Probing the Structure and Photophysics of Porphyrinoid Systems for Functional Materials

Porphyrins (Pors) and their many cousins, including phthalocyanines (Pcs), corroles (Cors), subphthalocyanines (SubPcs), porphyrazines (Pzs), and naphthalocyanines (NPcs), play amazingly diverse roles in biological and non-biological systems because of their unique and tunable physical and chemical properties. These compounds, collectively known as porphyrinoids, can be employed in any number of functional devices that have the potential to address the challenges of modern society. Their incorporation into such devices, however, depends on many structural factors that must be well understood and carefully controlled in order to achieve the desired behavior. Self-assembly and self-organization are key processes for developing these new technologies, as they will allow for inexpensive, efficient, and scalable designs. The overall goal of this dissertation is to elucidate and ultimately control the interplay between the hierarchical structure and the photophysical properties of these kinds of systems. This includes several case studies concerning the design and spectroscopic analysis of supramolecular systems formed through simple, scalable synthetic methods. We also present detailed experimental and computational studies on some porphyrin and phthalocyanine compounds that provide evidence for fundamental changes in their molecular structure. In addition to their impact on the photophysics, these changes also have implications for the organization of these molecules into higher order materials and devices. It is our hope that these findings will help to drive chemists and engineers to look more closely at every level of hierarchical structure in the search for the next generation of advanced materials

Non-standard Hubbard models in optical lattices: a review

Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher $p$-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schr\"odinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.Comment: expanded version 47pp, accepted in Rep. Prog. Phy

Ultracold quantum scattering in the presence of synthetic spin-orbit coupling

Two-body scattering constitutes one of the most fundamental processes in various physical systems ranging from ultracold dilute quantum gases to energetic quark- gluon plasmas. In this dissertation, we study the low-energy atomic collision physics in the presence of synthetic gauge fields, which are generated by atom-light interaction. One category of synthetic gauge fields is the artificial spin-orbit coupling. We discuss three different aspects in scattering theory: ultracold collision, scattering resonance, and bound state formation from a few-body perspective when the atomic spin states are coupled with their center-of-mass motion. The understanding of the spin-orbit effects on the modification of the scattering processes not only builds the foundation of collision physics in the presence of non-abelian gauge fields but also paves the way towards unraveling the few-body correlations in many-body systems

Topological superconductors from a materials perspective

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (non-universal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSC, focusing on how a system is identified as a TSC candidate, and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.Comment: 42 pages, 6 figure