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].

The amphiphilic property of phospholipids drives the spontaneous formation of various molecular aggregates in response to their surrounding environment. In this study the concentration of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipids in water was varied in order to investigate the naturally occurring arrangements over time, and specifically the propensity to form monolayers on the water-vacuum interface. Several forms of aggregates developed during the 1000 ns long simulations, including monolayers and spherical- as well as cylindrical micelles. In all simulations the majority of lipids remained in the bulk and with varying sized patches of monolayers on the 8×8 nm surfaces formed. During a large portion of time the micelles kept close to the surface without ever opening up. By constructing and simulating 245 new unique systems with one of the micelles placed close to the surface, it could be confirmed that the possibility of these lipids forming a monolayer become greatly enhanced when no other lipids are present on the surface. Once a micelle had started to open up, it never reversed back to its original form but transformed, or could be expected to transform, into monolayers in all cases. In the concentration simulations it was furthermore found that a single lipid could be attached to the surface monolayer as well as a micelle simultaneously for over 400 ns. Not a single instance could be found where a lipid with both its tails on the surface travelled back to the bulk, in any of the simulations performed.

The spin-lattice coupling is due to itinerant electrons interacting with both spins of ions and phonons, mediating a coupling between magnetic spin moments and lattice vibrations. In this project, the coupling is studied systematically for finite quantum spin chains of size 2 – 10. The coupling is included in a Hamiltonian model with the Heisenberg exchange interaction and an external magnetic field resulting in an eigenvalue problem which is solved numerically to find phase diagrams of the magnetic moment of the system depending on an external magneticfield and the lattice vibration parameter. The eigenvalue problem is also solved analytically for the 2-ion chain, dimer, and 3-ion chain, trimer, systems. Based on these phase diagrams two propositions are made: the effect of the coupling is larger than an external magnetic field and the behavior of the coupling converges to a common phase diagram for larger spin chains. / Kopplade spinn- och vibrationsfrihetersgrader beror på kringvandrande elektroner som växelverkar med både spin och fononer, vilket förmedlar en koppling mellan magnetiskt spinmoment och gittervibrationer. I detta projekt studeras denna koppling systematiskt för ändliga spin-kedjor av 2–10 joner. Systemet beskrivs av en Hamiltonian med Heisenberg modellen som beskriver spin-spin kopplingen samt ett externt magnetiskt fält. Detta egenvärdesproblem löses analytiskt för dimer- och trimersystem samt numeriskt för längre kedjor. Lösningarna används för att ta fram fasdiagram av de magnetiska momenten av kedjorna beroende på externt magnetfält och spin- och vibrationsfrihetsgradsparametern. Baserat på dessa fasdiagram, framförs två propositioner: kopplingens effekt är större än ett externt magnetfält och kopplingens beteende konvergerar till ett enhetligt fasdiagram för större spinnkedjor. / <p>Subject reader/ämnesgranskare: Anders Bergman</p>

Investigations have been done as of why dust particles appear in a circular pattern on the backside of solar cells produced in sputtering chambers at Midsummer AB. An experimental approach was conducted, where solar cells were produced at standard conditions and their backside studied by material analytical methods. The solar cells dust particles were analyzed by energy-dispersive x-ray spectroscopy and x-ray diffraction, deducing that they consisted of iron selenide (Fe0.89Se). Furthermore, the dust particles appear due to formation of a thin iron selenide film that cracks and delaminate upon cooling from process temperature to room temperature. Iron selenide film thickness was found by energy-dispersive x-ray spectroscopy to occur in a pattern with radial symmetry with respect to the cell center, correlating with the film delamination pattern. The reason to the film formation was due to selenium reacting with the substrate steel at high temperatures (&gt;400 ◦C) in deposition chambers having a selenium environment. The film delamination occurs at a critical film thickness at which stresses in the film is high enough for the film to yield and fracture. It was concluded that iron selenide film formation or delamination must be minimized in order to control dust particle formation. These two phenomena can be mitigated by protective substrate films, change of substrate material, selenium environment optimization or temperature profile optimization and should be researched further to find the most effective and viable solution.

In this thesis, the diffusion of lithium was studied on boron-doped diamond (BDD) as a potential anode material in lithium ion batteries (LIB). The initial interaction between deposited lithium and BDD thin films was studied using X-ray Photoelectron Spectroscopy (XPS). Diffusion is directly linked to reactions between lithium and carbon atoms in the BDD-lithium interface. By measuring binding energies of core-electrons of carbon and lithium before and after deposition, these reactions can be analyzed. Scanning Electron Microscopy (SEM) was used to study the BDD surface and the behaviour of deposited lithium. Experiments show that a chemical interaction occurs between lithium and carbon atoms in the surfacelayers of the BDD. The diffusion of lithium is discussed from spectroscopic data and suggests that surface diffusion is occurring and no proof of bulk diffusion was found. The results do not exclude bulk diffusion in later states but it was not found in the initial interaction at the interface after depositing lithium. SEM images show that lithium clusters in the nanometer range are formed on the BDD surface. The results of this study give insights in the initial diffusion behaviour of lithium at the BDD interface and possible following events are discussed.

Nanowires with Rashba spin-orbit coupling represent a promising platform for the realization of one-dimensional topological superconductivity and Majorana bound states. In this work we investigate Majorana bound states in hybrid normal-superconductor and short superconductor-normal-superconductor junctions based on nanowires with Rashba spin-orbit coupling. In particular, we explore consequences of the topological phase transition as well as the non-locality and self conjugation properties of the Majorana states on the low-energy spectrum and the Josephson effect in the case of superconductor-normal-superconductor junctions. Our work shows the great potential of hybrid junctions as a platform for the study of topological superconductivity and Majorana bound states.

No description available.

Many modern materials and material systems are layered. The properties related to layers are connected to interactions between atomic layers. In the present thesis, we introduce the interlayer potential (ILP), a novel model potential which fully describes the interaction between layers. The ILPs are different from the usual interatomic potentials which present interaction between atoms. We use the Chen-Möbius inversion method to extract the ILPs from ab initio total energy calculations. The so obtained ILPs can be employed to investigate several physical parameters connected with the particular set of atomic layers, e.g. surface energy, stacking fault energy, elastic parameters, etc. The interactions between the face centered cubic (fcc) (111) planes are described by two different ILPs. Using two close-packed model structures, namely the ABC stacking along the fcc ⟨111⟩ direction and AB stacking along the hcp ⟨0001⟩ direction, we demonstrate how these two ILPs are obtained via the Chen-Möbius method. Density function theory (DFT) is employed to generate the ILPs and also to compute the equilibrium structural properties of elemental metals Al, Ni, Cu, Ag, Au and Pd as well as of Pd-Ag random solid solutions. With the so established ILPs, we adopt the supercell method and the axial interaction model to calculate the stacking fault energy along the fcc ⟨111⟩ direction, including the intrinsic stacking fault energy, extrinsic stacking fault energy and twin stacking fault energy as well as the interactions between the intrinsic stacking faults. We find that the data derived from ILPs are consistent with those obtained in direct ab initio calculations. Along the fcc ⟨111⟩ direction, we study the surface energy and surface relaxation using the ILPs. The phonon dispersions are also described. We conclude that the interlayer potentials based on the Chen-M¨obius inversion technique may provide a new way to investigate the properties related to layers in layered materials. / <p>QC 20121101</p>

Graphene has many interesting physical properties which makes it useful for plenty of applications. In this work we investigate the possibility of using graphene as a carbon dioxide and humidity sensor. Carbon dioxide and water adsorbates are modeled on top of the surface of a graphene sheet, which themselves lie on one of two types of silica substrates or sapphire substrate. We evaluate the changes in the electronic and structural properties of the graphene sheet in the presence of the described adsorbates as well as the accompanying substrate. We perform the study using ab-initio calculations based on density functional theory (DFT), that allows fast, accurate and efficient investigations. In particular, we focus our attention on investigating the effects of defects in the substrate and how it influences the properties of the graphene sheet. The defects of the substrate contribute with impurity bands leading to doping effects on the graphene sheet, which in turn together with the presence of the adsorbates result in changes of the electronic charge distribution in the system. We provide charge density difference plots to visualize these changes and also determine the relaxed minimum distances of the adsorbates from the graphene sheet together with the respective minimum energy configurations. We also include the density of states, Löwdin charges and work functions for further investigations. / Grafen har många intressanta fysikaliska egenskaper, vilket gör det användbart för många  tillämpningar. I detta arbete har vi teoretiskt undersökt möjligheten att använda grafen som gassensor för koldioxid och fukt. Adsorberade koldioxid- och vattenmolekyler modelleras ovanför ytan av ett lager grafen, som i sig ligger ovanpå en av två typer av kiseldioxidsubstrat eller ett aluminiumoxidsubstrat. Vi har utvärderat förändringar i de elektroniska och strukturella egenskaperna hos grafenlagret i närvaro av de beskrivna molekylerna samt åtföljande substrat. Vi utför studien med ab-initio beräkningar baserade på täthetsfunktionalteori (DFT), som möjliggör snabba, korrekta och effektiva elektronstruktursberäkningar. Framför allt fokuserar vi på effekten av defekter i underlaget, och hur dessa påverkar egenskaperna hos grafenlagret. Defekter i underlaget bidrar genom att införa elektroniska band som leder till dopningseffekter i grafenlagret, vilket i sin tur tillsammans med närvaron av adsorbatmolekylerna leder till förändringar av den elektroniska laddningsfördelningen i systemet. Vi tillhandahåller s.k. laddningsdensitet-skillnadsfigurer som visualiserar dessa förändringar. Vi har även beräknat jämviktsavståndet mellan adsorbatmolekylerna och grafenlagret  tillsammans med respektive minimienergikonfigurationer för molekylerna, Vi åksa tillhandahåller täthet av stater, Löwdin laddningar och arbetsfunktion för fortsatta undersökningar. / <p>QC 20160218</p>