An exploration of some organic-inorganic hybrid metal fluorides and lanthanide containing metal organic frameworks (Ln-MOFs) has been carried out under ionothermal conditions. In this synthesis technique an ionic liquid (IL) or deep eutectic mixture (DES) is used as the solvent and in many cases as the provider of the organic structure directing agent. A wide range of ILs and DESs have been investigated as the reaction solvent for the synthesis of organically templated vanadium fluorides and oxyfluorides (VOFs), and initially this has proved to be successful with the isolation of 13 phases, including eight new materials. In the VOFs synthesis the IL acts as a solvent, however the DES acts as a solvent and also as a template delivery agent, where the expected template is provided by the partial breakdown of the urea derivative component. Interestingly, it has been shown that the same structure can be accessible via two different ways; either by using IL with an added templating source, or simply through the use of a DES without any other additive; since the template is provided by the in situ breakdown of the DES. The synthesis of VOFs with extended structures was achieved by the use of the hydrophobic IL 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM Tf₂N) as the solvent. [HNC₅H₅][V₂O₂F₅] represents the first VOF with a 2D network that contains exclusively V⁴⁺. This material may be considered as arising via condensation of the previously known ladder-like chains. Furthermore, using imidazole as an added template has produced another layer material that has significant similarities to the [HNC₅H₅][V₂O₂F₅] structure, but with some key differences. Within the same system three other phases were also isolated, including two novel materials displaying the known ladder-type building units. Further investigations in the ionothermal synthesis of VOF using EMIM Tf₂N resulted in a successful synthesis of [NH₄]₂[HNC₇H₁₃][V₇O₆F₁₈], a novel material displaying a unique double layered topology featuring a S = ½ kagome type lattice of V⁴⁺ ions (d¹). Two of the V⁴⁺ based kagome sheets are pillared by V³⁺ ions to form a double layered structure templated by both ammonium and quinuclidinium cations. This compound exhibits a high degree of magnetic frustration, with significant antiferromagnetic interactions but no long range ordering was observed above 2 K. This material presents an interesting comparison to the famous Herbertsmithite, ZnCu₃(OH)₆Cl₂, and may provide an excellent candidate for realising a quantum spin liquid (QSL) ground state. Interestingly, in this system the use of EMIM Tf₂2N as a solvent produces mainly V⁴⁺-containing materials, despite the high reaction temperature (170 °C). This characteristic is unprecedented in VOFs synthesis, as rising the reaction temperature above 150 °C in other techniques (i.e. hydrothermal synthesis) would often result in further reduction of V⁴⁺ to V³⁺. Using the ionothermal technique in the synthesis of hybrid iron fluorides resulted in the isolation of three chain-type materials. Again, the IL acts as the solvent and the DES acts as the solvent and also as the template provider where the expected template is released by the partial breakdown of the urea derivative component of the DES. The synthesis of Ln-MOF using a choline chloride/ 1,3-dimethylurea deep eutectic mixture has produced three novel isostructural materials. Usually, in ionothermally prepared materials (i.e. zeolites) the urea portion of the DES is unstable and breaks down in situ to form ammonium or alkylammonium cations. In the ionothermal synthesis of Ln-MOF, 1,3-dimethyurea (DMU) remains intact and is occluded in the final structure. Using a choline chloride/ethylene glycol deep eutectic solvent led to the isolation of a Ln-MOF with interesting structural properties, however none of the DES components appeared in the final structure. These results demonstrate once more the usefulness and applicability of the ionothermal synthesis method and emphasise how this synthesis technique can be further extended and applied in the preparation of important structures with unique properties and functionalities.

No description available.

The study of topological phases in condensed matter physics has seen remarkable advancements, primarily focusing on systems with a well-defined bulk and boundary. However, the emergence of topological phenomena on self-similar systems, characterized by the absence of a clear distinction between bulk and boundary, presents a fascinating challenge. This thesis focuses on the topological phases on self-similar systems, shedding light on their unique properties through the lens of adiabatic charge pumping. We observe that the spectral flow in these systems exhibits striking qualitative distinctions from that of translationally invariant non-interacting systems subjected to a perpendicular magnetic field. We show that the instantaneous eigenspectra can be used to understand the quantization of the charge pumped over a cycle, and hence to understand the topological character of the system. Furthermore, we establish a correspondence between the local contributions to the Hall conductivity and the spectral flow of edge-like states. We also find that the edge-like states can be approximated as eigenstates of the discrete angular-momentum operator, with their chiral characteristics stemming from this unique perspective. We also investigate the effect of local structure on the topological phases on self-similar structures embedded in two dimensions. We study a geometry dependent model on two self-similar structures having different coordination numbers, constructed from the Sierpinski gasket. For different non-spatial symmetries present in the system, we numerically study and compare the phases on both structures. We characterize these phases by the localization properties of the single-particle states, their robustness to disorder, and by using a real-space topological index. We find that both structures host topologically nontrivial phases and the phase diagrams are different on the two structures, emphasizing the interplay between non-spatial symmetries and the local structure of the self-similar unit in determining topological phases. Furthermore, we demonstrate the presence of topologically ordered chiral spin liquid on fractals by extending the Kitaev model to the Sierpinski Gasket. We show a way to perform the Jordan-Wigner transformation to make this model exactly solvable on the Sierpinski Gasket. This system exhibits a fractal density of states for Majorana modes and showcases a transition from a gapped to a gapless phase. Notably, the gapped phase features symmetry-protected Majorana corner modes, while the gapless phase harbors robust zero-energy and low-energy self-similar Majorana edge-like modes. We also study the vortex excitations, characterized by remarkable localization properties even in small fractal generations. These localized excitations exhibit anyonic behavior, with preliminary calculations hinting at their fundamental differences from Ising anyons observed in the Kitaev model on a honeycomb lattice.

No description available.