A rich variety of phases can exist in quantum systems. For example, the fractional quantum Hall states have persistent topological characteristics that derive from strong interaction. This thesis uses the exact diagonalization method to investigate quantum lattice models with strong interaction. Our research topics revolve around quantum phase transitions between novel phases. The goal is to find the best schemes for realizing these novel phases in experiments. We studied the fractional Chern insulator and its transition to uni-directional stripes of particles. In addition, we studied topological Mott insulators with spontaneous time-reversal symmetry breaking induced by interaction. We also studied emergent kinetics in one-dimensional lattices with spin-orbital coupling. The exact diagonalization method and its implementation for studying these systems can easily be applied to study other strongly correlated systems. / PHD / Topological quantum states are a new type of quantum state that have properties that cannot be described by local order parameters. These types of states were first discovered in the 1980s with the integer quantum Hall effect and the fractional quantum Hall effect. In the 2000s, the predicted and experimentally discovered topological insulators triggered studies of new topological quantum states. Studies of strongly correlated systems have been a parallel research topic in condensed matter physics. When combining topological systems with strong correlation, the resulting systems can have novel properties that emerge, such as fractional charge. This thesis summarizes our work that uses the exact diagonalization method to study topological states with strong interaction.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this thesis the structural dynamics, upon photo-excitation, of the charge-densitywave (CDW) material 4Hb-TaSe2 is investigated on the time-scale of atomic motion and simultaneously on the spatial-scale of atomic dimensions. CDW materials have been of interest since their discovery in the 1970’s because of their remarkable non-linear and anisotropic electrical properties, gigantic dielectric constants, unusual elastic properties and rich dynamical behaviour. Some of these exotic properties were extensively investigated in thermal equilibrium soon after their discovery but only recently have ultrafast techniques like femtosecond spectroscopy become available to study their out-of-equilibrium behaviour on the time-scale of atomic motion. By studying their behaviour on this time-scale a more in-depth understanding of their macroscopic properties can be gained. However, to do investigations on the atomic time-scale and simultaneously directly observe the evolution of the atomic arrangements is another challenge. One approach is through the previously mentioned technique of femtosecond pump-probe spectroscopy but converting the usual ultrashort optical probing source to an ultrashort electron or x-ray source that can diffract off the sample and reveal structural detail on the atomic level. Here, the femto-to-picosecond out-of-equilibrium behaviour upon photo-excitation in 4Hb-TaSe2 is investigated using an ultrashort electron probe source. Two variations of using an electron probe source are used: conventional scanning Femtosecond Electron Diffraction (FED) and a new approach namely Femtosecond Streaked Electron Diffraction (FSED). The more established FED technique, based on femtosecond pumpprobe spectroscopy, is used as the major investigating tool while the FSED technique, based on ultrafast streak camera technology, is an attempt at broadening the scope of available techniques to study structural dynamics in crystalline material on the subpicosecond time-scale. With these two techniques, the structural dynamics during the phase transition from the commensurate- to incommensurate-CDW phase in 4Hb-TaSe2 is observed through diffraction patterns with a temporal resolution of under 500 fs. The study reveals strong coupling between the electronic and lattice systems of the material and several time-constants of under and above a picosecond are extracted from the data. Using these time-constants, the structural evolution during the phase transition is better understood and with the newly gained knowledge, a model of all the processes involved after photo-excitation is proposed. / AFRIKAANSE OPSOMMING: In hierdie tesis word die strukturele dinamika van die lading-digtheid-golf (LDG) materiaal 4Hb-TaSe2 ondersoek op die tydskaal van atomiese bewegings en gelyktydig op die ruimtelikeskaal van atomiese dimensies. LDG materie is al van belang sedert hul ontdekking in die 1970’s as gevolg van hul merkwaardige nie-lineêre en anisotrope elektriese eienskappe, reuse diëlektriese konstantes, ongewone elastiese eienskappe en ryk dinamiese gedrag. Sommige van hierdie eksotiese eienskappe is omvattend ondersoek in termiese ewewig kort na hul ontdekking, maar eers onlangs is dit moontlik deur middle van ultravinnige tegnieke soos femtosekonde spektroskopie om hulle uit-ewewigs gedrag te bestudeer op die tydskaal van atomiese beweging. Deur die gedrag op hierdie tydskaal te bestudeer kan ’n meer insiggewende begrip van hul makroskopiese eienskappe verkry word. Om ondersoeke in te stel op die atomiese tydskaal en gelyktydig direk die evolusie van die atoom posisie te waarneem is egter ’n moeilike taak. Een benadering is deur middle van femtosekonde “pump-probe” spektroskopie maar dan die gewone optiese “probe” puls om te skakel na ’n electron of x-straal puls wat van die materiaal kan diffrak en dus strukturele inligting op die atomiese vlak kan onthul. Hier word die femto-tot-pico sekonde uit-ewewig gedrag in 4Hb-TaSe2 ondersoek met behulp van elektron pulse. Twee variasies van die gebruik van ’n elektron bron word gebruik: konvensionele “Femtosecond Electron Diffraction” (FED) en ’n nuwe benadering, naamlik, “Femtosecond Streaked Electron Diffraction” (FSED). Die meer gevestigde FED tegniek, wat gebaseer is op femtosekonde “pump-probe” spektroskopie, word gebruik as die hoof ondersoek metode terwyl die FSED tegniek, wat gebaseer is op die ultra vinnige “streak camera” tegnologie, ’n poging is om beskikbare tegnieke uit te brei wat gebruik kan word om strukturele dinamika in materie te bestudeer op die sub-picosekonde tydskaal. Met behulp van hierdie twee tegnieke, word die strukturele dinamika tydens die fase oorgang van die ooreenkomstige tot nie-ooreenkomstige LDG fase in 4Hb-TaSe2 deur diffraksie patrone met ’n tydresolusie van minder as 500 fs waargeneem. Die studie toon ’n sterk korrelasie tussen die elektroniese sisteem en kristalrooster. Verskeie tydkonstantes van onder en bo ’n picosekonde kon ook uit die data onttrek word en gebruik word om die strukturele veranderinge beter te verstaan. Hierdie nuwe kennis het ons in staat gestel om ’n model van al die betrokke prosesse voor te stel.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Ultrafast electron diffraction is a powerful method to study atomic movement in crystals on sub-picosecond timescales. This thesis consists of three parts. In part one the ultrafast electron diffraction machine is described, followed by improvements that were made and techniques that were developed in order to bring the system to state of the art level and enable the acquisition of suffcient data to obtain information on the structural dynamics in crystals. The second part contains a description of the sample which was studied in our fi rst time-resolved measurements, the transition-metal dichalcogenide 4Hb-TaSe2. This particular crystal is an example of a strongly coupled electronic system which develops a charge density wave (CDW) accompanied by a periodic lattice distortion (PLD). An overview of the formation of electron diffraction patterns and what can be learned from them are also given, followed by the results of the ultrafast electron diffraction experiments done with 4Hb-TaSe2. Part three describes an alternative source to study dynamics in crystalline samples, namely laser plasma-based ultrafast X-ray diffraction. The ultrafast electron diffraction group functions as a unit, but my tasks ranged from sample preparation and characterisation of the electron beam to the setting up and execution of experiments. I was involved in analysing the data and contributed small parts to the data analysis software. / AFRIKAANSE OPSOMMING: Ultravinnige elektron diffraksie is a metode om die beweging van atome in kristalle op sub-pikosekonde tydskale te bestudeer. Hierdie tesis bestaan uit drie dele. In deel een van die tesis word die ultravinnige elektron diffraksie masjien beskryf, gevolg deur verbeteringe wat aangebring is en tegnieke wat ontwikkel is om die sisteem tot op 'n wêreldklas vlak te bring waar die insameling van genoegsame data om inligting oor die strukturele dinamika in kristalle te bekom, moontlik is. Die tweede deel bevat 'n beskrywing van die monster wat in ons eerste tydopgeloste eksperimente gebruik is, naamlik die oorgangsmetaaldichalkogenied 4Hb-TaSe2. Hierdie kristal is 'n voorbeeld van 'n sterk gekoppelde elektroniese sisteem wat 'n ladingsdigtheid-golf en 'n gepaardgaande periodiese versteuring van die kristalrooster ontwikkel. 'n Oorsig van die formasie van elektron diffraksiepatrone en wat ons daaruit kan leer word ook gegee. Daarna word die resultate van die ultravinnige elektron diffraksie eksperimente wat op 4Hb-TaSe2uitgevoer is beskryf en bespreek. In deel drie word 'n alternatiewe metode om die dinamika in kristalmonsters te bestudeer, naamlik laser plasma-gebaseerde ultravinnige X-straal diffraksie, beskryf. Die ultravinnige elektron diffraksie groep funksioneer as 'n eenheid, maar my verantwoordelikhede het gestrek van die voorbereiding van monsters en die karakterisering van die elektron bundel tot die opstel en uitvoer van eksperimente. Ek was ook betrokke by die analisering van data en het dele van die data analise sagteware geskryf.

Transition metal oxides (TMO) have proven to exhibit novel properties such as high temperature superconductivity, magnetic ordering, charge and spin density waves, metal to insulator transitions and colossal magnetoresistance. Among these are a spin-orbit coupling (SOC) induced Mott insulator Sr2IrO4. The electric transport properties of this material remain finite even at cryogenic temperatures enabling its complex electronic structure to be investigated by a scanning tunneling microscope. At T = 77 K, we observed two features which represent the Mott gap with a value of 2D ~ 615 meV. Additionally an inelastic loss feature was observed inside this gap due to a single magnon excitation at an energy of ~ 125 meV. These features are consistent with similar measurements with other probes. In addition to these features, at T = 4.2 K lower energy features appear which are believed to be due to additional magnetic ordering. Another material that exhibits a unique physical behavior is the sliding charge density wave (CDW) material TaS3. It is a quasi-one dimensional material that forms long narrow ribbon shaped crystals. It exhibits anomalies including non-ohmic conductivity, a decrease in the Young’s modulus, a decrease in the shear modulus and voltage induced changes in the crystal’s overall length. In addition, we have observed the torsional piezo-like response, voltage induced torsional strain (VITS), in TaS3 which was first discovered by Pokrovskii et. al. in 2007. Our measurements were conducted with a helical resonator. The VITS response has a huge effective piezoelectric coefficient of ~ 104 cm/V. In addition we have concluded that the VITS is a very slow response with time constants of ~ 1 s near the CDW depinning threshold, that these time constants are dependent on the CDW current, and we suggest that the VITS is due to residual twists being initially present in the crystal.

The understanding of new emerging unconventional ground states is a great challenge for experimental and theoretical solid-state physicists. New ground states are developing, where different energy scales compete, leading to a high sensitivity of the system to external tuning parameters like doping, pressure or magnetic field. The exploration of superconductivity proved to be a fascinating and challenging scientific undertaking. Discovered by H. Kammerlingh Onnes in 1911, prior to the development of the quantum theory of matter, superconductivity was defying a microscopic theory for more than four decades until the BCS theory was formulated in 1957 by J. Bardeen, L. N. Cooper and J. R. Schrieffer. Superconductivity of most of the simple metals or metallic alloys is well described within the frame of the BCS scenario, however, in the last thirty years numerous new superconducting materials were found to exhibit exotic properties not accounted for by the BCS theory. Among them are included the high-Tc compounds, the heavy-fermion superconductors and as well the organic superconductors. It was the purpose of this work to probe different facets of superconductivity in heavy-fermion and in low-dimensional metallic compounds. This dissertation is divided into six chapters. After this introduction, in Chapter 1 we will outline the basic theoretical concepts later needed for the analysis of the experimental results. In Chapter 2 we briefly introduce the experimental techniques with a special focus on the new pressure cells developed during this thesis and used for the measurements presented in Chapters 3 to 5. In Chapter 3 the possible realization of the inhomogeneous superconducting FFLO state in CeCoIn5 is studied by specific heat measurements under hydrostatic pressure, while in Chapter 4 the results of AC specific heat experiments on UBe13 under uniaxial pressure are presented. The ambient pressure properties as well as results obtained by resistivity measurements under hydrostatic pressure on the one-dimensional metallic compounds TlxV6S8 are discussed in Chapter 5. At the end, Chapter 6 summarizes and concludes this thesis.

The charge-density-wave (CDW) material orthorhombic tantalum trisulfide (TaS3) is a quasi-one dimensional material that forms long ribbon shaped crystals, and exhibits unique physical behavior. We have measured the dependence of the hysteretic voltage-induced torsional strain (VITS) in TaS3, which was first discovered by Pokrovskii et. al. in 2007, on temperature and applied torque. Our experimental results shows that the application of torque to the crystal could also change the VITS time constant, magnitude, and sign. This suggests that the VITS is a consequence of residual torsional strain originally present in the sample which twists the polarizations of the CDW when voltage is applied. This polarization twist then results in torque on the crystal. Another group of materials that may attract interest is that of small-molecule soluble organic semiconductors. Due to their assumed small phonon thermal conductivities and higher charge carrier mobilities, which will increase their seebeck coefficients with doping as compared to polymers, the small-molecule organic materials are promising for thermoelectric applications. In our experiments, we have measured the interlayer thermal conductivity of rubrene (C42H28), using ac-calorimetry. For rubrene, we find that the interlayer thermal conductivity, ≈ 0.7 mW/cm·K, is several times smaller than the (previously measured) in-plane value. Also, we have measured the interlayer and in-plane thermal conductivities of 6,13-bis((triisopropylsilyl)ethynyl) pentacene (TIPS-Pn). The in-plane value is comparable to that of organic metals with excellent π-orbital overlap. The interlayer (c-axis) thermal diffusivity is at least an order of magnitude larger than the in-plane, and this unusual anisotropy implies very strong dispersion of optical modes in the interlayer direction, presumably due to interactions between the silyl-containing side groups. Similar values for both in-plane and interlayer conductivities have been observed for several other functionalized pentacene semiconductors with related structures.

No description available.

The interplay between different self-organized electronically ordered states and their relation to unconventional electronic properties like superconductivity constitutes one of the most exciting challenges of modern condensed matter physics. In the present thesis this issue is thoroughly investigated for the prototypical layered material 1T-TaS2 both experimentally and theoretically. At first the static charge density wave order in 1T-TaS2 is investigated as a function of pressure and temperature by means of X-ray diffraction. These data indeed reveal that the superconductivity in this material coexists with an inhomogeneous charge density wave on a macroscopic scale in real space. This result is fundamentally different from a previously proposed separation of superconducting and insulating regions in real space. Furthermore, the X-ray diffraction data uncover the important role of interlayer correlations in 1T-TaS2. Based on the detailed insights into the charge density wave structure obtained by the X-ray diffraction experiments, density functional theory models are deduced in order to describe the electronic structure of 1T-TaS2 in the second part of this thesis. As opposed to most previous studies, these calculations take the three-dimensional character of the charge density wave into account. Indeed the electronic structure calculations uncover complex orbital textures, which are interwoven with the charge density wave order and cause dramatic differences in the electronic structure depending on the alignment of the orbitals between neighboring layers. Furthermore, it is demonstrated that these orbital-mediated effects provide a route to drive semiconductor-to-metal transitions with technologically pertinent gaps and on ultrafast timescales. These results are particularly relevant for the ongoing development of novel, miniaturized and ultrafast devices based on layered transition metal dichalcogenides. The discovery of orbital textures also helps to explain a number of long-standing puzzles concerning the electronic self-organization in 1T-TaS2 : the ultrafast response to optical excitations, the high sensitivity to pressure as well as a mysterious commensurate phase that is commonly thought to be a special phase a so-called “Mott phase” and that is not found in any other isostructural modification.

La formation des ondes de densité de charge (ODC) est un phénomène de brisure de symétrie qui apparaît dans systèmes électroniques, et particulièrement dans les conducteurs quasi-unidimensionnels. Elle est observée aussi bien dans les matériaux très anisotropes que les isotropes comme par exemple les supraconducteurs pnictures. L'ODC peut être vue comme une déformation sinusoïdale de la densité électronique et de la modulation du réseau, ou également comme un cristal de singulets électroniques. Dans un état d'ODC, les cellules élémentaires peuvent être modifiées en absorbant ou en rejetant des paires d'électrons. Un tel processus passe par des configurations topologiquement non triviales: des solitons et des dislocations, ou plus généralement des vortex d'ODC. Ces états inhomogènes peuvent être obtenus expérimentalement dans des nano-produits appelés ''mésa-jonctions'', et observés à l'aide d'un microscope à effet tunnel ou d’une radiographie par micro-diffraction. Afin de simuler ces expériences, nous avons réalisé un programme modélisant les états stationnaires d'ODC ainsi que leur dynamique transitoire à travers des géométries restreintes auxquelles sont appliquées une tension ou un courant. Le modèle prend en compte plusieurs champs en interaction non linéaire: le paramètre d'ordre complexe d'ODC, la distribution de champ électrique, ainsi que la densité et le courant des autres porteurs de charge. Nous avons utilisé une approche de type Ginzburg-Landau ainsi qu'une extension basée sur une propriété d'invariance chirale. A l'aide de ce programme, nous avons observé la création progressive de dislocations statiques dans les jonctions. La dynamique transitoire est alors très riche avec notamment des créations, des annihilations et des balayages de vortex multiples. Des chutes de tension apparaissent au centre des dislocations, créant ainsi des jonctions tunnel microscopiques à travers lesquelles transitent des paires électron-trou. Les résultats qualitatifs obtenus sont en très bon accord avec les observations expérimentales. Ce model peut aussi être étendu à tout type de cristaux électronique comme les cristaux de Wigner dans les hétéro-jonctions et les nano-fils, les ODC dans les composés de chaîne, les ondes de densité de spin dans les conducteurs organiques, ou encore les structures de bandes dans les oxydes dopés. La reconstruction des ODC dans les jonctions tunnel peut aussi trouver son importance dans l'étude des effets de champs sur les matériaux fortement corrélés induisant des brisures spontanées de symétries. / Formation of charge density waves (CDW) is a symmetry breaking phenomenon found in electronic systems, which is particularly common in quasi-one-dimensional conductors. It is widely observed from highly anisotropic materials to isotropic ones like the superconducting pnictides. The CDW is seen as a sinusoidal deformation of coupled electronic density and lattice modulation; it can be also viewed as a crystal of singlet electronic pairs. In the CDW state, the elementary units can be readjusted by absorbing or rejecting pairs of electrons. Such a process should go via topologically nontrivial configurations: solitons and dislocations - the CDW vortices. An experimental access to these inhomogeneous CDW states came from studies of nano-fabricated mesa-junctions, from the STM and from the X-ray micro-diffraction. Following these requests, we have performed a program of modeling stationary states and of their transient dynamic for the CDW in restricted geometries under applied voltage or at passing normal currents. The model takes into account multiple fields in mutual nonlinear interactions: the two components of the CDW complex order parameter, and distributions of the electric field, the density and the current of normal carriers. We were using the Ginzburg-Landau type approach and also we have derived its extension based on the property of the chiral invariance. We observed the incremental creation of static dislocations within the junctions. The transient dynamics is very rich showing creation, annihilation and sweeping of multiple vortices. The dislocations cores concentrate the voltage drops thus providing self-tuned microscopic junctions where the tunneling creation of electron-hole pairs can take place. The results obtained from this model agree with experiment observations. The methods can be extended to other types of charge organization known under the general name of the Electronic Crystal. It takes forms of Wigner crystals at hetero-junctions and in nano-wires, CDWs in chain compounds, spin density waves in organic conductors, and stripes in doped oxides. The studied reconstruction in junctions of the CDW may be relevant also to modern efforts of the field-effect transformations in strongly correlated materials with a spontaneous symmetry breaking.

Formation of charge density waves (CDW) is a symmetry breaking phenomenon found in electronic systems, which is particularly common in quasi-one-dimensional conductors. It is widely observed from highly anisotropic materials to isotropic ones like the superconducting pnictides. The CDW is seen as a sinusoidal deformation of coupled electronic density and lattice modulation; it can be also viewed as a crystal of singlet electronic pairs. In the CDW state, the elementary units can be readjusted by absorbing or rejecting pairs of electrons. Such a process should go via topologically nontrivial configurations: solitons and dislocations - the CDW vortices. An experimental access to these inhomogeneous CDW states came from studies of nano-fabricated mesa-junctions, from the STM and from the X-ray micro-diffraction. Following these requests, we have performed a program of modeling stationary states and of their transient dynamic for the CDW in restricted geometries under applied voltage or at passing normal currents. The model takes into account multiple fields in mutual nonlinear interactions: the two components of the CDW complex order parameter, and distributions of the electric field, the density and the current of normal carriers. We were using the Ginzburg-Landau type approach and also we have derived its extension based on the property of the chiral invariance. We observed the incremental creation of static dislocations within the junctions. The transient dynamics is very rich showing creation, annihilation and sweeping of multiple vortices. The dislocations cores concentrate the voltage drops thus providing self-tuned microscopic junctions where the tunneling creation of electron-hole pairs can take place. The results obtained from this model agree with experiment observations. The methods can be extended to other types of charge organization known under the general name of the Electronic Crystal. It takes forms of Wigner crystals at hetero-junctions and in nano-wires, CDWs in chain compounds, spin density waves in organic conductors, and stripes in doped oxides. The studied reconstruction in junctions of the CDW may be relevant also to modern efforts of the field-effect transformations in strongly correlated materials with a spontaneous symmetry breaking.