thickness. The SmCo layer made it easier for theTbCo films to change preferred magnetization direction from out-of-plane to in-plane.

In this work potentials of carbon nanomaterials calculated with Density Functional Theory (DFT) are approximated using an Artificial Neural Network (ANN). Previous work in this field has focused on estimating potential energies of bulk structures. We investigate the possibility to approximate both the potential energies and the forces of periodic carbon nanotubes (CNTs) and fullerenes. The results indicate that for test structures similar to those in the training set the ANN approximates the energies to within 270 meV/atom (&lt; 3.7% error, RMSE 40 meV/atom) and the forces to within 7.5 eV/Å (&lt; 73% error, RMSE 1.34 eV/Å) per atom compared with DFT calculations. Furthermore, we investigate how well the ANN approximates the potentials and forces in structures that are combinations of CNTs and fullerenes (capped CNTs) and find that the ANN generalizes the potential energies to within 100 meV/atom (&lt; 1.1% error, RMSE 78 meV/atom) and the forces to within 6 eV/Å (&lt; 60% error, RMSE 0.55 eV/Å) per atom. The ANN approximated potentials and forces are used to geometry optimize CNTs and we observe that the optimized periodic CNTs match DFT calculated structures and energies while the capped CNTs result in comparable energies but incorrect structures compared to DFT calculations. Considering geometry optimization performed with ANN on CNTs the errors lie within 170 meV/atom (&lt; 1.8% error) with an RMSE of 20 meV/atom. For the geometry optimizations of the capped CNTs the errors are within 430 meV/atom (&lt; 5.5% error) with an RMSE of 14 meV/atom. All results are compared with empirical potentials (ReaxFF) and we find that the ANN approximated potentials are more accurate than the best tested empirical potential. This work shows that machine learning may be used to approximate DFT calculations. However, for further applications our conclusion is that the error of the estimated forces must be reduced further. Finally, we investigate the computing time (number of core hours) required and find that the ANN is about two orders of magnitude faster than DFT and three to four orders of magnitude slower than ReaxFF. For the unseen data the ANN is still around 2 orders of magnitude quicker than the DFT but here it is around 4 order of magnitude slower than ReaxFF. / <p>Supervisors: Daniel Hedman and Fredrik Sandin</p> / F7042T - Project in Engineering Physics

Topological insulators and topological crystalline insulators are materials that have a bulk band structure that is gapped, but that also have toplogically protected non-gapped surface states. This implies that the bulk is insulating, but that the material can conduct electricity on some of its surfaces. The robustness of these surface states is a consequence of time-reversal symmetry, possibly in combination with invariance under other symmetries, like that of the crystal itself. In this thesis we review some of the basic theory for such materials. In particular we discuss how topological invariants can be derived for some specific systems. We then move on to do band structure calculations using the tight-binding method, with the aim to see the topologically protected surface states in a topological crystalline insulator. These calculations require the diagonalization of block tridiagonal matrices. We finish the thesis by studying the properties of such matrices in more detail and derive some results regarding the distribution and convergence of their eigenvalues.

The increasing demand of renewable energy is the big driving force for the research and development of more efficient solar energy conversion solutions. Solar cells, which use the photovoltaic effect to convert the photon energy to electrical current, are an important solar energy conversion technique. One solar cell technology is thin-film solar cells. Thin-film solar cells use an absorption layer with a direct band gap. A direct band gap has the advantage that the photons will penetrate less deep until a photoexcitation occur compared to semiconductors with an indirect band gap (e.g. silicon). For this reason the thin-film solar cells can be made very thin.CIGS is a common thin-film solar cell absorber material containing copper (Cu), indium (In), gallium (Ga) and selenium (Se). One objective of this work has been to determine element concentrations of CIGS absorption layers from sample measurements. The GGI ratio determines the band gap, which is an important factor for optimising the efficiency of the solar cell.1 The copper vacancy is the main acceptor dopant in CIGS. The Cu concentration has shown to be important for the efficiency and for other properties of the absorber [2].The measuring technique used in this work has been photoelectron spectroscopy (PES). PES produces a spectrum showing distinct peaks corresponding to electron binding energy levels for specific element subshells. Measurements with different photon energies have been performed on samples with and without post deposition treatment (PDT). A great deal of the effort has been to calculate relative element concentrations based on the PES peak intensities. Two important parameters when performing the calculations are the photoionization cross section (including the angular dependence of the cross section) and the inelastic mean free path of the photoelectrons.The results show that the GGI and the corresponding band gap will be almost the same with and without PDT except for close to the surface where PDT lowers the GGI.The calculations showed that the copper concentration is lowest at the surface. Moreover, PDT with RbF results in lower copper concentration closer to the junction.The results show a discrepancy of the GGI and CGI ratios when using the angular dependent cross sections in [10] and [11] compared to using the cross sections in [6] and [7]. / Det ökande behovet av förnybar energi gör att forskning och utveckling av solenergilösningar är av största vikt. Solceller, vilka utnyttjar den fotovoltaiska effekten, är den vanligaste tekniken för omvandling av solenergi till elektricitet. Tunnfilmssolceller är en typ av solceller vars absorbent har ett direkt bandgap, till skillnad från kisel som har ett indirekt bandgap. Fördelen med ett direkt bandgap är att det ljusabsorberande materialet kan göras mycket tunt.En vanlig tunnfilmssolcell är CIGS. Det är en komposit bestående av koppar (Cu), indium (In), gallium (Ga) och selen (Se). Ett syfte med detta självständiga arbete har varit att beräkna koncentrationerna av de ingående ämnena i halvledarskiktet av CIGS. GGI-kvoten bestämmer bandgapet, vilket är en viktig faktor för solcellens verkningsgrad. Kopparvakansen är den huvudsakliga halvledaracceptorn i CIGS. Kopparkoncentrationen har visat sig vara viktig för bl.a. solcellens verkningsgrad [2].Mättekniken som används i detta arbete kallas fotoelektronspektroskopi (PES). PES-mätningar ger ett spektrum där spektrallinjerna representerar olika nivåer av elektroners bindningsenergi för olika grundämnen. Mätningar med olika fotonenergier, på prover med och utan ytbehandling (PDT), har utförts. En stor del av arbetet har varit att beräkna relativa koncentrationer av de olika grundämnena från spektrallinjerna i spektrumet. Viktiga parametrar som man behöver ta hänsyn till i uträkningarna är sannolikheten för en fotoemissionsprocess hos fotonerna, vinkelberoendet och den fria medelväglängden hos fotoelektronerna.Resultaten visar att GGI-kvot och bandgap blir nästan detsamma med eller utan PDT, förutom närmast ytan där PDT minskar GGI-kvoten.Resultaten visar också att kopparkoncentrationen är lägst på ytan och att PDT med RbF minskar kopparkoncentrationen närmast ytan.Resultaten visar att det blir skillnader mellan GGI- och CGI-kvoterna beroende på om beräkningarna baserats på vinkelberoende träffytor enligt [10] och [11] eller baserats på träffytor enligt [6] och [7].