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 Maciejko, Joseph, 1982
 2011.
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 Book — 1 online resource.
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This dissertation brings together a number of topics in the theory of timereversal invariant topological insulators. The first four chapters are devoted to the transport properties of the twodimensional (2D) quantum spin Hall state. We explain nonlocal transport measurements in mercury telluride (HgTe) quantum wells in terms of a LandauerBüttiker theory of helical edge transport and confirm the discovery of the quantum spin Hall state in this material. We find that decoherence can lead to backscattering without breaking microscopic timereversal symmetry. As an example of incoherent scattering, we study a Kondo impurity in an interacting helical edge liquid. A renormalization group analysis shows the existence of an impurity quantum phase transition governed by the Luttinger parameter of the edge liquid between a local helical Fermi liquid with T^6 scaling of the lowtemperature conductance, and an insulating strongly correlated phase with fractionally charged emergent excitations. In the presence of a timereversal symmetry breaking magnetic field, it is known that even coherent scattering can lead to backscattering. Through exact numerical diagonalization we find that nonmagnetic quenched disorder has a strong localizing effect on the edge transport if the disorder strength is comparable to the bulk gap. The predicted magnetoconductance agrees qualitatively with experiment. The last two chapters are devoted to 3D topological insulators. We propose a combined magnetooptical Kerr and Faraday rotation experiment as a universal measure of the Z_2 invariant. Finally, we propose a fractional generalization of 3D topological insulators in strongly correlated systems, characterized by ground state degeneracy on topologically nontrivial spatial 3manifolds, a quantized fractional bulk magnetoelectric polarizability without timereversal symmetry breaking, and a halved fractional quantum Hall effect on the surface.
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Online 2. STM and STS studies of electronic states near macroscopic defects in topological insulators [electronic resource] [2012]
 Alpichshev, Zhanybek.
 2012.
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Bi2Te3 and Bi2Se3 have been argued to be 3D topological insulators, exhibiting a bulk gap and a single, nondegenerate Dirac fermion surface band topologically protected by timereversal symmetry. In this dissertation we will discuss the physics of topological insulators. We will show that scanning tunneling spectroscopy studies on highquality Bi2Te3 and Bi2Se3 crystals exhibit perfect correspondence to ARPES data, hence enabling identification of different regimes measured in the local density of states. Unique to Bi2Te3, we will discuss observation of oscillations of LDOS near a step. Within the main part of the surface band we found that the oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear which disperse with a particular wavevector that results from an unconventional hexagonal warping term in the surfacestateband Hamiltonian. For both systems, a "bound state" was observed in the bulk gap region that runs parallel to the edge of the defect and is bound to it at some characteristic distance. An expression that fits the data, and provides insight into the general properties of the surface band near strong structural defects, can be obtained using the full threedimensional Hamiltonian of the system. In the case of Bi2Se3 whose band structure doesn't exhibit warping we studied the effect of local defects (impurities) on the local density of states. Although no visible interference pattern was detected we observed resonances localized around the defects. Such resonances agree quantitatively with a theory due Biswas and Balatsky which treats impurities as local potential wells interacting with a 2D Dirac gas which models the surface state of a topological insulator.
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Online 3. DMRG studies of ferromagnetic phase diagram of infiniteU hubbard ladders [electronic resource] [2014]
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The Hubbard model is one of the most important models in theoretical condensed matter physics. The model, which captures the strong interactions among the electrons, has not been solved analytically in more than one dimension. Therefore, over the past tens of year, there has been a tremendous analytic and computational effort to understand the parameter dependent ground state of this model, especially for intermediate strengths of the onsite repulsion U  the regime of parameters relevant to the properties of real material. Possible approaches to understand this model includes perturbative methods which start with the noninteracting kinetic term and treats the potential to low order in an expansion in powers of the interaction strength. A less intuitive approach is to attack the problem from the opposite extreme U> > t, where t is the electron hopping matrix element. In my thesis, I present the results concerning the groundstate phase diagram of Hubbard model in the infiniteU limit with an emphasis on the 2leg ladder and the extrapolation of these results to the 2D limit. We will show that there is a half metallic ferromagnetic ground state when the density of electrons per site n> =n_c ~ 0.80. When n=0.75, the ground state is a commensurate antiferromagnetically ordered plaquette phase with bond density order. We show evidence that in the range of n between n_c and 0.75, the ground state is phase separated between these two states. These properties hold not only for the twoleg ladder, but wider ladders as well, which we assume implies that they continue smoothly to the fully 2D limit. However for 0.75 > n > 0.5 while the ground state is found to be unpolarized for wider ladders, the two leg ladder exhibits a partially polarized ferromagnetic ground state , with a peak in the magnetization density occurring at around n=2/3 where we have demonstrated the existence of another commensurate phase. The ground state of the 2leg ladder when n=0.5 is an antiferromagnetic dimerized phase. A study of the charge carrying elementary excitations in the various commensurate phases suggests that there are further intermediate phases rather than direct first order transitions between them. Moving from infinite to large but finite U, we trace out the boundary of half metallic ferromagnetic phase of the 2leg ladder as a function of n and U. As the transition seems to be everywhere first order, we propose that outside this phase gives way to a phaseseparated ground state between such boundary and the two commensurate phases at n=1 and n=3/4 respectively. The plaquette phase is observed to be stable down to at least values of U~20t, but below a smaller critical value of U/t the ground state enters a stripe ordered phase. We also test the correspondence between Hubbard and tJ at least down to values of U~100t.
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Online 4. Electronic structures of novel complex materials studied by angle resolved photoemission spectroscopy [electronic resource] [2014]
 Liu, Zhongkai.
 2014.
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Electronic Structure is the key factor for identifying new material or phases and understanding the underlying physics behind emergent phenomena. In the investigation of the electronic structures of novel complex materials, the angular resolved photoemission spectroscopy (ARPES) serves as a powerful tool. The thesis summarizes two of my graduate research projects, which both involves probing electronic structures and analyzing underlying physics on novel complex materials with stateoftheart ARPES techniques: In the first part, I would summarize our investigation on the materials with nontrivial topology. I would start from our initial work on the threedimensional topological insulators where we identified the characteristic surface states and verified that they are robust from perturbations. Following the line of search, we discovered threedimensional topological insulators with other interesting properties, including the strongly inversion asymmetric topological insulator BiTeCl, and the strongly correlated topological Kondo insulator SmB6. We further extended our research to Na3Bi and Cd3As2, where we found them hosting a threedimensional Dirac point and are first examples of topological Dirac semimetals, a threedimensional analogue of graphene. In the second part of my thesis, I would discuss the ARPES study on the electron correlation level in the iron chalcogenide family Fe(Se, Te). For the parent compound FeTe, we discovered "peakdiphump" spectra with heavily renormalized quasiparticles in the low temperature antiferromagnetic state, characteristic of coherent polarons seen in other correlated materials. The increase of Se ratio leads to an incoherent to coherent crossover in the electronic structure. Furthermore, the reduction of the electronic correlation in Fe(Se, Te) evolves in an orbitaldependent way, where the dxy orbital is influenced most significantly. Finally, in comparison with other members of iron chalcogenides (AxFe2ySe2, A=K, Rb, Cs; and monolayer FeSe film on SrTiO3 substrate), we found the strong correlation behavior is universal in all iron chalcogenides. Specifically, the dxy orbital is always heavily renormalized and loses spectral weight upon raising temperature. Several physical models of the orbital dependent physics and electron correlations would be discussed.
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3781 2014 L  Inlibrary use 
 Keller, Andrew Joseph.
 2015.
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In systems involving a continuum of energy scales, one can imagine that under renormalization an effective Hamiltonian valid at low energies could possess a symmetry that the bare Hamiltonian does not. We are interested in the extent to which measurements of a physical system may reflect such emergent symmetries. Localized spins coupled to reservoirs of electrons are a natural domain to study these phenomena. Such "quantum impurity" systems can be realized using quantum dots. We report transport measurements of two lithographically patterned quantum dot systems in GaAs/AlGaAs heterostructures: 1. In a capacitivelycoupled double quantum dot, gate voltage can be used to tune the system so that it is equally favorable for either dot to hold one electron. The effective Kondo Hamiltonian valid at low energies has been predicted to have an emergent SU(4)symmetric exchange interaction based on the spin and orbital degrees of freedom. We provide evidence for emergent SU(4) symmetry by carefully comparing temperaturedependent conductance with numerical renormalization group calculations. In our device, conductance may be measured through each dot individually, uniquely enabling orbital stateresolved spectroscopy of the Kondo state. 2. A quantum dot tunnelcoupled to a metallic grain can host a nonFermi liquid twochannel Kondo state, where a spin1/2 impurity is exchangecoupled to two independent electron reservoirs. It occurs at the critical point of a secondorder quantum phase transition, which surprisingly has exact theoretical descriptions both at and away from the critical point, even at finite temperature. We confirm transport signatures of quantum criticality as first reported by Potok, et al. (Nature 446, 167 (2007)), and then go further by quantitatively validating a universal theory for the crossover to a Fermi liquid. The universality of this crossover in the presence of arbitrary symmetrybreaking perturbations is a consequence of emergent symmetry at the nonFermi liquid fixed point.
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Online 6. Exact mappings in condensed matter physics [electronic resource] [2015]
 Lee, Ching Hua.
 2015.
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 Book — 1 online resource.
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Condensed matter systems are complex yet simple. Amidst their complexity, one often find order specified by not more than a few parameters. Key to such a reductionistic description is an appropriate choice of basis, two of which I shall describe in this thesis. The first, an exact mapping known as the Wannier State Representation (WSR), provides an exact Hilbert space correspondence between two intenselystudied topological systems, the Fractional Quantum Hall (FQH) and Fractional Chern Insulator (FCI) systems. FQH states exist within the partially filled Landau levels of interacting 2D electron gases under strong magnetic fields, where quasiparticles exhibit topologically nontrivial braiding statistics. FCI systems, which are novel lattice realizations of FQH systems without orbital magnetic field, are still not completely understood and will benefit from a basis that explicitly connects them to the much better understood FQH systems. The second basis mapping, the Exact Holographic Mapping (EHM), maps any lattice system to a holographic 'bulk' with an additional emergent dimension representing scale. Devised in the spirit of the highly popular AdSCFT correspondence, it attempts to understand the relationship between a given system and its equivalent dual geometry. In particular, I found excellent theoretical agreement of certain dual geometries from EHM with those expected from the RyuTakanayagi formula relating bulk geometry with entanglement entropy. Additionally, the EHM also proves useful in providing a link between different topological quantities, such as relating the Chern number of the abovementioned Chern Insulators with the Axion angle of 3D topological insulators.
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3781 2015 L  Inlibrary use 
 Lederer, Samuel Stone.
 2015.
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Electrons in solid state materials display a remarkable diversity of strong correlation effects, many of which are poorly understood theoretically. In this regard, the cuprate high temperature superconductors are the shining example, remaining enigmatic despite decades of study. This dissertation examines basic questions in condensed matter physics inspired by these remarkable materials. In the first part, I consider aspects of the phenomenology of the cuprate and ruthenate unconventional superconductors. Emphasis is placed on the interpretation of existing experiments, and the proposal of new ones, to clarify the electronic structure of these materials and permit a more thorough microscopic understanding. In the second part, I focus on the abstract problem of nematic quantum criticality in metals, which recent experiments suggest may play a crucial role in the physics of both cuprate and ironbased superconductors. I attack this problem using both a field theoretic approach, valid at weak coupling, as well as fully nonperturbative, numerically exact Monte Carlo simulations in the strong coupling regime, yielding simple, unexpected results that are reminiscent of experiment.
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Online 8. Imaging current in materials [electronic resource] [2016]
 Spanton, Eric M.
 2016.
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 Book — 1 online resource.
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Scanning superconducting quantum interference device (SQUID) microscopy is an incredibly sensitive way to image magnetic fields. One application of this technique is to spatially map magnetic fields which originate from moving electrons (i.e. electrical current), and interpret the pattern of current in order to learn more about how electrons behave in interesting materials. In lanthanum aluminatestrontium titanate, two insulators which can host a twodimensional conducting state at their interface, we discovered locally enhanced conduction due to domain structure in the strontium titanate. 2D topological insulators are a class of materials which are predicted to host special conducting states along the edges of patterned devices, and we were able to image current along the edges of devices in two such materials: HgTe quantum wells and InAs/GaSb quantum wells. In InAs/GaSb, we found that backscattering in the edges was temperature independent and elucidated the presence of edge states in socalled 'trivial' regimes. These results call into question the prevailing interpretation of edge states in InAs/GaSb as topological, and conclude that better experimental evidence is required to definitively identify a 2D topologically insulating state in this material. Finally, we've investigated a fundamental property of Josephson junctions called the currentphase relation in fewmode InAs nanowire junctions. InAs nanowires which are in close contact with conventional superconductors are of great interest due to the possible realization of exotic particles called Majorana quasiparicles which may be of use for quantum computation. We've probed the disorder associated with adding superconductivity to nanowires by measuring the shape of the currentphase relation and finding that it fluctuates as a function of electron density and from junction to junction.
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3781 2016 S  Inlibrary use 
 Jian, Chaoming.
 2016.
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In this thesis, we study the topological phenomena in 2+1 dimensional topologically ordered states with additional extrinsic structures. One type of extrinsic structures we will study in this thesis is extrinsic defect. We first introduce the conceptual scheme of extrinsic twist defects which are pointlike defects associated with symmetries of the 2+1 dimensional topological states. We explicitly study several classes of examples. In particular, we study several class the projective nonAbelian braiding statistics of the twist defects which are fundamentally different from the statistics of intrinsic excitations in topological systems. We also find an example where the projective nonAbelian statistics of twist defects can be exploited for universal topological quantum computation, while the host state itself is not suitable for this purpose. Apart from twist defects, extrinsic defects in 2+1 dimensional topological states can take various other forms including linelike defects and pointlike defects. For 2+1 dimensional Abelian topological states, we establish a general classification of all linelike and pointlike defects. We develop a general method to analyze the quantum dimensions of all the pointlike defects, a general understanding of their localized "parafermion" zero modes, and study the projective nonAbelian statistics of them. Another type of extrinsic structure this thesis focuses on is the layering structure of 2+1 dimensional topological states. We propose a general formalism for constructing a large class of 3+1 dimensional topological states by stacking layers of 2+1 dimensional topological states and introducing coupling between them. Using this construction, we can study interesting topological phenomena in 3+1 dimensions, including surface topological orders and 3+1 dimensional topological orders. As an interesting consequence of this construction, we obtain example systems with nontrivial braiding statistics between stringlike excitations. In addition to studying the stringstring braiding in the example system, we propose a generic topological field theory description which can capture both stringparticle and stringstring braiding statistics. Lastly, we provide a proof of a general identity for Abelian string statistics, and discuss an example system with nonAbelian strings.
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3781 2016 J  Inlibrary use 
 Gu, Yingfei.
 2017.
 Description
 Book — 1 online resource.
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The butterfly effect, as an icon for the chaotic dynamics, refers to the exponential sensitivity on the initial conditions. This phenomenon is common in daily life, e.g. it explains the difficulty of long time weather reports. For physicists, the idea of the chaotic dynamics helps to understand the ergodicity of a classical complex system and therefore is essential for the statistical mechanics and thermodynamics. In the microscopic manybody systems governed by quantum mechanics, the chaotic dynamics is also expected to be generic and ultimately helpful for the understanding of the quantum thermalization. What I will show in this dissertation is that the quantum butterfly effect could also provide precise information about the nontrivial properties of the manybody interacting systems, such as thermal transport and topological properties. I will employ two classes of solvable models: the SachdevYeKitaev model in high dimensions and the rational conformal field theories in two dimensions to explicitly present the unexpected connection between the butterfly effect and other aspects of the model.
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Online 11. High pressure study of metal chalcogenides [electronic resource] [2017]
 Zhao, Zhao.
 2017.
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 Book — 1 online resource.
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Twodimensional (2D) materials, topological insulators (TIs), and sesquioxides have attracted huge research interest recently due to their scientific and industrial importance. The study of these materials explores the fundamentals of condensed matter physics while also shedding light on potential applications such as optoelectronics and spintronics. Pressure is an important thermodynamic parameter in changing structural and electronic configuration of a material, which can dramatically alter material properties. The integration of multiple in situ experimental probes with a diamond anvil cell enables the investigation of structural and electronic tuning of a material, exploration of novel high pressure phases, and optimization of material performances. This dissertation focuses on the effect of pressure on three systems in metal chalcogenides. First, the high pressure behavior of a representative 2D material molybdenum diselenide (MoSe2) was studied up to 60 GPa. Upon compression, MoSe2 evolves from an anisotropic 2D layered network to a threedimensional (3D) structure without a phase transition, which is different from the case of MoS2. The role of the chalcogenide anions in stabilizing different layered patterns is underscored by our layer sliding calculations. MoSe2 possesses highly tunable transport properties under pressure, determined by the gradual narrowing of its bandgap followed by metallization. The continuous tuning of its electronic structure and bandgap in the range of visible light to infrared suggests possible optoelectronics applications. Second, the high pressure behavior of potential TIs silver chalcogenides (Ag2X, X = S, Se, and Te) were studied up to 40 GPa. Under pressure, Ag2X exhibits a series of structural transitions and an increase in Ag to nearby X coordination number. Interestingly, a triple layer stacking pattern appears while the existence of two Ag crystallographic sites is maintained. Phase Is of Ag2Te and of Ag2Se are proposed as TIs from the bandgap increase under pressure and band structure calculations. Higher pressure induces metallization of Ag2X where large electronic evolution occur, for example, phase II of Ag2Te is found to be bulk semimetallic with topological nontrivial nature while phase III of Ag2Te becomes bulk metallic. Strong changes in infrared transmittance and reflectivity support the changes in their electronic structures. The results demonstrate silver chalcogenides as candidate materials for study of pressure induced TI to nonTI transitions under pressure. Third, the high pressure behavior of XV group sesquioxide αSb2O3 was investigated up to 50 GPa. During compression, a firstorder structural transition occurs at ~ 15 GPa, where the "molecular" cubic Sb2O3 phase I gradually transforms into a layered tetragonal phase II through local distortions and symmetry breaking. Firstprinciples calculations indicate that the bandgap decreases dramatically from phase I to phase II, consistent with changes in sample color and transparency. At higher pressure, a sluggish amorphization process occurs. Our results highlight the structural connections between late XV group sesquioxides and the role of the lone electron pair in determining local structures under pressure. These results underscore pressure as a powerful tool for modifying the lattice and electronic structure of metal chalcogenides and influencing their material properties.
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Online 12. Holographic duality and random tensor network [electronic resource] [2017]
 Yang, Zhao.
 2017.
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 Book — 1 online resource.
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Holographic duality is a proposed correspondence between quantum manybody systems living on the conformal boundary of an asymptotically antide Sitter space and the quantum gravity living in one higher dimension in the bulk. A particularly interesting aspect of this duality is played by the quantum entanglement. According to the RyuTakayanagi formula, the entanglement entropy of a boundary region corresponds to the area of the minimal surface bounding this region, which agrees with the entropy properties of the tensor network states. This dissertation aims to build concrete relations between the holographic duality and the tensor networks. We first propose the concept of the bidirectional holographic code, which means all the boundary states can be represented in the bulk while the states within a constrained code subspace play the role of "classical geometries". We implement the bidirectional holographic code explicitly using the random tensors, which generates a class of solvable tensor network models that reproduce many properties of the holographic duality. We further generalize the random tensor network approach to allow quantum superposition of di erent spatial geometries, which moves one step towards the quantum description of the gravity theory. Lastly, we study the dynamical properties in the holographic duality using the tensor networks and find that the quantum error correction properties bridge the lightcone structure in the bulk and the buttefly velocity (i.e. the speed of chaos propagation) on the boundary.
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Online 13. Imaging of electron forces, interactions, and topological states in designer quantum materials [electronic resource] [2017]
 Rastawicki, Dominik.
 2017.
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 Book — 1 online resource.
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We have developed atomic manipulation with a scanning tunneling microscope (STM) into a compelling new tool to investigate the fundamental properties of condensed matter systems. Our new capability to assemble and finetune essentially any twodimensional lattice combined with the ability to probe density of states at subatomic scale allows us to investigate the physics of electronic states with unprecedented freedom and precision. Here I aim to answer questions that so far proved too elusive for traditional material synthesis and measurement methods, in particular, questions about topological states in complex nonperiodic systems and about manybody instabilities driven by electron interactions. In this thesis, I focus on corrals and lattices created by patterning a free electron gas of a Cu(111) surface with carbon monoxide (CO) molecules. The CO molecules provide act as potential wells and constrain the surface state electrons to an effective lattice or corral pattern. In the first part I explain a series of quantum force measurement experiments, where I try to shed some light on the quantum force distance dependence and focusing inside several corral structures. Next part describes charge fractionalization in molecular polyacetylene as well as in Kekule distorted molecular graphene. I discuss how a domain wall or a vortex defect in a bond strength wave, leads to an emergence of a midgap state, and the fractional charge associated with it. Following that, I talk about effective gauge fields in graphene induced by strain as well as through direct modulation in bond strength and onsite potential. I explain how these induced perturbations to the lattice can be described by gauge fields, equivalent to the ones associated electromagnetic fields. One remarkable consequence of this equivalence is strain gauge invariance that allows one to produce lattices with the same electronic energy spectrum, but very different local structure. In the next part, I show how electronelectron interactions lead to instabilities as the lattice constant changes. In particular, I show that in a honeycomb lattice doped to the Van Hove singularity, the instability leads to a spontaneous nematic and polarized pseudospin phase. I also research investigate the instability in the flat band of a honeycomb 558 grain boundary where the leading phase is likely magnetic. Next, I describe quasicrystalline molecular lattices based on Penrose tilings and the electron fractalization that happens in them. I show the deep connection between penteract and electrons in a KiteandDart quasicrystal that form localized states at energies related by the golden ratio. I end by briefly discussing some possible future experiments that can exhibit an even larger variety of effects such as an emergence of a quantum spin Hall state or topological currents can be expected. These effects might show when one introduces stronger interactions and stronger spinorbit coupling present for example on surfaces of gold and topological insulators.
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Online 14. Novel phenomena in topological states of matter [electronic resource] [2017]
 Lian, Biao.
 2017.
 Description
 Book — 1 online resource.
 Summary

Topological states of matter exhibit properties that are protected by certain topological invariants and are invariant under perturbations. Depending on whether they have an excitation gap or not, these topological states can be classified into gapped and gapless phases. In this thesis, we first discuss the novel properties and recent developments of two kinds of gapped topological states in twodimensions (2D): the quantum anomalous Hall (QAH) insulator and the chiral topological superconductor (TSC), which can be realized in thin films of 3D topological insulators. In particular, we identify the presence of a zero Hall conductance plateau and a unique half plateau of twoterminal conductance in the QAH state and the chiral TSC state, respectively, both of which are confirmed by experiments. In the second part, we present two novel kinds of gapless topological states of matter characterized by linking numbers: the 5D Weyl semimetal and the 3D time reversal invariant superconductor with linked nodal lines, which show interesting bulkboundary correspondences and topological responses.
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3781 2017 L  Inlibrary use 
 Nie, Laimei.
 2017.
 Description
 Book — 1 online resource.
 Summary

Strongly correlated electronic systems have stimulated numerous developments in theoretical frameworks, numerical tools, and experimental techniques. One group of materials that have been attracting meticulous efforts is the hightemperature (highTc) superconductors, not merely due to its large transition temperature, but also because it offers a well characterized laboratory for the study of exotic phenomena such as quantum criticality and nonFermi liquid behavior. One pressing question in the field is the role played by disorder: inevitable in real materials, disorder is able to fundamentally alter the properties of system under certain circumstances. This thesis studies, from a theoretical point of view, how disorder affects various electronic orders in several model highTc superconductors, in particular copperbased highTc materials (cuprates). Various recent experiments in these materials are readily interpreted in light of our results.
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Online 16. Topological aspects of gapless phases [electronic resource] [2017]
 Bulmash, Daniel.
 2017.
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The development of topological phases of matter has greatly expanded our understanding of what a phase of matter could be. Topological phases have highly robust features; this robustness is typically protected by an energy gap. However, with the recent discovery of Weyl and Dirac semimetals, it has been realized that not only can gapless systems be topologically nontrivial, often with gaplessness itself being topologically protected. This thesis is a theoretical exploration of gapless topological phases from several perspectives. First, we propose that Hg_{1xy}Cd_xMn_yTe can be a timereversalbroken WSM. This proposal has several benefits, including that the singledopant (x=0 or y=0) cases are already very wellstudied, the Weyl points are tunable using magnetic field, and the Hall conductivity behaves highly nontrivially as a function both of temperature and of magnetic field angle. Next, we investigate WSM and DSM thin films, looking for quantum oscillations that involve the Fermi arcs. We extend known results in the weakfield limit, and propose a new experiment with a strong inplane component in the field which has highly unusual dependence of the quantum oscillations on field angle. Inspired by the ensuing theoretical understanding of a 3D metal in a strong magnetic field, we then investigate the effect of interactions on metallic wires subject to the orbital effects of a strong magnetic field. Using an analogy between fermions in the zeroth Landau level and truly 1D fermions with a (potentially large) pseudospin, we are able to apply powerful 1D tools like bosonization to find a plethora of interesting phases. This includes phases where the correlation functions of either charge density wave order or superconducting order obey magnetic fieldtuned power laws, as well as a phase with power law correlations of both pseudospintriplet superconductivity and pseudospindensity wave order. Finally, we construct a framework for unifying the topological response properties of both gapped and gapless free fermion systems by mapping a ddimensional system in real space (gapped or gapless) to a gapped 2ddimensional quantum Hall system in phase space. This allows us to construct a phase space response theory for any free fermion system and to demonstrate that the generic topological feature of a gapless system is a quantized anomaly related to the edge anomaly of the phase space quantum Hall system.
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3781 2017 B  Inlibrary use 
 Yang, Qi, author.
 [Stanford, California] : [Stanford University], 2018.
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To investigate the effects due to proximity between a threedimensional topological insulator (TI) and an insulating ferromagnet (IF), TIIF thin film bilayers were fabricated with pulsed laser deposition. Either bismuth(III) selenide (Bi2Se3) or bismuthantimony(III) telluride (BST) was used for the TI layer, whereas the IF layer was formed by the Heisenberg ferromagnet EuS. While a positive magnetoresistance was observed above the Curie temperature of EuS, as ubiquitously observed in highquality TI thin films, an unusual negative magnetoresistance was observed below the Curie temperature in the variablerange hopping regime. The angular dependence of such negative magnetoresistance indicates an orbit origin. Specific to BSTEuS bilayers, when the bulk conduction is minimized, magnetic anomalies in AC susceptibility were observed concurrently with resistive anomalies at the same temperatures, suggesting an interface magnetic order. These phenomena together suggest twostage proximity effects between the topological insulators and the insulating ferromagnet, and provide first steps to realize the halfinteger quantum anomalous Hall effect.
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3781 2018 Y  Inlibrary use 