Tesi: "Topological physics"

1

Tapio, O. (Ossi). "Topological defects in cosmology". Master's thesis, University of Oulu, 2013. http://urn.fi/URN:NBN:fi:oulu-201302121030.

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In this dissertation I use one dimensional numerical simulations of classical scalar field theories to study density of topological defects. I devise and compare three methods of counting defects and run multiple simulations with varying parameters. Thesis begins with general description of evolution of the Universe and how topological defects might have influenced it. This is followed by general mathematical description of Kibble-Zurek Mechanism (the mechanism that causes topological defects to form). In the first chapter I go through of all textbook theory regarding one dimensional field and defects needed to understand the model I am simulating, the model itself being a 1+1 dimensional scalar field theory with O(N) symmetry. In the second chapter I derive three methods for finding defects in the simulation data. In the third chapter I describe the simulations themselves and go through the immediate results. In the fourth chapter I discuss the results of the simulations and suggest future simulations in order to study this subject further. In the Appendix are exact results of simulations, more detailed derivation of certain equations and the simulation code written in pseudo-code.

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2

Moore, Christopher Paul. "Tunneling Transport Phenomena in Topological Systems". Thesis, Clemson University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=13420479.

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Originally proposed in high energy physics as particles, which are their own anti-particles, Majorana fermions have never been observed in experiments. However, possible signatures of their condensed matter analog, zero energy, charge neutral, quasiparticle excitations, known as Majorana zero modes (MZMs), are beginning to emerge in experimental data. The primary method of engineering topological superconductors capable of supporting MZMs is through proximity-coupled semiconductor nanowires with strong Rashba spin-orbit coupling and an applied magnetic field. Recent tunneling transport experiments involving these materials, known as semiconductor-superconductor heterostructures, were capable for the first time of measuring quantized zero bias conductance plateaus, which are robust over a range of control parameters, long believed to be the smoking gun signature of the existence of MZMs. The possibility of observing Majorana zero modes has garnered great excitement within the field due to the fact that MZMs are predicted to obey non-Abelian quantum statistics and therefore are the leading candidates for the creation of qubits, the building blocks of a topological quantum computer. In this work, we first give a brief introduction to Majorana zero modes and topological quantum computing (TQC). We emphasize the importance that having a true topologically protected state, which is not dependent on local degrees of freedom, has with regard to non-Abelian braiding calculations. We then introduce the concept of partially separated Andreev bound states (ps-ABSs) as zero energy states whose constituent Majorana bound states (MBSs) are spatially separated on the order of the Majorana decay length. Next, through numerical calculation, we show that the robust 2 e²/h zero bias conductance plateaus recently measured and claimed by many in the community to be evidence of having observed MZMs for the first time, can be identically created due to the existence of ps-ABSs. We use these results to claim that all localized tunneling experiments, which have been until now the main way researchers have tried to measure MZMs, have ceased to be useful. Finally, we outline a two-terminal tunneling experiment, which we believe to be relatively straight forward to implement and fully capable of distinguishing between ps-ABSs and true topologically protected MZMs.

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3

Timothy, H. Hsieh Timothy (Timothy Hwa-wei). "Topological materials and quantum entanglement". Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/103228.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 83-91).
As the title implies, this thesis consists of two main topics: materials which realize topological phases of matter and applications of the concept of entanglement in understanding topological phases and their transitions. The first part will focus on a particular class of materials called topological crystalline insulators (TCI), which are bulk insulators with metallic boundary states protected by crystal mirror symmetries. The realization of TCIs in the SnTe class of materials and the anti-perovskite family will be described. The second part will focus on using entanglement notions to probe a topological phase transition, based on a single topological wavefunction. This is achieved by performing extensive partitions of the wavefunction, such as a checkerboard partition. Implementing this technique in one dimension naturally involves the use of tensor networks, which will be reviewed and then utilized.
by Timothy H. Hsieh.
Ph. D.

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4

Chess, Jordan J. "Mapping Topological Magnetization and Magnetic Skyrmions". Thesis, University of Oregon, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10684160.

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A 2014 study by the US Department of Energy conducted at Lawrence Berkeley National Laboratory estimated that U.S. data centers consumed 70 billion kWh of electricity. This represents about 1.8% of the total U.S. electricity consumption. Putting this in perspective 70 billion kWh of electricity is the equivalent of roughly 8 big nuclear reactors, or around double the nation's solar panel output. Developing new memory technologies capable of reducing this power consumption would be greatly beneficial as our demand for connectivity increases in the future. One newly emerging candidate for an information carrier in low power memory devices is the magnetic skyrmion. This magnetic texture is characterized by its specific non-trivial topology, giving it particle-like characteristics. Recent experimental work has shown that these skyrmions can be stabilized at room temperature and moved with extremely low electrical current densities. This rapidly developing field requires new measurement techniques capable of determining the topology of these textures at greater speed than previous approaches. In this dissertation, I give a brief introduction to the magnetic structures found in Fe/Gd multilayered systems. I then present newly developed techniques that streamline the analysis of Lorentz Transmission Electron Microscopy (LTEM) data. These techniques are then applied to further the understanding of the magnetic properties of these Fe/Gd based multilayered systems.

This dissertation includes previously published and unpublished co-authored material.

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5

Damodaran, K. "Topological defects in cosmology and nuclear physics". Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598261.

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This dissertation is concerned with topological defects that arise from symmetry breaking in the non-linear sigma model limits of scalar field theories. The nonlinear evolution of global topological defects in O (N) field theories provide a mechansims for sourcing hte cosmic microwave background (CMB) temperature anisotropy on the sky today. In these theories, N determines the type of defect based on the homotopy group of the underlying vacuum manifold. Additionally, in models of nuclear physics based on SU (2) gauge theories, π₃ defects can manifest themselves as static soliton solutions. A simple class of O (N) scalar fields are studied here. The defects considered were strings with N =2, monopoles with N =3, textures with N = 4 and a class of "non-topological" textures, with N =6. Calculations of the temperature anisotropy are computationally challenging. High precision is needed in order to cmopare predictions with new and future CMB observations. The anisotropy is calculated from the classic Sachs-Wolfe formula by using a real space evolution for the matter and radiatino fluids. In order to properly account for diffusion damping and the finnite thickness of the last scattering surface, the power spectra were compared to high precision calculations based on defect source stress energy tensor unequal-time correlators. Matching the tails of the spectra yielded an angualr smoothing scale l _D for the fluctuation maps. Ensembles of 10° maps of the sky today were produced for each defect. Defects also have implications in modesl of nucelar physics. The first π₃ soliton to be studied in nuclear physics was the Skyrmion, a topological solution to the nonlinear sigma model for pion fields. Skyrme introduced a four-derivative term to stabilize the soliton. Alternatively one could introduce gauge fields to stabilize the texture. It is shown that the presence of an extra identical Higgs doublet in a gauged SU (2) nonlinear sigma model can produce soliton solutions. The solution is related to the Sphaleron and Electroweak Skyrmion in the Standard Model, but unlike these solitons, it is dyanmically stable to small spherically symmetric perturbations. A similar solution is shown to exist in the Vector Dominance model, with p-mesons representing the gauge bosons of a hidden local SU (2) gauge symmetry of the nonlinear sigma model. This is in agreement with similar work done by Igarashi, Johmuar, Kobayashi, Otsu, Sato and Sawada.

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6

Yang, Biao. "Photonic topological metamaterials". Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8103/.

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Topology, a mathematical concept associated with global perspectives, was found to represent geometric aspects of physics. To date, various topological phases have been proposed and classified. Among them, topological gapless phases focusing on the degeneracies of energy bands serving as the singularities in the momentum space, attract much attention. Especially in the three-dimension, various topological semimetals have been proposed. With unit topological charge ±1, Weyl degeneracies have laid the foundation. Also, they show loads of exotic properties, such as Fermi arcs and chiral anomalies. Being relied on the band topology theory, topological gapless phases have also been transferred into classic systems, such as photonics, acoustics and mechanics. Here, we experimentally investigated photonic Weyl systems in the photonic continuum media, where electromagnetic intrinsic degrees of freedom play key roles in constructing the state space. Firstly, we researched chiral hyperbolic metamaterials, a type-II Weyl metamaterials, from which we directly observed topological surface-state arcs. Then, we report the discovery of ideal photonic Weyl systems, where helicoid structure of nontrivial surface states has been demonstrated. Finally, we construct photonic Dirac points, through analysing eigen reflection field, we found the correlation of topological charges in momentum and real spaces.

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7

Lu, Fuyan. "Topological Phases with Crystalline Symmetries". The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524790822570583.

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8

Lifschytz, Gilad. "Quantum gravity and topological field theory". Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/33529.

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9

Tang, Evelyn (Evelyn May Yin). "Topological phases in narrow-band systems". Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/103220.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 64-72).
I discuss several novel topological phases in correlated electron systems, realized through spin-orbit interactions and lattice effects especially narrow-band systems. The first realizes the fractional quantum Hall effect using geometric frustration and ferromagnetism to obtain a nearly flat band with a large bandgap and non-zero Chern number. This system can support this effect at high temperatures upon partial filling of the flat band. The second proposal builds upon this system: as the ground state is a fractional quantum Hall state, excitations of this state are anyons when there is an incommensurate filling. The underlying lattice allows access to a new regime in which the anyon gas can form a charged superfluid, including states with intrinsic topological order or that similar to a BCS-type state. The third proposal studies topological crystalline insulators and strain as an effective gauge field on the surface state Dirac fermions. The zero-energy Landau orbitals form a flat band where the high density of states gives rise to the interface superconductivity observed in IV-VI semiconductor multilayers at high temperatures, with non-BCS behavior. A discussion of superconductivity in flat band systems concludes and is contrasted with classic results for a typical electron gas. This work closely parallels that in references [1, 2, 3].
by Evelyn Tang.
Ph. D.

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10

Wu, Hao. "Excitations in Topological Superfluids and Superconductors". Thesis, Northwestern University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10259423.

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In this thesis I present the theoretical work on Fermionic surface states, and %the bulk Bosonic collective excitations in topological superfluids and superconductors. Broken symmetries %Bulk-edge correspondence in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. (Abstract shortened by ProQuest.)

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11

Wray, Andrew M. "Topological defects and black holes". Thesis, University of Newcastle Upon Tyne, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332341.

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12

Michieletto, Davide. "Topological interactions in ring polymers". Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/77355/.

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Ring polymers offer a richness of behaviours that are of broad interest and have deep consequences in many fields of Science. In this Thesis I investigate some general and universal properties, i.e. independent of the chemical nature of the polymers, emerging from systems made of a collection of rings. These will be studied by using methods of equilibrium and non-equilibrium Statistical Mechanics together with Molecular Dynamics and Monte Carlo simulations of coarse-grained models for the systems under investigation. Within these frameworks, important questions regarding the macroscopic behaviour of ring-shaped polymers have yet to find a satisfactory answer. The work presented in this Thesis finds its principal motivations in problems arising in Material Science, the so called \melt" of rings, and in Biology, such as the organisation of mitochondrial DNA in some organisms and the mechanisms governing the electrophoretic separation of DNA samples in gels. There are several theoretical challenges in these fields which represent state-of-the-art scientific research and whose partial answers are provided in the work presented in this Thesis. One of the major achievements of the work presented is the general understanding of the role played by topological properties, i.e. those invariant under smooth deformations of the polymer contour, on the macroscopic behaviour of the investigated systems. Finally, the conclusions drawn from the presented work can have important scientific consequences as they may ultimately lead to a more complete understanding of complicated issues in Biology and to the design of next-generation soft materials.

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13

Farrell, Aaron. "Topological superconductivity without proximity effect". Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119741.

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The search for a Majorana Fermion has been an area of intense interest in condensed matter research of late. This elusive particle, predicted to exist in 1937, has been sought after for both fundamental and practical reasons. On the fundamental level, no particle to date has been observed to be a Majorana fermion, meanwhile on the practical level a Majorana fermion, if found, would represent a non-abelian anyon and could thus be used to build a quantum computer. The search for a Majorana Fermion has recently shifted to topological superconductivity. Topological superconductors are categorized by the nontrivial winding of their order parameter phase and for this reason are expected to support Majorana Fermions in their vortex cores. Owing to this, the study of topological superconductors has intensified in recent years. Current proposals for a device that may behave as a topological superconductor are based on semiconductor heterostructures, where the spin-orbit coupled bands of a semiconductor are split by a band gap or Zeeman field and superconductivity is induced by proximity to a conventional superconductor. In this setup, topological superconductivity is obtained in the semiconductor layer and the proposed heterostructures typically include two or three layers of different materials. In this thesis we propose a simplification to these types of devices, suggesting a way in which the superconducting layer can be replaced. Part of our proposal includes a model Hamiltonian for these types of systems. This thesis will also develop several different methods to analyze this model Hamiltonian in various different parameter regimes with the ultimate goal of classifying its topology.
Récemment, une région d'intérêt en la recherché de la matière condensée est le recherche pour les "Majorana Fermions". Les physiciens sont fascinés avec cette particule pour des raisons fondamentales et pratiques. Fondamentalement, une particule se comporte comme un Majorana Fermion n'a jamais été trouvée avant. Pratiquement, un Majorana Fermion pourrait être utilisé pour la construction d'un ordinateur quantique. Dans les dernières années, les chercheurs ont commencé à chercher pour des Majorana Fermions dans les supraconducteurs. En particulier, les supraconducteurs topologiques sont crus de supportes les Majorana Fermions dans leur vortex cores et de ce fait des nombreux dispositifs supraconducteurs topologiques ont été proposées. Les propositions récemment sont basées sur les hétérostructures de trois ou deux couches. Dans ces hétérostructures, les bandes d'un semiconducteur avec le couplage de spin-orbit sont séparées par le champ Zeeman d'une couche ferromagnétique (ou un champ appliqué). Après cette, supraconductivité topologique est établie dans la couche de semiconductrice en raison de la proximité d'une couche de supraconducteur ordinaire. Dans cette thèse nous proposons une simplification des dispositifs décrits ci-dessus; nous suggérons un moyen d'enlever la couche de supraconductivité. Nous commençons par proposer un Hamiltonian du cette système et procède à développer des nombreuses méthodes pour analyser cette Hamiltonian avec l'objectif ultime de classifier la topologie de ce système.

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14

Zhong, Shudan. "Linear and Nonlinear Electromagnetic Responses in Topological Semimetals". Thesis, University of California, Berkeley, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=13421373.

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The topological consequences of time reversal symmetry breaking in two dimensional electronic systems have been a focus of interest since the discovery of the quantum Hall effects. Similarly interesting phenomena arise from breaking inversion symmetry in three dimensional systems. For example, in Dirac and Weyl semimetals the inversion symmetry breaking allows for non-trivial topological states that contain symmetry-protected pairs of chiral gapless fermions. This thesis presents our work on the linear and nonlinear electromagnetic responses in topological semimetals using both a semiclassical Boltzmann equation approach and a full quantum mechanical approach. In the linear response, we find a ``gyrotropic magnetic effect" (GME) where the current density $j

B$ in a clean metal is induced by a slowly-varying magnetic field. It is shown that the experimental implications and microscopic origin of GME are both very different from the chiral magnetic effect (CME). We develop a systematic way to study general nonlinear electromagnetic responses in the low-frequency limit using a Floquet approach and we use it to study the circular photogalvanic effect (CPGE) and second-harmonic generation (SHG). Moreover, we derive a semiclassical formula for magnetoresistance in the weak field regime, which includes both the Berry curvature and the orbital magnetic moment. Our semiclassical result may explain the recent experimental observations on topological semimetals. In the end, we present our work on the Hall conductivity of insulators in a static inhomogeneous electric field and we discuss its relation to Hall viscosity.

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15

Li, Cheng. "Engineering High Dimensional Topological Matters in Quantum Gases". The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1585827770946136.

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16

Pugh, David John Rhydwyn. "Topological structures in lattice gauge theory". Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279896.

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17

Clarke, David A. "Scale Setting and Topological Observables in Pure SU(2) LGT". Thesis, The Florida State University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=10935396.

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In this dissertation, we investigate the approach of pure SU(2) lattice gauge theory to its continuum limit using the deconfinement temperature, six gradient scales, and six cooling scales. We find that cooling scales exhibit similarly good scaling behavior as gradient scales, while being computationally more efficient. In addition, we estimate systematic error in continuum limit extrapolations of scale ratios by comparing standard scaling to asymptotic scaling. Finally we study topological observables in pure SU(2) using cooling to smooth the gauge fields, and investigate the sensitivity of cooling scales to topological charge. We find that large numbers of cooling sweeps lead to metastable charge sectors, without destroying physical instantons, provided the lattice spacing is fine enough and the volume is large enough. Continuum limit estimates of the topological susceptibility are obtained, of which we favor χ^1/4/T_c = 0.643(12). Differences between cooling scales in different topological sectors turn out to be too small to be detectable within our statistical error.

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18

Fatemi, Valla. "Quantum electronic transport in atomically layered topological insulators". Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115683.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 153-180).
The merger of topology and symmetry established a new foundation for understanding the physics of condensed matter, beginning with the notion of topological insulators (TIs) for electronic systems. For the time-reversal invariant TIs, a key aspect is the "helical" mode at the boundary of the system - that is, the ID edge of a 2D topological insulator or the 2D surface of a 3D topological insulator. These helical modes represent the extreme limit of spin-orbit coupling in that the spin-degenercy has been completely lifted while preserving time-reversal symmetry. This property is crucial for proposals realizing exotic excitations like the Majorana bound state. In this thesis, I present a series of experiments investigating electronic transport through the boundary modes of 3D and 2D topological insulators, specifically Bi1.5 Sb0.5 Te1.7 Se1.3 and monolayer WTe 2 , respectively. For the case of ultra-thin WTe 2 , I also present experiments detailing investigations of the 2D bulk states, finding a semimetallic state for the trilayer and a superconducting phase for the monolayer, both of which are strongly tunable by the electric field effect. The discovery of 2D topological insulator and 2D superconductor phases within the same material, accessible by standard solid state elecrostatic gates, places WTe2 in a unique situation among both TIs and superconductors, potentially enabling gate-configurable topological devices within a homogenous material platform.
by Valla Fatemi.
Ph. D.

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19

Barkeshli, Maissam. "Topological order in the fractional quantum Hall states". Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/68964.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 231-237).
This thesis is focused on the theoretical characterization of topological order in non-Abelian fractional quantum Hall (FQH) states. The first part of the thesis is concerned with the ideal wave function approach to FQH states, where the idea is to try to obtain model wave functions and model Hamiltonians for all possible FQH states and to have a physical way of characterizing their topological order. I will explain recent attempts to do this through the so-called pattern of zeros framework and its relation to conformal field theory. The first chapter about the pattern of zeros introduces the basic concepts for single-component FQH states, how it relates to the conformal field theory approach to FQH wave functions, and how it can be used to derive various topological properties of FQH states. The second chapter extends the pattern of zeros framework to multi-component non-Abelian FQH states; this is an attempt at a full classification of possible topological orders in FQH states. Aside from the ideal wave function methods. the other known general method of constructing non-Abelian FQH states is through the parton construction. Here the idea is to break apart the electron into other fermions, called partons. and assume that they form integer quantum Hall states. This method allows us to describe all known FQH states. After reviewing the parton construction, I will demonstrate how it can be used to derive the low energy effective field theories for some of the most well-known non-Abelian FQH states, the Zk parafermion (Laughlin/Moore-Read/Read-Rezayi) states. The parton construction will motivate yet another topological field theory, the U(1) x U(1) x Z2 Chern-Simons (CS) theory. I will demonstrate how to calculate many highly non-trivial topological properties of the U(1) x U(1) x Z2 CS theory, such as ground state degeneracy on genus g surfaces and various fusion properties of the quasiparticles. Using the U(1) x U(1) x Z2 CS theory, we will study phase transitions between bilayer Abelian states and non-Abelian states. The non-Abelian ones contain a series of new states, which we call the orbifold FQH states. These orbifold FQH states turn out to be important for the conceptual foundations of the pattern of zeros/vertex algebra approach to ideal FQH wave functions. We also find a series of non-Abelian topological phases - which are not FQH states and do not have protected gapless edge modes - that are separated from the deconfined phase of ZN gauge theories by a continuous phase transition. We give a preliminary analysis of these Z2 "twisted" ZN topological phases.
by Maissam Barkeshli.
Ph.D.

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20

Valentini, Stefano. "Transport properties in multi-terminal topological superconductors". Doctoral thesis, Scuola Normale Superiore, 2017. http://hdl.handle.net/11384/85902.

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[excerpt from the introduction:] This PhD thesis project is set in the broad area of mesoscopic physics, which deals with systems with size of few nanometers up to some micrometers. In particular, we focus on hybrid structures composed of superconductors and normal metals or semiconductors.

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21

Igram, Dale J. "A Topological Explanation of the Urbach Tail". Ohio University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1459885929.

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22

Bleu, Olivier. "Physics of quantum fluids in two-dimensional topological systems". Thesis, Université Clermont Auvergne‎ (2017-2020), 2018. http://www.theses.fr/2018CLFAC044/document.

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Cette thèse est consacrée à la description de la physique à une particule ainsi qu'à celle de fluides quantiques bosoniques dans des systèmes topologiques. Les deux premiers chapitres sont introductifs. Dans le premier, nous introduisons des éléments de théorie des bandes et les quantités géométriques et topologiques associées : tenseur métrique quantique, courbure de Berry, nombre de Chern. Nous discutons différents modèles et réalisations expérimentales donnant lieu à des effets topologiques. Dans le second chapitre, nous introduisons les condensats de Bose-Einstein ainsi que les excitons-polaritons de cavité.La première partie des résultats originaux discute des phénomènes topologiques à une particule dans des réseaux en nid d'abeilles. Cela permet de comparer deux modèles théoriques qui mènent à l'effet Hall quantique anormal pour les électrons et les photons dû à la présence d'un couplage spin-orbite et d'un champ Zeeman. Nous étudions aussi l'effet Hall quantique de vallée photonique à l'interface entre deux réseaux de cavités avec potentiels alternés opposés.Dans une seconde partie, nous discutons de nouveaux effets qui émergent due à la présence d'un fluide quantique interagissant décrit par l’équation de Gross-Pitaevskii dans ces systèmes. Premièrement, il est montré que les interactions spin anisotropes donnent lieu à des transitions topologiques gouvernées par la densité de particules pour les excitations élémentaires d’un condensat spineur d’exciton-polaritons.Ensuite, nous montrons que les tourbillons quantifiés d'un condensat scalaire dans un système avec effet Hall quantique de vallée, manifestent une propagation chirale le long de l'interface contrairement aux paquets d'ondes linéaires. La direction de propagation de ces derniers est donnée par leur sens de rotation donnant lieu à un transport de pseudospin de vallée protégé topologiquement, analogue à l’effet Hall quantique de spin.Enfin, revenant aux effets géométriques linéaires, nous nous sommes concentrés sur l’effet Hall anormal. Dans ce contexte, nous présentons une correction non-adiabatique aux équations semi-classiques décrivant le mouvement d’un paquet d’ondes qui s’exprime en termes du tenseur géométrique quantique. Nous proposons un protocole expérimental pour mesurer cette quantité dans des systèmes photonique radiatifs
This thesis is dedicated to the description of both single-particle and bosonic quantum fluid Physics in topological systems. After introductory chapters on these subjects, I first discuss single-particle topological phenomena in honeycomb lattices. This allows to compare two theoretical models leading to quantum anomalous Hall effect for electrons and photons and to discuss the photonic quantum valley Hall effect at the interface between opposite staggered cavity lattices.In a second part, I present some phenomena which emerge due to the interplay of the linear topological effects with the presence of interacting bosonic quantum fluid described by mean-field Gross-Pitaevskii equation. First, I show that the spin-anisotropic interactions lead to density-driven topological transitions for elementary excitations of a condensate loaded in the polariton quantum anomalous Hall model (thermal equilibrium and out-of-equilibrium quasi-resonant excitation configurations). Then, I show that the vortex excitations of a scalar condensate in a quantum valley Hall system, contrary to linear wavepackets, can exhibit a robust chiral propagation along the interface, with direction given by their winding in real space, leading to an analog of quantum spin Hall effect for these non-linear excitations. Finally, coming back to linear geometrical effects, I will focus on the anomalous Hall effect exhibited by an accelerated wavepacket in a two-band system. In this context, I present a non-adiabatic correction to the known semiclassical equations of motion which can be expressed in terms of the quantum geometric tensor elements. We also propose a protocol to directly measure the tensor components in radiative photonic systems

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23

Nemytov, Vadim. "Topological insulators: theory and electronic transport calculations". Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=114415.

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In this thesis we investigate quantum transport properties of topological insulator (TI) Bi2 Se3 from atomistic point of view. TI is a material having an energy gap in its bulk but supporting gapless helical states on its boundary. The helical states have Dirac-like linear energy dispersion continuously crossing the bulk band gap with a spin texture in which the electron spin is locked perpendicular to the electron momentum. The peculiar electronic structure of TI material Bi2 Se3 is due to a strong spin-orbit interaction and is protected by the time reversal symmetry. The thesis consists of two main parts. The first reviews the theory of TI and the second presents our atomistic calculations of electron transport in the Bi2 Se3 material. In the theoretical review of the physics of TI, I follow the literature and attempt to present it in a reasonably accessible manner. The theory of TI is explained in terms of well known physical phenomena including classical and quantum Hall effects, spin-orbit coupling, spin current, and spin-Hall effect. The concept of Berry's phase is then introduced to link with the formal conventionalclassification of TI by the topological Z2 invariants. The entire discussion is within the well known Bloch band theory. In the second part of this thesis, numerical studies of transport properties of Bi2 Se3 are presented. After a brief discussion of the relevant quantum transport theory and the tight binding atomistic model, we present our calculated quantum transport results of Bi2 Se3 films having a trench in the middle. Such a large defect, if on normal conductors, would cause significant back scattering of the carriers. Here, by topological protection of the helical states, back scattering is forbidden due to the spin-momentum locking. Nevertheless, large trenches in the film may cause the helical states on the surface to mix inside the trench, thereby affecting the transmission.
Dans cette thèse, nous étudions le transport quantique dans l'isolant topologique (TI) Bi2Se3 à partir d'un modèle d'échelle atomique. Un TI est un matériau ayant une structure de bande de type isolant bien qu'on y retrouve des états hélicodaux en surface. Ces états hélicoı̈daux ont une relation de dispersion linéaire, dite dispersion de Dirac, qui traverse la bande interdite du cristal. Ces électrons voyageant selon les relations de Dirac sont contraints à se mouvoir perpendiculairement à leur spin. La structure électronique particulière de l'isolant topologique Bi2Se3 est due à une forte interaction spin-orbite et est protégée par une symétrie par renversement du temps. Cette thse comporte deux grands segments. Dans un premier temps, nous présentons une synthèse de la théorie générale des isolants topologiques. Nous présentons ensuite les résultats de nossimulation de transport quantique dans le matériau Bi2Se3. Dans notre résumé de la théorie des TI, nous présentons une revue de littérature et décrivons conceptuellement, dans la mesure du possible, le comportement des TI de sorte à rendre notre texte intelligible au non-expert. La théorie des TI est expliquée à artir de phénomènes classiques et quantiques connus tels que l'effet Hall, l'interaction spin-orbite, le courant de spin, l'effet Hall de spin, etc. Le concept de la phase de Berry est ensuite introduit pour faire le pont avec la classiﬁcation traditionnelle des TI, laquelle se base sur les invariants topologiques de Z2. Le tout est présenté avec la théorie des bandes en ﬁligrane. Dans le second segment de cette thése, nous étudions les propriétés physiques du Bi2Se3 à partir de simulations numériques. Après une brève discussion de certains éléments pertinents empruntés de la théorie du transport quantique et du modèle des liens étroits d'échelle atomique, nous présentons les résultats d'une simulation dans laquelle des électrons voyagent à travers un film de Bi2Se3 ayant une dépression en son milieu. Un tel défaut provoquerait une forte diffusion des porteurs de charge dans un conducteur standard. Dans le cas qui nous concerne, la diffusion des états hélicoı̈daux est endiguée par la contrainte qui force ces états à voyager perpendiculairement à leur spin. Néanmoins, de larges dépressions dans le ﬁlm peuvent provoquer le mélange des états hélicoı̈daux de surface et des états localisés à l'intérieur du cristal, ce qui affecte le transport des porteurs de charge.

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24

Cooper, Leith. "The topological membrane approach to string theory". Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390412.

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25

Higginbotham, Andrew Patrick. "Quantum Dots for Conventional and Topological Qubits". Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:23845477.

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This thesis presents a series of quantum dot studies, performed with an eye towards improved conventional and topological qubits. Chapters 1-3 focus on improved conventional (spin) qubits; Chapters 4-6 focus on the topological Majorana qubits. Chapter 1 presents the first investigation of Coulomb peak height distributions in a spin-orbit coupled quantum dot, realized in a Ge/Si nanowire. Strong spin-orbit coupling in this hole-gas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the open-wire regime places a bound on the spin-orbit length (lso < 20 nm), consistent with values extracted in the Coulomb blockade regime (lso < 25 nm). Chapters 2 & 3 demonstrate operation of improved spin qubits. Chapter 2 continues the investigation of Ge/Si nanowires, demonstrating a qubit with tenfold-improved dephasing time compared to the standard GaAs case. e combination of long dephasing time and strong spin-orbit coupling suggests that Ge/Si nanowires are promising for a spin-orbit qubit. In Chap. 3, multi-electron spin qubits are operated in GaAs, and improved resilience to charge noise is found compared to the single-electron case. Chapters 4 & 5, present a series of studies on composite superconductor/semiconductor Al/InAs quantum dots. Detailed study of transport cycles and Coulomb blockade peak spacings in zero magnetic field are presented in Chap. 4, and the parity lifetime of a bound state in the nanowire is inferred to exceed 10 milliseconds. Next, in Chap. 5, finite magnetic field behavior is investigated while varying quantum dot length. Coulomb peak spacings are consistent with the emergence of Majorana modes in the quantum dot. The robustness of Majorana modes to magnetic-field perturbations is measured, and is found to be exponential with increasing nanowire length. Coulomb peak heights are also investigated, and show signatures of electron teleportation by Majorana fermions. Finally, Chap. 6 outlines some schemes to create topological Majorana qubits. Using experimental techniques similar to those in Chap.’s 2 & 3, it may be possible to demonstrate Majorana initialization, readout, and fusion rules.
Physics

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26

Hart, Sean. "Electronic Phenomena in Two-Dimensional Topological Insulators". Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493567.

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In recent years, two-dimensional electron systems have played an integral role at the forefront of discoveries in condensed matter physics. These include the integer and fractional quantum Hall effects, massless electron physics in graphene, the quantum spin and quantum anomalous Hall effects, and many more. Investigation of these fascinating states of matter brings with it surprising new results, challenges us to understand new physical phenomena, and pushes us toward new technological capabilities. In this thesis, we describe a set of experiments aimed at elucidating the behavior of two such two-dimensional systems: the quantum Hall effect, and the quantum spin Hall effect. The first experiment examines electronic behavior at the edge of a two-dimensional electron system formed in a GaAs/AlGaAs heterostructure, under the application of a strong perpendicular magnetic field. When the ratio between the number of electrons and flux quanta in the system is tuned near certain integer or fractional values, the electrons in the system can form states which are respectively known as the integer and fractional quantum Hall effects. These states are insulators in the bulk, but carry gapless excitations at the edge. Remarkably, in certain fractional quantum Hall states, it was predicted that even as charge is carried downstream along an edge, heat can be carried upstream in a neutral edge channel. By placing quantum dots along a quantum Hall edge, we are able to locally monitor the edge temperature. Using a quantum point contact, we can locally heat the edge and use the quantum dot thermometers to detect heat carried both downstream and upstream. We find that heat can be carried upstream when the edge contains structure related to the $\nu=2/3$ fractional quantum Hall state. We further find that this fractional edge physics can even be present when the bulk is tuned to the $\nu=1$ integer quantum Hall state. Our experiments also demonstrate that the nature of this fractional reconstruction can be tuned by modifying the sharpness of the confining potential at the edge. In the second set of experiments, we focus on an exciting new two-dimensional system known as a quantum spin Hall insulator. Realized in quantum well heterostructures formed by layers of HgTe and HgCdTe, this material belongs to a set of recently discovered topological insulators. Like the quantum Hall effect, the quantum spin Hall effect is characterized by an insulating bulk and conducting edge states. However, the quantum spin Hall effect occurs in the absence of an external magnetic field, and contains a pair of counter propagating edge states which are the time-reversed partners of one another. It was recently predicted that a Josephson junction based around one of these edge states could host a new variety of excitation called a Majorana fermion. Majorana fermions are predicted to have non-Abelian braiding statistics, a property which holds promise as a robust basis for quantum information processing. In our experiments, we place a section of quantum spin Hall insulator between two superconducting leads, to form a Josephson junction. By measuring Fraunhofer interference, we are able to study the spatial distribution of supercurrent in the junction. In the quantum spin Hall regime, this supercurrent becomes confined to the topological edge states. In addition to providing a microscopic picture of these states, our measurement scheme generally provides a way to investigate the edge structure of any topological insulator. In further experiments, we tune the chemical potential into the conduction band of the HgTe system, and investigate the behavior of Fraunhofer interference as a magnetic field is applied parallel to the plane of the quantum well. By theoretically analyzing the interference in a parallel field, we find that Cooper pairs in the material acquire a tunable momentum that grows with the magnetic field strength. This finite pairing momentum leads to the appearance of triplet pair correlations at certain locations within the junction, which we are able to control with the external magnetic field. Our measurements and analysis also provide a method to obtain information about the Fermi surface properties and spin-orbit coupling in two-dimensional materials.
Physics

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27

Teh, Nicholas Joshua Yii Wye. "On topological objects in field theory". Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610763.

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28

Liu, Jimmy Fangzhou. "Many-body entanglement : topological orders, tensor networks and superconductivity". Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99299.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 147-152).
In this thesis, we discuss the characterization and application of quantum many-body entanglements. We try to establish a non-local "order parameter" description of different patterns of many-body entanglement, which are also named topological orders. In 2+ 1D, we show that this could be achieved by calculating the non-Abelian geometric phase (S, T)-matrices from the fixed-point wave functions, obtained in the string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen. In doing so, (S, T)-matrices act as our non-local "order parameter" and give a full characterization of 2+ 1D exact topological orders (topological orders that have a gappable edge). For a generic non-fixed-point wave function, however, obtaining the (S, T)-matrices is numerically formidable. To go around this problem, we introduce a new tensor-network method that works on any generic wave function, and obtain the "environment matrix" as a less powerful "order parameter" description. The "environment matrix" can characterize topological orders described by any gauge theory as well as ID symmetry protected topological (SPT) orders. As an application of both the concept of many-body entanglement and the new tensor-network method developed earlier, in the last chapter of the thesis, we propose a non-BCS mechanism for superconductivity, in which the driving force is not traditional pair-attraction, but statistical confusion of charge carrier induced by strong many-body entanglement. This may open new doors for identifying and constructing new superconducting states.
by Jimmy Fangzhou Liu.
Ph. D.

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29

Demers, Jean-Guy. "Aspects of theories with dynamical, topological or gauge symmetries". Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28058.

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30

Starodubtsev, Artem. "Topological methods in quantum gravity". Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1217.

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The main technical problem with background independent approaches to quantum gravity is inapplicability of standard quantum field theory methods. New methods are needed which would be adapted to the basic principles of General Relativity. Topological field theory is a model which provides natural tools for background independent quantum gravity. It is exactly soluble and, at the same time, diffeomorphism invariant. Applications of topological field theory to quantum gravity include description of boundary states of quantum General Relativity, formulation of quantum gravity as a constrained topological field theory, and a new perturbation theory which uses topological field theory as a starting point. The later is the central theme of the thesis. Unlike the traditional perturbation theory it does not require splitting metric into a background and fluctuations, it is exactly diffeomorphism invariant order by order, and the coupling constant of this theory is dimensionless. We describe the basic ideas and techniques of this perturbation theory as well as inclusion of matter particles, boundary states, and other necessary tools for studying scattering problem in background independent quantum gravity.

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31

Dos, Santos Luiz Henrique Bravo. "Topological Properties of Interacting Fermionic Systems". Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10195.

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This thesis is a study of three categories of problems in fermionic systems for which topology plays an important role: (i) The properties of zero modes arising in systems of fermions interacting with a bosonic background, with a special focus on Majorana modes arising in the superconductor state. We propose a method for counting Majorana modes and we study a mechanism for controlling their number parity in lattice systems, two questions that are of relevance to the protection of quantum bits. (ii) The study of dispersionless bands in two dimensions as a platform for correlated physics, where it is shown the possibility of stabilizing the fractional quantum Hall effect in a flat band with Chern number. (iii) The extension of the hierarchy of quantum Hall fluids to the case of time-reversal symmetric incompressible ground states describing a phase of strongly interacting topological insulators in two dimensions.
Physics

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32

Ellis, K. V. "TRAPS : Topological Reconstruction Algorithm for Parton Scatters". Thesis, Queen Mary, University of London, 2012. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8556.

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There is strong motivation to study standard model physics using the highest-energy data provided by the Large Hadron Collider. This is aided by the process of defining clusters of hadrons to form ‘jets’. Existing jet-finders are dependent on pre-defined parameters which, to some extent, influence their properties. This thesis introduces a novel algorithm which aims to reconstruct partons outgoing from hard interactions, prior to any splitting, by concentrating solely on the highest momentum transfer scale. In this way parton properties such as fragmentation and structure functions from hadron colliders may be compared directly with results from DIS and e+e− annihilation. This original, standalone tool is named ‘traps’ - the Topological Reconstruction Algorithm for Parton Scatters. The algorithm was developed using Pythia Monte Carlo QCD events, under a pragmatic approach that assumes the model provides a good approximation to reality at both hadronic and partonic level. Various tests were made to gauge the performance of the algorithm against standard jet-finders. The infrared safety and algorithm speed were also assessed. The objective of traps is to have low sensitivity to parameters, and to be fast and robust. A high event acceptance is necessary, as maximum statistics are required where cross-sections are at their lowest. A chapter of this thesis is dedicated to a description of the author’s studies in calibration and monitoring of the timing of the ATLAS Level-1 Calorimeter Trigger system. Pulses from triggered energy are sent via largely η× φ = 0.1 × 0.1 granularity ‘trigger towers’. Synchronous triggering with 1-2 ns precision is required for the system to make an accurate energy estimate.

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33

Pagano, Michael. "21 cm cosmology of topological defects". Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110543.

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Cosmic strings are linear concentrations of trapped energy produced throughsymmetry breaking processes of eld theory models. Though they can onlycontribute a maxiumum of 10 percent to structure formation they have beenshown to arise as a generic consequence of many inationary setups of supergravitymodels. In addition they provide another avenue to probe physicsbeyond the "Standard Model". Cosmic strings can intersect producing stringloops. These topological defects are formed at early times creating largeamounts of accretion and thus lead to large amounts of baryon overdensities.These baryonic overdensities of hydrogen lead to a unique 21cm signature.We focus on cosmic string loops in addition to global monopoles and computethe 21cm signature produced by these structures. It is found that both defectsproduce an elliptical region in 21cm radiation maps with a large emissionsignal which may serve as a prediction for upcoming 21cm redshift surveys.
Les défauts topologiques sont des configurations linéaires d'énergie concentrée produites par certaines brisures de symétries en théorie des champs. Aussi fût-il montré qu'ils sont une conséquence de plusieurs modèles de supergravité. Ces défauts topologiques, formés très tôt dans l'évolution de l'univers, créent d'importantes quantités d'accrétion et produisent une grande quantité de surdensité de baryons. Les surdensités de baryons d'hydrogène génèrent une signature unique de 21cm. Nous focussons sur deux défauts topologique particuliers soit le monopole global et la corde cosmique bouclée et calculons la signature à 21cm produite par chacunes de ces structures. Nous montrons que les deux défauts topologique ci-haut produisent une région elliptique dans la carte de radiation à 21cm avec un grand signal d'émission qui pourrait éventuellement servir comme prédiction pour le future relevé du décalage vers le rouge à 21cm.

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34

Pan, Yue. "Topological Origin of the Urbach Tail". Ohio University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1235514573.

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35

Chiel, Joshua R. "Natural Mechanical Topological Insulators". Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1586315731890489.

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36

Muhamed, Abera Ayalew. "Moduli spaces of topological solitons". Thesis, University of Kent, 2015. https://kar.kent.ac.uk/47961/.

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This thesis presents a detailed study of phenomena related to topological solitons (in $2$-dimensions). Topological solitons are smooth, localised, finite energy solutions in non-linear field theories. The problems are about the moduli spaces of lumps in the projective plane and vortices on compact Riemann surfaces. Harmonic maps that minimize the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions in real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the behaviour of lumps and their symmetries. An interesting feature is that the moduli space of charge $3$ lumps is a $7$- dimensional manifold of cohomogeneity one. In this thesis, we discuss the charge $3$ moduli space, calculate its metric and find explicit formula for various geometric quantities. We discuss the moment of inertia (or angular integral) of moduli spaces of charge $3$ lumps. We also discuss the implications for lump decay. We discuss interesting families of moduli spaces of charge $5$ lumps using the symmetry property and Riemann-Hurwitz formula. We discuss the K\"ahler potential for lumps and find an explicit formula on the $1$-dimensional charge $3$ lumps. The metric on the moduli spaces of vortices on compact Riemann surfaces where the fields have zeros of positive multiplicity is evaluated. We calculate the metric, K\"{a}hler potential and scalar curvature on the moduli spaces of hyperbolic $3$- and some submanifolds of $4$-vortices. We construct collinear hyperbolic $3$- and $4$-vortices and derive explicit formula of their corresponding metrics. We find interesting subspaces in both $3$- and $4$-vortices on the hyperbolic plane and find an explicit formula for their respective metrics and scalar curvatures. We first investigate the metric on the totally geodesic submanifold $\Sigma_{n,m},\, n+m=N$ of the moduli space $M_N$ of hyperbolic $N$-vortices. In this thesis, we discuss the K\"{a}hler potential on $\Sigma_{n,m}$ and an explicit formula shall be derived in three different approaches. The first is using the direct definition of K\"ahler potential. The second is based on the regularized action in Liouville theory. The third method is applying a scaling argument. All the three methods give the same result. We discuss the geometry of $\Sigma_{n,m}$, in particular when $n=m=2$ and $m=n-1$. We evaluate the vortex scattering angle-impact parameter relation and discuss the $\frac{\pi}{2}$ vortex scattering of the space $\Sigma_{2,2}$. Moreover, we study the $\frac{\pi}{n}$ vortex scattering of the space $\Sigma_{n,n-1}$. We also compute the scalar curvature of $\Sigma_{n,m}$. Finally, we discuss vortices with impurities and calculate explicit metrics in the presence of impurities.

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37

Archer, Francis John. "A simplicial approach to topological quantum field theory". Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260593.

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38

Levin, Michael Aaron Ph D. Massachusetts Institute of Technology. "String-net condensation and topological phases in quantum spin systems". Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/36810.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
Includes bibliographical references (p. 81-86).
For many years, it was thought that Landau's theory of symmetry breaking could describe essentially all phases and phase transitions. However, in the last twenty years, it has become clear that at zero temperature, quantum mechanics allows for the possibility of new phases of matter beyond the Landau paradigm. In this thesis, we develop a general theoretical framework for these "exotic phases" analogous to Landau's framework for symmetry breaking phases. We focus on a particular type of exotic phase, known as "topological phases", and a particular physical realization of topological phases - namely frustrated quantum magnets. Our approach is based on a new physical picture for topological phases. We argue that, just as symmetry breaking phases originate from the condensation of particles, topological phases originate from the condensation of extended objects called "string-nets." Using this picture we show that, just as symmetry breaking phases can be classified using symmetry groups, topological phases can be classified using objects known as "tensor categories."
(cont.) In addition, just as symmetry breaking order manifests itself in local correlations in a ground state wave function, topological order manifests itself in nonlocal correlations or quantum entanglement. We introduce a new quantity - called "topological entropy" - which measures precisely this nonlocal entanglement. Many of our results are applicable to other (non-topological) exotic phases.
by Michael Aaron Levin.
Ph.D.

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39

Lue, Arthur. "Topological structure in classical and quantum SU(2)-Higgs theories". Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/10373.

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40

Rauch, Marco [Verfasser]. "Topological string theory, modularity and non-perturbative physics / Marco Rauch". Bonn : Universitäts- und Landesbibliothek Bonn, 2011. http://d-nb.info/1016219601/34.

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41

Jaubert, Ludovic D. C. "Topological Constraints and Defects in Spin Ice". Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2009. http://tel.archives-ouvertes.fr/tel-00462970.

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La glace de spin est un matériau magnétique frustré (cristal de Titane d'Holmium ou de Dysprosium par exemple ...), ayant pour propriété essentielle l'existence d'un état fondamental macroscopiquement dégénéré et donc une entropie non nulle à 0 Kelvin. La frustration géométrique dans ce composé donne lieu à de fortes contraintes topologiques sur les spins. Dans cette thèse, je présenterai certaines conséquences de ces contraintes, telles que l'apparition de transition de phases exotiques en présence de champ magnétique ou de pression, ou bien l'émergence d'excitations locales analogues à des monopoles magnétiques dont l'influence est primordiale dans la dynamique des composés de glace de spin !

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42

Ronquillo, David C. "Identifying topological order in the Shastry-Sutherland model via entanglement entropy". Thesis, California State University, Long Beach, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1596474.

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It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, –γ, called the topological entanglement entropy. We theoretically study the entanglement entropy of the two-dimensional Shastry-Sutherland quantum antiferromagnet using exact diagonalization on clusters of 16 and 24 spins. By utilizing the Kitaev-Preskill construction, we extract a finite topological term, –γ , in the region of bond-strength parameter space corresponding to high geometrical frustration. Thus, we provide strong evidence for the existence of an exotic topologically ordered state and shed light on the nature of this model's strongly frustrated, and long controversial, intermediate phase.

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43

Cacciuto, Angelo. "Statistical mechanics of self-avoiding crystalline membranes and topological defect formation". Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2002. http://wwwlib.umi.com/cr/syr/main.

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44

Wolf, Michael Scott. "Infrared and Optical Studies of Topological Insulators BI2TE3 BI2SE3 and SB2TE3". University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1310675743.

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45

Chow, Chee-Seng. "Phoenix : an interactive hierarchical topological floorplanning placer". Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/77677.

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; and, (B.S.)--Massachusetts Institute of Technology, Dept. of Physics; and, (B.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1985.
Bibliography: leaf 141.
by Chee-Seng Chow.
M.S.
B.S.

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46

Brell, Courtney Gordon Gray. "Many-body models for topological quantum information". Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/13539.

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We develop and investigate several quantum many-body spin models of use for topological quantum information processing and storage. These models fall into two categories: those that are designed to be more realistic than alternative models with similar phenomenology, and those that are designed to have richer phenomenology than related models. In the first category, we present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the perturbative low-energy limits of entirely two-body Hamiltonians. This construction reproduces the target models' behavior using only couplings which are natural in terms of the original Hamiltonians. As an extension of this work, we construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). We define a perturbative Hamiltonian with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. We then move on to define models that generalize the phenomenology of several well-known systems. We first define generalized cluster states based on finite group algebras, and investigate properties of these states including their PEPS representations, global symmetries, relationship to the Kitaev quantum double models, and possible applications. Finally, we propose a generalization of the color codes based on finite groups. For non-Abelian groups, the resulting model supports non-Abelian anyonic quasiparticles and topological order. We examine the properties of these models such as their relationship to Kitaev quantum double models, quasiparticle spectrum, and boundary structure.

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47

Hagan, Scott. "Scale invariant and topological approaches to the cosmological constant problem". Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=39926.

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The cosmological constant is historically reviewed from its introduction in classical and relativistic cosmology through its modern quantum guise where it appears as a vacuum energy density. Limits on the empirical value are in glaring contradiction to the expectations of field theoretical calculations.
Motivated by the natural connection between dilatation invariance and the extinction of the vacuum energy density, a phenomenological realization of a global scale symmetry is constructed. A complete treatment of such a realization in the context of a supergravitational toy model is calculated to one loop using an effective potential formalism. Particular attention is paid to the quantization of both supersymmetric and general coordinate gauges and to the concomitant ghost structure since traditional treatments have introduced non-local operators in the ghost Lagrangian and generating functional. Contributions to the effective potentid from the gravity sector are thus determined that contradict the literature. A particular class of tree-level scalar potentials that includes the 'no-scale' case is studied in the that space limit. While it is found that scale invariance can be maintained at the one-loop level and the cosmological constant made to vanish for all potentials in the class this is directly attributable to supersymmetry. A richer form of the Kahler potential or an enlarged particle content may facilitate the breaking of supersymmetry.
Phenomenological consequences of supergravity are investigated through a one-loop calculation of the electromagnetic form factor of the gravitino. Should such a form factor exist a signature of the gravitino might be found in processes with unlabeled products such as $e sp+e sp- to nothing.$ It is found that the form factor vanishes to this order, the Lorentz structures generated being too impoverished to withstand a constraining set of polarization conditions.
Finally the wormhole solution to the cosmological constant problem is examined in a semiclassical approximation. The notion that scalar field worm-holes must have associated conserved charges is questioned and a model of massive scalar field wormholes is delineated and proven to provide a counterexample. As the model allows baby universes nucleated with a certain eigenvalue of the scalar field momentum to classically evolve to a different value, competing semiclassical paths contribute to the same transition amplitude. Numerical simulations demonstrate that the novel semiclassical paths available to massive solutions cannot be overlooked in approximating the tunneling amplitude.

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48

Nikolic, Aleksandar. "The physics of multilayer topological insulator heterostructures using low-energy models". Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283001.

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This thesis studies the physics of multilayer heterostructures grown from topological insulators (TIs), primarily bismuth selenide and antimony telluride, and other topologically trivial materials. This is done by extending a standard low-energy 3D TI Hamiltonian and varying its associated material parameters across the simulation domain. New results arising from the position-dependent TI interface model are found. For the first time, this method is incorporated into a density-functional theory (DFT) solver in order to study the self-consistent charge density in multilayer TI heterostructures due to the interface states. The thesis is structured as follows. The introduction (Ch. 1) presents a pedagogical review of the theory of 3D TIs and low-energy Hamiltonians used to study them, as well as typical methods in solid state physics that are made use of throughout the thesis. Chapter 2 presents the position-dependent Hamiltonian, showing new evidence for topological features of bulk states including varying degrees of band mixing and inversion; also, interface state tunnelling is shown to be affected by atomic layer orbital overlap, and incomplete localisation of surface states is demonstrated for antimony telluride. Chapter 3 presents a new DFT model of TI heterostructure interfaces and shows how conduction through TI interface states can be controlled with an electric field. Chapter 4 covers the extension of the model in Ch. 1 to 2D cross-sections of TI wires and heterostructures, showing for the first time evidence of localisation of conduction almost entirely within the inner interfaces of a 2D heterostructure wire. Chapter 5 presents our work with magnetic fields, demonstrating evolution of interface and bulk states with changing magnetic field and Landau level, as well as presenting new evidence for more complex spin structures in bismuth selenide arising from Landé factor signs. Our conclusions are presented in Chapter 6.

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49

Lo, Wei-Chang. "Ring polymers as topological glass, a new phase of matter?" Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/46819/.

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In this thesis the dynamic properties of unknotted ring polymers at high densities is investigated. We hypothesise an unusual type of glass transition which is purely attributed to the topological constraints between the penetrating rings. A mean-field model is developed to describe the strongly constrained ring polymers as ideal lattice trees. Equilibrium properties can be derived within the framework of statistical thermodynamics using an argument based on structural recurrence. Here each ring can be seen as a linear object|as a loop strand with branching protrusions. The ring polymers were simplified as loop strands without any branching. We focused on the constraints emerging from the circular topology, and the polymer dynamics was simulated using a Monte Carlo technique. The degree of inter-ring penetrations essentially controls the slowing of dynamics and represents a universal parameter for the glass transition. The penetrating rings form a percolating network involving reversible quasi-topological entanglements. As such, the stress relaxation of each ring is prolonged by the coupled penetrations which have limited pathways to release constraints from one another. The simulation data suggest the existence of a glassy material exclusively formed by the topological constraints associated with the circular structure. In order to test the picture of topological glass, the uorescence-labelled circular DNA was used to observe its self-diffusion in the entangled state. The experimental method has demonstrated its potential for the future investigation of the dynamics of entangled ring polymers despite the fact that it failed to provide evidence of the glassy state in our experiment.

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50

Latief, Andy Octavian. "Tunnelling density of states studies of the topological Kondo effect". Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8475/.

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Coupling Majorana fermions to metallic conduction electrons will lead to the so-called topological Kondo effect, which is an embodiment of the exotic non-local properties that Majorana fermions possess. Using its minimal setup, this thesis studies the influence of this effect on the scattering properties of conduction electrons by analysing the component of the electron tunnelling density of states (tDOS) which oscillates at twice the Fermi wavenumber kF. We find that at zero bias this 2kF-tDOS displays a non-monotonic behaviour as the temperature is lowered. Starting from the exponential suppression at temperatures much larger than the characteristic Kondo temperature, the 2kF-tDOS may show a Kondo logarithmic peak before it crosses over to a T"3 decay, depending on the ratio of the junction-to-tunnelling distance at which the tDOS is being measured and the characteristic Kondo length. This then provides a way to estimate the extent of the Kondo screening cloud. At energies much below the Kondo temperature, the 2kF-tDOS is described by a universal scaling function indicative of strong correlations. The non-Fermi-liquid scattering occurs in this energy regime, which can be identified by the vanishing of single-particle-to-single-particle scattering at topological Kondo fixed point that in turn manifests in the complete suppression of the 2kF-tDOS at zero temperature and bias. Furthermore, we also have provided a practical method to use the 2kF-tDOS to extract information about the single-particle scattering matrix for more general quantum impurity systems.

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Tesi sul tema "Topological physics"

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