Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Two problems in the field of materials-based condensed matter physics, specifically in the field of superconductivity, are studied theoretically. In both problems, where each is of current exper- imental interest, an extension of Ginzburg-Landau theory is used to describe a physical system, with focus on the energy associated to the interface(s) occurring in the respective systems. The first physical system under consideration is that of a two-band superconductor. Using Ginzburg-Landau theory for two-band superconductors, the interface energy ¾s between normal and superconducting states coexisting at the thermodynamic critical magnetic field is determined. From the theoretical and numerical analysis of the interface energy, it is found that close to the transition temperature, where the Ginzburg-Landau theory is applicable, the two-band problem maps onto an effective single band problem. This finding puts into question the possibility of intermediate, so called type-1.5 superconductivity, in the regime where the Ginzburg-Landau theory applies. The second physical system is that of a system with competing superconductivity and anti- ferromagnetism. From Ginzburg-Landau theory for such competing systems in a thermodynamic critical magnetic field, it is shown that two possible interfaces can occur: an interface between a pure anti-ferromagnetic state and a pure superconducting state; and an interface between a state with coexisting superconductivity and anti-ferromagnetism and a pure anti-ferromagnetic state. The energy associated to both these interfaces is analysed theoretically and numerically from which the boundary between type-I and type-II superconductivity is obtained for certain specific cases. / AFRIKAANSE OPSOMMING: Twee probleme in die veld van materiaal-gebaseerde gekondenseerde materie fisika, spesifiek in die veld van supergeleiding, word teoreties bestudeer. In beide probleme, albei tans van eksper- imentele belang, word ’n fisiese sisteem beskryf deur ’n uitbreiding van enkel-band Ginzburg- Landau teorie, met fokus op die energie geassosieer met die koppelvlak(ke) wat in die onderskeie sisteme aangetref word. Die eerste fisiese sisteem wat beskou word is die van ’n twee-band supergeleier. Deur van Ginzburg-Landau teorie vir twee-band supergeleiers gebruik te maak, word die koppelvlak energie ¾s tussen die gelyktydig bestaande normaal- en supergeleidende toestand in die termodinamiese kritieke magneetveld bepaal. Deur beide teoretiese en numeriese analieses word bepaal dat na aan die oorgangstemperatuur, waar Ginzburg-Landau teorie geldig is, die twee-band probleem op ’n effektiewe een-band probleem afbeeld. Hierdie bevinding bevraagteken dus die moontlikheid van onkonvensionele, of sogenaamde tipe-1.5 supergeleiding, vir gevalle waar Ginzburg-Landau teorie geldig is. Die tweede fisiese siteem wat beskou word is ’n sisteem met kompeterende supergeleiding en anti-ferromagnetisme. Met behulp van Ginzburg-Landau teorie vir sulke sisteme in ’n termod- inamiese kritiese magneetveld word gewys dat daar twee moontlike koppelvlakke kan ontstaan: ’n koppelvlak tussen ’n uitsluitlik anti-ferromagnetiese toestand en ’n uitsluitlik supergeleidende toestand; sowel as ’n koppelvlak tussen ’n uitsluitlik anti-ferromagnetiese toestand en ’n toes- tand van beide supergeleiding en anti-ferromagnetisme. Die energie geassosieer met beide hierdie koppelvlakke word teoreties en numeries geanaliseer wat lei tot ’n beskrywing van die grenslyn tussen tipe-I en tipe-II supergeleiding in sekere spesifieke gevalle.

La découverte de l'effet Hall quantique par von Klitzing en 1980 a ouvert la voie à ce qui sera connu plus tard comme la théorie topologique des bandes. Dans le cadre de cette théorie, on ne s'intéresse plus uniquement à la relation de dispersion énergétique des électrons dans les cristaux, mais aussi à l'organisation topologique de la structure de bande. Cette théorie a permis la découverte d'une nouvelle phase de la matière, représentée par les isolants topologiques. Ces isolants topologiques ont de particulier qu'ils se comportent comme des isolants normaux dans le bulk, mais présentent des états de surface conducteurs. Dans cette thèse, on s'intéresse particu- lièrement aux isolants topologiques dits Z2, pour lesquels les états de surface sont protégés par la symétrie de renversement du temps : ils ne peuvent disparaître en présence d'une perturbation qui préserve cette symétrie sans que le système ne traverse une transition de phase quantique. Pour les isolants topologiques à trois dimensions, nous proposons dans cette thèse, un critère expérimental utilisant les oscillations quantiques magnétiques, permettant d'identifier un type particulier d'isolants topologiques : les isolants topologiques forts. Pour les systèmes à deux dimensions, nous nous sommes intéressés aux phénomènes liés à la rupture de la symétrie par renversement du temps à cause de la présence d'un ordre antiferro- magnétique. Dans ce cas, la symétrie d'importance devient le renversement du temps fois une translation. Dans ce contexte, nous avons tout d'abord établi analytiquement l'expression d'un invariant topologique pour les systèmes présentant aussi la symétrie d'inversion. Nous avons ensuite adapté trois méthodes numériques normalement utilisées dans le cadre des isolants topo- logiques invariants par renversement du temps : la méthode de la phase de jonction, la méthode des centres de charge des fonctions de Wannier et la construction explicite des états de bord. Nous avons montré qu'elles permettaient de tester la nature triviale ou topologique de plusieurs modèles théoriques pour lesquelles aucune méthode n'existait, par exemple les systèmes sans symétrie d'inversion. / The discovery of the quantum Hall effect by von Klitzing in 1980 paved the way for what is now known as topological band theory. In this theory, we are interested not only in the energy spectra of the electrons in crystals, but also in the topological structure of the bands. A new phase of matter was discovered thanks to this theory : the topological insulators. Topological insulators are unique in the sense that they behave like trivial insulators in the bulk, but possess metallic edge states. In this thesis, we are particularly interested in so-called Z2 topological insulators, whose edge states are protected by time reversal symmetry : they cannot disappear in the presence of a perturbation that respects this symmetry, without the system undergoing a quantum phase transition. For three-dimensional topological insulators, we propose an experimental criterion based on magnetic quantum oscillations to identify a special kind of topological insulators : the strong topological insulator. In two dimensions, we study the consequences of time reversal symmetry breaking due to anti-ferromagnetic order. In this case, the important symmetry is time reversal times a trans- lation. In this context, we first establish an analytical expression for systems that also have inversion symmetry. We then adapt three numerical methods usually employed for time reversal symmetric systems : the reconnection phase method, the Wannier charge center method and the explicit construction of edge states. We show that they are useful to probe the topology of models for which no methods were available ; such as non-centrosymmetric systems.

The following treatise is a collection of three experimental reports, detailing measurements made over the last several years on the magnetic properties of specific correlated electron systems. Each of these systems is an unconventional superconductor at low temperatures, but in each the metallic state from which the superconductivity condenses is poorly understood. The experiments presented will focus on temperatures greater than the superconducting transition temperature, and in particular on magnetic properties of the normal state, which are thought to be important. Original work is contained in Chapters 3, 4 and 5. Chapter 3 describes our search for the presence of time-reversal symmetry breaking in the pseudo-gap state of La2-xSrxCuO4 with zero-field μSR, and is largely based on previously published data. Additional data on the related systems La(1.875)Ba(0.125)CuO(4) and HgBa(2)CuO(4+δ) are also presented. Based on this data, we put strict upper limits on any time-reversal symmetry breaking field which can be associated with the pseudo-gap, and show that the current interpretation of recent neutron scattering results in the literature cannot be correct. Chapter 4 summarizes our explorations of overdoped La(2)-(x)Sr(x)CuO(4) in applied magnetic field with transverse-field μSR. We see an unconventional broadening of the local magnetic field distribution in response to applied field, and discuss possible interpretations. This chapter has also been prepared for publication. Chapter 5 describes measurements of the non-linear magnetic susceptibility of URu(2)Si(2) as a function of temperature and hydrostatic pressure. By examining the temperature dependence, we draw conclusions about the existence of the anti-ferromagnetism and 'hidden order' at each pressure, and construct a preliminary pressure-temperature phase diagram. / Thesis / Doctor of Philosophy (PhD)

Polycrystalline Zn1-xCrxO (0.01 ≤ x ≤ 0.09) samples synthesized by solid state reaction technique were sintered at different temperatures following slow step sintering schedule. Structural, micro-structural, optical, magnetic properties and homogeneity were investigated using suitable characterisation techniques. Cr2O3 and CrO2 phases have been detected in the XRD patterns and Raman spectra of Zn1-xCrxO samples with x ≥ 0.05. Photoluminescence study has indicated improved optical property of the samples compared to undoped ZnO. While low percentage Cr doped samples showed diamagnetic behaviour, higher percentage doped samples (≥ 5%) exhibited ferromagnetic, paramagnetic and anti-ferromagnetic behaviours depending upon the sintering temperatures. The magnetic properties have been analysed through Electron Spin Resonance study. A g-value of 1.97 indicates Cr in +3 valence state in doped ZnO system. Presence of Cr3+ and Cr4+ in ZnO is understood to facilitate super exchange interactions to promote ferromagnetism at room temperature. ESR study shows improved magnetic homogeneity achieved by slow step sintering process. / Physics / M. Sc. (Physics)

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