Interplay of queer symmetries and topology in laser written waveguide lattices

In this thesis the interplay of topological systems with symmetries is investigated both, theoretically and experimentally. The theoretical models are experimentally implemented and confirmed by means of femtosecond laser written waveguide structures.In dieser Arbeit wird das Zusammenspiel von topologischen Systemen mit Symmetrien sowohl theoretisch als auch experimentell untersucht. Die theoretischen Modelle wurden in Wellenleiterstrukturen, die mit einem Femtosekundenlaser geschriebenen wurden, experimentell realisiert und bestätigt

Interactions and Topology in Quantum Matter: Auxiliary Field Approach & Generalized SSH Models

Presented in this thesis are a set of projects which lie at the intersection between strong correlations and topological phases of matter. The first of these projects is a treatment of an infinite dimensional generalization of the SSH model with local Coulomb interactions which is solved exactly using DMFT-NRG. Observed in the solution is power-law augmentation of the non-interacting density of states, as well as a Mott transition. This calculation represents an exact solution to an interacting topological insulator in the strongly correlated regime at zero temperature. The second set of projects involves the development of methods for formulating non-interacting auxiliary models for strongly correlated systems. These auxiliary models are able to capture the full dynamics of the original strongly correlated model, but with only completely non-interacting degrees of freedom, defined in an enlarged Hilbert space. We motivate the discussion by performing the mapping analytically for simple interacting systems using non-linear canonical transformations via a Majorana decomposition. For the nontrivial class of interacting quantum impurity models, the auxiliary mapping is established numerically exactly for finite-size systems using exact diagonalization, and for impurity models in the thermodynamic limit using NRG, both at zero and finite temperature. We find that the auxiliary systems take the form of generalized SSH models, which inherit the topological characteristics of those models. These generalized SSH models are also formalized and investigated in their own right as novel systems. Finally, we apply this methodology to study the Mott transition in the Hubbard model. In terms of the auxiliary system, we find that the Mott transition can be understood as a topological phase transition, which manifests as the formation and dissociation of topological domain walls.Comment: PhD Thesis, University College Dublin. Supervisor: Andrew K. Mitchel

Design and characterization of functional nanomaterials on surfaces

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física de la Materia Condensada. Fecha de lectura: 21-10-2020The urgent need for developing new strategies to afford the increasing energy demand remains a challenge for many research fields, such as material science or energy engineering. In this respect, the field of nanoscience has emerged as a powerful field towards the design of functional nanomaterials, synthesized from both organic and inorganic materials. This new scientific discipline has led to the design of novel materials and opened up new avenues for traditional compounds. For instance, transition metal oxides have been proposed as promising catalysts in the oxygen evolution reaction for water splitting, of crucial relevance in clean energy. Additionally, the development of organic electronics, focused on the study of the electronic properties of carbon-based materials, plays an important role in the synthesis and transformation of traditional electronics by designing low-cost, flexible and sustainable electronic devices. In this thesis, we have grown and studied different nanomaterials on metallic surfaces related to energy efficiency, targeting to achieve global sustainability. First, we have studied the catalytic activity of CoO at the atomic scale towards the water splitting reaction. We have grown single bilayer CoO nanoislands, where the co-existence of two distinct phases has been observed. Such polymorphism has been rationalized due to the distinct lattice parameter and the registry with the substrate which induces the modification of its electronic properties, reactivity and, hence, of its catalytic activity. In addition, we have shown the capability to tune the phase by an electric field. Second, we have described the on-surface synthesis of new π-conjugated polymers with important applications in organic electronics. An innovative strategy towards the synthesis of low band gap π-conjugated polymers formed by acene or periacene units has been developed, which allows the control of their electronic structure, resonance form and topological quantum class by tuning the repeating unit size. Our results shed light into the atomistic adsorption and dissociation of water on a CoO model catalyst. Furthermore, we introduced pathways for controlling the electronic properties and quantum topological class of one dimensional polymers on metallic surface

Revealing hidden topologies in photonic crystals

This thesis is part of an effort to bring together two very active fields of physics: band topology and photonics. The field of band topology has revealed exotic phenomena such as robust, unidirectional edge states that occur at the interfaces between materials that belong to different topological phases. The Nobel Prize in Physics 2016 was awarded to Thouless, Haldane, and Kosterlitz, for predicting such phases in electronic systems where the topological edge states may revolutionise electronics and quantum computing. There is now great interest in reproducing such topological phases in photonics using photonic crystals: periodic nanostructures with tunable photonic bands. Realising such topological edge states in photonic devices could revolutionise optical data transport and optical quantum computing. In this thesis, we focus on two symmetry-protected topological phases that have been difficult to realise in photonics: the quantum spin-Hall effect (QSHE, protected by the fermionic time-reversal symmetry of electrons) and square-root topological semimetals (protected by chiral symmetry, also known as sublattice symmetry). We introduce a new topological index for C2T symmetric crystals that emulate the QSHE using the angular momentum of light to mimic the spin of electrons. For example, in 2015 Wu & Hu proposed a photonic analogue of the QSHE where the crystalline symmetries and bosonic time-reversal symmetries of the photons generated a pseudo-fermionic time-reversal symmetry. Subsequent works suggested that this crystal was a trivial phase rather than a non-trivial QSHE phase. However, we believe that our new topological index demonstrates the non-trivial QSHE-like nature of the photonic crystal introduced by Wu & Hu while accounting for all of the valence bands determined from full-wave calculations. We then study the topology of networks of voids and narrow connecting channels that are formed by the space between closely spaced perfect conductors. In photonics, chiral symmetry is often broken by long-range interactions, but Vanel et al 2017 showed that such void-channel networks can be mapped to analagous mass-spring systems in an asymptotically rigorous manner and therefore have only short-range interactions. We demonstrate that topological tight-binding models, such as square-root semimetals, can be reproduced in these void-channel networks with appropriate boundary conditions. Finally, we discuss an interesting application of closely spaced nanoscopic metallic particles in the mid-to-far infrared and larger wavelengths. We show that despite being composed of highly dispersive and lossy metals, the effective dielectrics are virtually dispersion-free throughout the infrared spectrum and can be even more transparent than natural dielectrics such as germanium in the far-infrared. The effective index can be tuned locally, allowing us to design gradient-index lenses where light is guided by a continuously varied local refractive index. We propose a novel gradient-index lens that exploits the simultaneous transparency and high metallic filling fraction of the effective dielectrics to create intense ‘doubly-enhanced’ hotspots where light is focused on the microscale and the electric field ‘squeezed’ between the metallic particles on the nanoscale.Open Acces

Novel wave phenomena in classical vibrations

In this thesis, from discrete spring-mass systems to continuous elastic solids, the possibility of achieving topological phases and elastic spin-Hall effect are analytically and numerically discussed. Originating from time-reversal symmetry breaking via applying external fields, a unidirectional and backscattering-immune edge state arises owing to the topological protection. Caused by the effective spin-orbit coupling, the elastic counterpart of spin-Hall effect arises at certain area of the momentum space. Also, the proposed arguments are verified by numerical calculation of practical mechanical crystals and elastic composites. We believe these studies pave the way for the future researches in topological elasticity. On the other hand, PT symmetry, which is a weaker restriction than Hermicity, allows real eigenvalues in a non-Hermitian Hamiltonian. However, it is challenging to introduce the PT condition into quantum mechanical systems. In this thesis, we consider an acoustic metamaterial made of periodically arranged spinning cylinders. By virtue of the rotational Doppler effects, the dispersion relation around the rotating speed of rods is significantly influenced by the rotation. The frequency shifts cause a PT symmetric Hamiltonian so that, at specific points, the spontaneous PT symmetry breaking emerges and exceptional points arise. Lastly a possible setup is discussed for the future experimental realisation

Investigations of topological phases for quasi-1D systems

For a long time, quantum states of matter have been successfully characterized by the Ginzburg-Landau formalism that was able to classify all different types of phase transitions. This view changed with the discovery of the quantum Hall effect and topological insulators. The latter are materials that host metallic edge states in an insulating bulk, some of which are protected by the existing symmetries. Complementary to the search of topological phases in condensed matter, great efforts have been made in quantum simulations based on cold atomic gases. Sophisticated laser schemes provide optical lattices with different geometries and allow to tune interactions and the realization of artificial gauge fields. At the same time, new concepts coming from quantum information, based on entanglement, are pushing the frontier of our understanding of quantum phases as a whole. The concept of entanglement has revolutionized the description of quantum many-body states by describing wave functions with tensor networks (TN) that are exploited for numerical simulations based on the variational principle. This thesis falls within the framework of the studies in condensed matter physics: it focuses indeed on the so-called synthetic realization of quantum states of matter, more specifically, of topological ones, which may have on the long-run outfalls towards robust quantum computers. We propose a theoretical investigation of cold atoms in optical lattice pierced by effective (magnetic) gauge fields and subjected to experimentally relevant interactions, by adding a modern numerical approach based on TN algorithms. More specifically, this work will focus on (i) interacting topological phases in quasi-1D systems and, in particular, the Creutz-Hubbard model, (ii) the connection between condensed matter and high energy physics studying the Gross-Neveu model and the discretization of Wilson-Hubbard model, (iii) implementing tensor network-based algorithms.Durante mucho tiempo, los estados cuánticos de la materia se han caracterizado con éxito por el formalismo de Ginzburg-Landau que permitió de clasificar todos los diferentes tipos de transiciones de fase. Esta visión cambió con el descubrimiento del efecto Hall cuántico y los aislantes topológicos. Estos últimos son materiales que albergan estados de borde metálicos en una masa aislante, algunos de los cuales están protegidos por las simetrías existentes. Conjuntamente a la búsqueda de fases topológicas en materia condensada, se han hecho grandes esfuerzos en simulaciones cuánticas basadas en gases atómicos fríos. Los sofisticados esquemas láser proporcionan redes ópticas con diferentes geometrías y permiten ajustar las interacciones y la realización de campos de gauge artificial. Al mismo tiempo, los nuevos conceptos que provienen de la información cuántica, basados en el entanglement, están empujando la frontera de nuestra comprensión de las fases cuánticas en su conjunto. El concepto de entanglement ha revolucionado la descripción de los estados cuánticos de muchos cuerpos al describir las funciones de onda con redes tensoras (TN) que se explotan para simulaciones numéricas basadas en el principio de variación. Esta tesis se enmarca en los estudios de física de la materia condensada: en particular, se centra en la llamada realización sintética de los estados cuánticos de la materia, más específicamente, de los topológicos, que pueden tener en las salidas a largo plazo hacia computadoras cuánticas robustas. Se propone una investigación teórica de los átomos fríos en la red óptica con campos de gauge efectivos y sometidos a interacciones relevantes experimentalmente, agregando un enfoque numérico moderno basado en algoritmos TN. Más específicamente, este trabajo se centrará en (i) fases topológicas en los sistemas cuasi-1D y, en particular, el modelo Creutz-Hubbard, (ii) la conexión entre la materia condensada y la física de alta energía estudiando el modelo Gross-Neveu y el discretización del modelo Wilson-Hubbard, (iii) implementación de algoritmos basados en redes tensoras

Magnetic Quantum Walks of Neutral Atoms in Optical Lattices

This thesis focuses on the simulation of the physics of a charged particle under an external magnetic field by using discrete-time quantum walks of a spin-1/2 particle in a two-dimensional lattice. By Floquet-engineering the quantum-walk protocol, an Aharonov–Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an abelian gauge field—the analog of a magnetic flux threading a two-dimensional electron gas. I show that in the strong-field regime, i.e. when the flux per plaquette of the lattice is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands. I demonstrate that the system behaves like a Chern insulator by computing the Chern numbers of the energy bands and studying the excitation of the midgap topologically protected edge modes. These modes are extended all along the boundaries of the magnetic domains and remain robust against perturbations that respect the gap closing conditions. Furthermore, I discuss a possible experimental implementation of this scheme using neutral atoms trapped in two dimensional spin-dependent optical lattices. The proposed scheme has a number of unique features, e.g. it allows one to generate arbitrary magnetic-field landscapes, including those with sharp boundaries along which topologically protected edge states can be localized and probed. Additionally, I introduce the scattering matrix approach in discrete-time quantum walks to probe the Hofstadter spectrum and compute its topological invariants. By opening up a discrete-time quantum walk system and connecting it to metallic leads, I demonstrate that the reflection/transmission probabilities of a particle from the scattering region give information on the energy spectrum and topological invariants of the system. Although the work presented here focuses on the physics of a single particle in a clean system, it sets the stage for studies of many-body topological states in the presence of interactions and disorder

Proceedings of the NASA Conference on Space Telerobotics, volume 1

The theme of the Conference was man-machine collaboration in space. Topics addressed include: redundant manipulators; man-machine systems; telerobot architecture; remote sensing and planning; navigation; neural networks; fundamental AI research; and reasoning under uncertainty