Rozprawy doktorskie na temat „Topological surface states”

Since the discovery of the long-range ferromagnetic order in two-dimensional and multi-layered van der Waals crystals, and the observation of a nontrivial topology of the magnon bulk bands in the chromium trihalides, the bosonic honeycomb lattices have drawn significant attention within the condensed matter community. In this thesis, we employ a Heisenberg model with a Dzyaloshinsky-Moriya interaction in a honeycomb ferromagnetic lattice to study the properties of bulk and edge spin-wave excitations (magnon). By the Holstein-Primakoff transformations in the linear spin-wave approximation, the spin Hamiltonian is written as the bosonic equivalent of the Haldane model for spinless fermions. We present a simple bosonic tight binding formalism which allows us to obtain analytical solutions for the energy spectrum and wavefunctions. We investigate three basic boundaries in the honeycomb lattice: zigzag, bearded and armchair, and we derive analytical expressions for the energy band structure and wavefunctions for the bulk and edge states, and with both zero and nonzero Dzyaloshinsky-Moriya interaction. We find that in a lattice with a boundary, the intrinsic on-site interactions along the boundary sites generate an effective defect and this gives rise to Tamm-like edge states. If a nontrivial gap is induced, both Tamm-like and topologically protected edge states appear in the band structure. The effective defect can be strengthened by an external on-site potential, and the dispersion relation, velocity and magnon density of the edge states all become tunable. We also investigate the bond modulation in the bosonic Haldane model, where by introducing a Kekule bond modulation and with the analysis of the gap closing conditions and the bulk band inversions, we find a rich topological phase diagram for this system yet to be discovered. We identify four topological phases, verified by a numerical calculation of the Chern number, in terms of the Kekule modulation parameter and the Dzyaloshinsky-Moriya interaction. We present the bulk-edge correspondence for the magnons in a honeycomb lattice for both armchair and zigzag boundaries. We believed that our study in this thesis will be important for possible applications of magnons in data process devices such as magnonics.

Thesis advisor: Vidya Madhavan
Spin-orbit coupling (SOC) is the interaction of an electron's intrinsic angular momentum (spin) with its orbital momentum. The strength of this interaction is proportional to Z4 where Z is the atomic number, so generally it is stronger in atoms with higher atomic number, such as bismuth (Z=83) and iridium (Z=77). In materials composed of such heavy elements, the prominent SOC can be sufficient to modify the band structure of the system and lead to distinct phase of matter. In recent years, SOC has been demonstrated to play a critical role in determining the unusual properties of a variety of compounds. SOC associated materials with exotic electronic states have also provided a fertile platform for studying emergent phenomena as well as new physics. As a consequence, the research on these interesting materials with any insight into understanding the microscopic origin of their unique properties and complex phases is of great importance. In this context, we implement scanning tunneling microscopy (STM) and spectroscopy (STS) to explore the surface states (SS) of the two major categories of SOC involved materials, Bi-based topological insulators (TI) and Ir-based transition metal oxides (TMO). As a powerful tool in surface science which has achieved great success in wide variety of material fields, STM/STS is ideal to study the local density of states of the subject material with nanometer length scales and is able to offer detailed information about the surface electronic structure. In the first part of this thesis, we report on the electronic band structures of three-dimensional TIs Bi₂Te₃ and Bi₂Se₃. Topological insulators are distinct quantum states of matter that have been intensely studied nowadays. Although they behave like ordinary insulators in showing fully gapped bulk bands, they host a topologically protected surface state consisting of two-dimensional massless Dirac fermions which exhibits metallic behavior. Indeed, this unique gapless surface state is a manifestation of the non-trivial topology of the bulk bands, which is recognized to own its existence to the strong SOC. In chapter 3, we utilize quasiparticle interference (QPI) approach to track the Dirac surface states on Bi₂Te₃ up to ~800 meV above the Dirac point. We discover a novel interference pattern at high energies, which probably originates from the impurity-induced spin-orbit scattering in this system that has not been experimentally detected to date. In chapter 4, we discuss the topological SS evolution in (Bi_1-xIn_x)₂Se₃ series, by applying Landau quantization approach to extract the band dispersions on the surface for samples with different indium content. We propose that a topological phase transition may occur in this system when x reaches around 5%, with the experimental signature indicating a possible formation of gapped Dirac cone for the surface state at this doping. In the second part of this thesis, we focus on investigating the electronic structure of the bilayer strontium iridate Sr₃Ir₂O₇. The correlated iridate compounds belong to another domain of SOC materials, where the electronic interaction is involved as well. Specifically, the unexpected Mott insulating state in 5d-TMO Sr₂IrO₄ and Sr₃Ir₂O₇ has been suggested originate from the cooperative interplay between the electronic correlations with the comparable SOC, and the latter is even considered as the driving force for the extraordinary ground state in these materials. In chapter 6, we carried out a comprehensive examination of the electronic phase transition from insulating to metallic in Sr₃Ir₂O₇ induced by chemical doping. We observe the subatomic feature close to the insulator-to-metal transition in response with doping different carriers, and provide detailed studies about the local effect of dopants at particular sites on the electronic properties of the system. Additionally, the basic experimental techniques are briefly described in chapter 1, and some background information of the subject materials are reviewed in chapter 2 and chapter 5, respectively
Thesis (PhD) — Boston College, 2014
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Physics

The aim of this thesis was to identify topologically protected states in the materials SnTe and Fe3Sn2. Such states are currently receiving a large amount of interest due to their applications for spintronic devices. Recently SnTe was discovered to be a crystalline topological insulator, a state of matter where its surface is highly conducting while the bulk remains insulating. However detection of these surface states is difficult using transport measurements, since the bulk is not totally insulating but still contains a large number of free carriers. SnTe undergoes a rhombohedral structural distortion on cooling caused by a soft transverse optic phonon, with the exact Tc strongly dependent on the carrier concentration. The distortion acts to lower crystal symmetry removing some of the symmetries that protect the surface state. Single crystal samples displaying the structural transition were grown and investigated using inelastic X-ray scattering to measure the phonon softening previously reported by other authors. The soft phonon was seen to recover again after distortion indicative of a 2nd order ferroelectric transition. This is the first reported discovery of the recovery showing the distortion is ferroelectric in nature. Shubnikov de Haas quantum oscillations were measured to study the Fermi surface under ambient and high hydrostatic pressure conditions. A distortion of the Fermi surface caused by the structural transition was evident, resulting in 4 distinct oscillation frequencies. However at applied pressures above 6 kbar, the transition was suppressed and only 1 oscillation measured. A two component Hall response also becomes apparent under high pressure. The possible origin of this and its relation to possible surface states is discussed. The anomalous Hall effect was also measured in the ferromagnet Fe3Sn2 which has a bilayer Kagome structure. Previous measurements on polycrystalline Fe3Sn2 suggested a non-collinear spin rotation from the spins pointing along the c-axis at high temperature to lying in the a-b plane below 80 K. A spin glass phase is then expected below 80 K. Single crystal magnetisation measurements carried out in this thesis show the spins are in the a-b plane at high temperatures and begin to display a ferromagnetic component along the c-axis approaching 80 K. The difference is accounted for by considering the demagnetising factor in the plate shaped single crystals. For this temperature range an applied field along the c-direction however rotates the moments towards c. At intermediate fields there are strong features evident in both the anomalous Hall effect and magnetoresistance. These features may be due to a topological Hall effect caused by a non-collinear spin structure. The possible existence of Skyrmion excitations was also recently discussed theoretically in Fe3Sn2. Our data is more suggestive of static Skyrmions known to cause topological Hall effects in MnSi.

Topological states of matter are a novel family of phases that elude the conventional Landau paradigm of phase transitions. Topological phases are characterized by global topological invariants which are typically reflected in the quantization of physical observables. Moreover, their characteristic bulk-boundary correspondence often gives rise to robust surface modes with exceptional features, such as dissipationless charge transport or non-Abelian statistics. In this way, the study of topological states of matter not only broadens our knowledge of matter but could potentially lead to a whole new range of technologies and applications. In this light, it is of great interest to find novel topological phases and to study their unique properties. In this work, novel manifestations of topological states of matter are studied as they arise when materials are subject to additional symmetries. It is demonstrated how symmetries can profoundly enrich the topology of a system. More specifically, it is shown how symmetries lead to additional nontrivial states in systems which are already topological, drive trivial systems into a topological phase, lead to the quantization of formerly non-quantized observables, and give rise to novel manifestations of topological surface states. In doing so, this work concentrates on weakly interacting systems that can theoretically be described in a single-particle picture. In particular, insulating and semi-metallic topological phases in one, two, and three dimensions are investigated theoretically using single-particle techniques.

The development and characterization of experimental setups for angle-resolved photoelectron spectroscopy (ARPES) and spin- and angle-resolved photoelectron spectroscopy (SARPES) is described. Subsequently, the two techniques are applied to studies of the electronic band structure in topologically non-trivial materials. The laser-based ARPES setup works at a photon energy of 10.5 eV and a typical repetition rate in the range 200 kHz to 800 kHz. By using a time-of-flight electron energy analyzer electrons emitted from the sample within a solid angle of up to ±15 degrees can be collected and analyzed simultaneously. The SARPES setup is equipped with a traditional hemispherical electron energy analyzer in combination with a mini-Mott electron polarimeter. The system enables software-controlled switching between angle-resolved spin-integrated and spin-resolved measurements, thus providing the possibility to orient the sample by mapping out the electronic band structure using ARPES before performing spin-resolved measurements at selected points in the Brillouin zone. Thin films of the topological insulators (TIs) Bi2Se3, Bi2Te3 and Sb2Te3 are grown using e-beam evaporation and their surface states are observed by means of ARPES. By using a combination of low photon energies and cryogenic sample temperatures the topological states originating from both the vacuum interface (surface) and the substrate interface are observed in Bi2Se3 films and Bi2Se3/Bi2Te3 heterostructures, with total thicknesses in the ultra-thin limit (six to eight quintuple layers), grown on Bi-terminated Si(111) substrates. Band alignment between Si and Bi2Se3 at the interface creates a band bending through the films. The band bending is found to be independent of the Fermi level (EF) position in the bulk of the substrate, suggesting that the surface pinning of EF in the Si(111) substrate remains unaltered after deposition of the TI films. Therefore, the type and level of doping of the substrate does not show any large influence on the size of the band bending. Further, we provide experimental evidence for the realization of a topological crystalline insulator (TCI) phase in the narrow-band semiconductor Pb1−xSnxSe. The TCI phase exists for temperatures below the transition temperature Tc and is characterized by an inverted bulk band gap accompanied by the existence of non-gapped surface states crossing the band gap. Above Tc the material is in a topologically trivial phase where the surface states are gapped. Thus, when lowering the sample temperature across Tc a topological phase transition from a trivial insulator to a TCI is observed. SARPES studies indicate a helical spin structure of the surface states both in the topologically trivial and the TCI phase.

QC 20130507

Dans cette thèse je me suis intéressé au caractère relativiste de matériaux topologiques tridimensionnels : les semi-métaux de Weyl et les isolants topologiques. Après une introduction aux états de surfaces et aux matériaux topologiques, je discute leurs propriétés de covariance sous les rotations trigonométriques et hyperboliques. Ces transformations me permettent de traiter les équations du mouvement d'un électron dans un champ magnétique ou à la surface, sous l'influence d'un champ électrique ou d'une inclinaison de la relation de dispersion. En première partie, je l'illustre dans le cas de la réponse magnéto-optique des semi-métaux de Weyl, en présence d'une inclinaison. Ces calculs sont en lien avec ma collaboration avec les expérimentateurs du LNCMI à Grenoble pour la caractérisation de la structure de bande de Cd₃As₂ où l'on montre que ce matériau est un semi-métal de Kane et non un semi-métal de Dirac dans la gamme de potentiels chimiques expérimentalement accessible. L'autre partie de cette thèse porte sur les états de surface des isolants topologiques où l'on montre qu'il existe des états de surface massifs au-delà de l'état de surface chiral. Ces états semblent avoir été observés par des études en ARPES d'échantillons de Bi₂Se₃ et Bi₂Te₃ oxydés et par des mesures de transport sur HgTe déformé. J'ai ainsi eu l'occasion de travailler avec les expérimentateurs du LPA à Paris sur le comportement des états de surface de HgTe sous forts effets de champ. Je termine par une discussion des états à l'interface entre un semi-métal de Weyl et un isolant dans le cas où le gap de ce dernier est suffisamment petit pour observer l'effet d'un champ magnétique et d'une inclinaison de la relation de dispersion sur les états de surface
During my PhD studies I focused on the relativistic properties of threedimensional topological materials, namely Weyl semimetals and topological insulators. After introducing surface states and topological materials I discuss their covariance in trigonometric and hyperbolic rotations. These transformations help to solve the equations of motion of an electron in a magnetic field or at the surface with an applied electric field or with a tilt in the band dispersion. In a first place, I illustrate these transformations for the magneto-optical response of tilted Weyl semimetals. This work is related to my collaboration with experimentalists at LNCMI, Grenoble for characterizing the band structure of Cd₃As₂ where we show that this material is a Kane semi-metal instead of a Dirac semi-metal in the experimentally accessible range of chemical doping. The other part of this thesis is concerned with the surface states of topological insulators. I show that massive surface states can also exist in addition to the chiral surface state due to band inversion. Such states may have already been observed in ARPES measurement of oxidized Bi₂Se₃ and Bi₂Te₃ and in transport measurement of strained bulk HgTe. I show the work we performed with experimentalists at LPA, Paris on the behavior of HgTe surface states for strong field effects. Finally, I discuss the states at the interface of a Weyl semimetal and a small gap insulator. In this situation, an applied magnetic field or the tilt of the band dispersion can strongly affect the observed surface states

Nous développons des métamatériaux élastiques à piliers pour manipuler les ondes de Lamb. Dans un premier temps, les propriétés négatives associées aux résonances de flexion, de compression et de torsion dans deux structures constituées de piliers sur un seul côté d’une membrane sont examinées. Nous décrivons deux mécanismes différents des propriétés de double négativité. Le potentiel de ces structures pour la réfraction négative et le cloaking acoustique est démontré. Deuxièmement, nous présentons le transport protégé topologiquement des ondes de Lamb par analogie avec les effets Hall quantiques de spin et de vallée. En réorganisant les structures précédentes en un réseau en nid d'abeille, un cône de Dirac simple et un cône de Dirac double sont introduits. Nous discutons de l’apparition d’états de bord protégés topologiquement par une vallée dans une structure à piliers double face asymétrique. La propagation unidirectionnelle des états de bord est étudiée. De plus, nous considérons un système double face symétrique. Les états de bord protégés topologiquement sur le pseudospin et sur le pseudospin-vallée sont démontrés. Troisièmement, nous proposons une approche pour contrôler activement la transmission de l’onde de Lamb antisymétrique se propageant à travers une ligne infinie de piliers. Deux situations différentes avec les résonances de flexion et de compression respectivement séparées ou superposées sont étudiées. Une force de traction externe et une pression sont appliquées sur les piliers, ce qui permet de les coupler avec les vibrations de flexion et de compression. La transmission est étudiée en fonction de l’amplitude et de la phase relative des sources externes
We develop elastic pillared metamaterials to manipulate Lamb waves. Firstly, the negative properties associated with bending, compression and torsion resonances in two structures consisting of pillars on one side of a thin plate are examined. We describe in details two different mechanisms at the origin of doubly negative property. The potential of these structures for negative refraction of Lamb waves and acoustic cloaking is demonstrated numerically. Secondly, we present the topologically protected transport of Lamb waves by analogy with quantum spin and valley quantum Hall effects. By rearranging the previous structures into a honeycomb network, a single Dirac cone and a double Dirac cone are introduced. We discuss the appearance of topologically valley-protected edge states in an asymmetrical double-sided pillar structure. The unidirectional propagation of edge states on different domain walls is studied. In addition, we consider a symmetrical double-sided system allowing the separation of the symmetric and antisymmetric modes. Combined edge states protected topologically by pseudospin and pseudospin-valley degree of freedom are demonstrated. Third, we propose an approach to actively control the transmission of the antisymmetric Lamb wave propagating through an infinite line of pillars. Two different situations with bending and compression resonances respectively separated or superimposed are studied. External tensile force and pressure are applied to the pillars, which allows them to couple with the bending and compressive vibrations. The transmission is studied as a function of the amplitude and the relative phase of the external sources

La spintronique classique utilise généralement des matériaux magnétiques pour produire un courant de spin à partir d’un courant de charge. Un autre moyen, plus récemment étudié, consiste à utiliser le couplage spin-orbite (SOC). Il permet de produire un courant de spin pur selon une direction transverse au courant de charge en tenant compte des principes de la mécanique quantique relativiste. Dans les matériaux à fort couplage spin-orbite, les courants de spin ainsi produits sont suffisamment importants pour imaginer les utiliser pour la commutation magnétique dans les dispositifs spintroniques. Le couplage spin-orbite, correspondant à une correction relativiste dans les équations du mouvement de l’électron, particule de spin 1/2, peut être grand dans des matériaux contenant des atomes lourds. Cela signifie qu’une conversion du courant de charge en courant de spin peut être obtenue en utilisant les propriétés de systèmes à fort SOC tel que le platine (Pt), le tungstène (W) ou le tantale (Ta), par exemple. Depuis peu, des systèmes électroniques bidimensionnels (2DEG), obtenus au niveau d’interfaces ou de surfaces particulières, ont démontré des propriétés permettant des effets d’inter-conversion particulièrement efficaces. En particulier des états Rashba ou des systèmes d’isolants topologiques, suscitent actuellement un fort engouement dans la communauté de la spintronique pour cette faculté d’inter-conversion spin-charge.Dans ce cadre particulier, depuis une dizaine d’années, les isolants topologiques ont été étudiés pour leurs propriétés électroniques non conventionnelles qui prennent racine dans la définition théorique de l’effet Hall quantique entier donnée par Thouless, ainsi que dans les travaux de Haldane dans le graphène et de Kane dans des systèmes semi-conducteurs à faible bande interdite pourvus d’un SOC fort. Ces systèmes 2D présentent des propriétés électriques intrigantes : ils sont isolants en volume et conducteurs en surface. Ces états de conductions sont pourvus d’une dispersion linéaire en énergie en fonction du vecteur d’onde k, comme dans le cas du graphène, avec une hélicité en spin déterminée.De nombreuses questions restent néanmoins ouvertes quant à la compréhension des mécanismes à l’origine de ces états de conduction en surface, mais également quant à la manière la plus simple de détecter ces états topologiques. En vue de leur intégration dans des dispositifs spintroniques et de la réalisation d’interface TI/Matériaux ferromagnétiques un certain nombre de questions se posent : comment préserver la nature des états topologiques à l’interface ? Quels matériaux utiliser et quelle est la nature atomique de l’interface (diffusion atomique) ? Quels sont les échanges électroniques à l’interface ? Etc.L’une des applications utilisant les propriétés des isolants topologiques, est d’utiliser les propriétés de conversion du courant de charge en courant de spin (et vice versa) afin de modifier ou commuter l’aimantation d’un élément ou mémoire ferromagnétique déposé directement (ou séparé par une couche tampon) sur le matériau topologique lui-même. Un tel système de bicouches ou multi-couches devrait être capable de s’intégrer dans une mémoire vive magnétique (MRAM) ou d’accroître le potentiel des disques électroniques (SSD) en raison du caractère permanent et non volatile de l’état d’aimantation du matériau. C’est dans ce cadre que s’inscrit cette thèse
Conventional spintronics generally uses magnetic materials to produce a spin current from a current of charge. Another means, more recently studied, is the use of spin-orbit coupling (SOC). It makes possible to produce a pure current of spin in a direction transverse to the charge current, taking into account the principles of relativistic quantum mechanics. In materials with strong spin-orbit coupling, the spin currents are large enough to imagine using them for magnetic switching in spintronic devices. The spin-orbit coupling, corresponding to a relativistic correction in the equations of motion of the electron, a spin 1/2 particle, can be large in materials containing heavy atoms. This means that a conversion from charge current to spin current can be obtained using the properties of SOC systems such as platinum (Pt), tungsten(W) or tantalum (Ta) for example. Recently 2 dimensionnal electronic gas (2DEG), obtained at particular interfaces or surfaces, have demonstrated properties allowing particularly effective inter-conversion effects. In particular Rashba states or topological insulator systems, are currently arousing a strong interest in the spintronics community for this faculty of spin-charge conversion.In this particular context, over the last ten years or so, topological insulators have been studied for their electronic properties which are rooted in the theoretical definition of the integer quantum Hall effect given by Thouless, as well as in the work of Haldane in graphene and Kane in low bandgap semiconductor systems with a strong SOC. These systems have intriguing electrical properties: they are insulating in volume and conductive on the surfaces. These conductivity states have a linear energy dispersion as a function of the k-wave vector, as in the case of the graphene, with a determined spin helicity.Nevertheless, many questions remain open as the understanding of the mechanisms at the origin of these states of surface conduction, but also as to the simplest way to detect these topological states. In order to integrate in spintronic devices and to realize TI/Ferromagnetic materials interface, a number of questions arise: how to preserve the nature of the topological states at the interface? What materials should be used and what is the atomic nature of the interface (inter-mixing) ? What are the electronic exchanges at the interface? Etc.One of the applications using the properties of topological insulators, is to use the conversion properties of the charge current to spin current in order to modify or switch the magnetization of a ferromagnetic element or memory deposited directly (or separated by a buffer layer) on the topological material itself. Such a two-layer system or multilayer should be capable of integration into a magnetic random access memory (MRAM) or of increasing the potential of disks (SSD) due to the permanent and non-volatile nature of the magnetisation state of the material. This is framework of this thesis

博士
國立臺灣大學
物理學研究所
105
In this thesis, we first introduce the previous study of topological insulator and the topological superconductor. The discovery of topological insulator (TI) is a recent breakthrough of physics. The topological protect surface in TI, forbidden the backscattering of electrons, gives new transport properties of the material. Combining the superconductor with the topological properties may host a type of new material called topological superconductor (TSC). The search for TSCs is one of the most urgent contemporary problems in condensed matter systems. TSCs are characterized by a full superconducting gap in the bulk and topologically protected gapless surface (or edge) states. Within each vortex core of TSCs, there exist the zero-energy Majorana bound states, which are predicted to exhibit non-Abelian statistics and to form the basis of the fault-tolerant quantum computation. To date, no stoichiometric bulk material exhibits the required topological surface states (TSSs) at the Fermi level (EF) combined with fully gapped bulk superconductivity. In the second chapter, we introduce the construction of an ultra-low-temperature (ULT) high-magnetic-field (HF) ultra-high-vacuum (UHV) scanning tunneling microscope. Sub-Kelvin temperature and strong field advance the ability of instrument in research. UHV environment keeps cleanness of the sample during the study. Such instrument working in three extreme environments needs to state-of –the-art design with the careful operation. The test result shows the STM has high resolution in energy and space. In the third chapter, we report atomic-scale visualization of the TSSs of the noncentrosymmetric fully gapped superconductor PbTaSe2. Using quasi-particle scattering interference imaging, we find two TSSs with a Dirac point at E ≅ 1.0 eV, of which the inner TSS and the partial outer TSS cross EF on the Pb-terminated surface. With sub-Kelvin energy resolution achieved in the ULT-HF-UHV STM, the fully superconducting gap of PbTaSe2 is clearly resolved, which suggests the TSS gapped out at EF. The tunneling conductance map shows the vortex is presented under the magnetic field, and zero energy conductance peak is observed at vortex core. This discovery reveals PbTaSe2 as a promising candidate for TSC. Lastly, the future improvement of the instrument and further study for PbTaSe2 are introduced. Increasing the holding time at 4 K and investigate the pairing mechanism are priorities. Keyword: Topological superconductor, topological insulator, Majorana fermion, scanning tunneling microscope, PbTaSe2

Scanning tunneling microscopy has been a powerful tool in expanding our understanding in the study of condensed matter physics. Many of the exotic materials of interest exhibit rich phases of matter at different temperatures and pressures. In order to probe the rich array of phases we developed a novel technique of combining scanning tunneling microscopy with tunable temperature and tunable mechanical strain in ultra high vacuum conditions. The mechanisms that give rise to high temperature superconductivity has been a long standing problem in physics. The discovered of iron-based high temperature superconductors (pnictides) have spurred much research into the mechanisms that give rise to the different exotic states observed in these new materials in hopes to better understand the underlying nature of unconventional superconductivity. Here we present a detailed study of the Nematic ordered phase in the prototypical iron- based high temperature superconductor, NaFeAs. Using our novel strain, temperature, scanning tunneling microscopy technique, we can attain an atomic-resolution view of the effects of the nematic phase on the local density of states along with the effects of anisotropic strain on the electronic structure. We further systematically study NaFeAs along both axes of the phase diagram, tuning temperature and Cu doping. We probe the material from the parent compound to beyond the supercon- ducting dome with increased Cu doping and from superconducting temperatures towell above the structural transition temperatures. Using our novel strain, temperature, scanning tunneling microscopy technique we nanoscopically identified the region of long-range nematic order and the region of nematic fluctuations in the phase diagram and find that true long range nematic order sets in at the tetragonal to orthorhombic structural transition temperature but nematic fluctuations continue at higher temperatures and also into the overdoped regime, then seemingly disappearing at the edge of the superconducting dome. We further find that our applied stain increasing the amplitude of the nematic fluctuations showing strong nonlinear coupling between strain and electronic nematicity. The power of our novel strain, temperature, scanning tunneling microscopy tech- nique in probing quasiparticle interference proves ideal for studying the topological, Weyl semimetal 1T’-MoTe 2 . In it’s orthorombic phase the material has topologically nontrivial protected surface Fermi arcs. By measuring quasiparticle interference in this material at different temperatures we can probe both topologically nontrivial phase (orthorhombic phase) and the topologically trivial phase (monoclinic phase). In the topologically nontrivial phase we see quasiparticle interference measurements in good agreement with angular resolved photoemission spectroscopy and theoretical calculations. In the topologically trivial phase we see the lack of the quasiparticle interference coming from the trivial surface state.

Topological states of matter are a novel family of phases that elude the conventional Landau paradigm of phase transitions. Topological phases are characterized by global topological invariants which are typically reflected in the quantization of physical observables. Moreover, their characteristic bulk-boundary correspondence often gives rise to robust surface modes with exceptional features, such as dissipationless charge transport or non-Abelian statistics. In this way, the study of topological states of matter not only broadens our knowledge of matter but could potentially lead to a whole new range of technologies and applications. In this light, it is of great interest to find novel topological phases and to study their unique properties. In this work, novel manifestations of topological states of matter are studied as they arise when materials are subject to additional symmetries. It is demonstrated how symmetries can profoundly enrich the topology of a system. More specifically, it is shown how symmetries lead to additional nontrivial states in systems which are already topological, drive trivial systems into a topological phase, lead to the quantization of formerly non-quantized observables, and give rise to novel manifestations of topological surface states. In doing so, this work concentrates on weakly interacting systems that can theoretically be described in a single-particle picture. In particular, insulating and semi-metallic topological phases in one, two, and three dimensions are investigated theoretically using single-particle techniques.

In almost any scientific experiment, we take into account some particular properties of materials, e.g. electromagnetic, mechanical, thermal, etc. These properties determine a majority of the physical phenomena that arise from the interaction with matter, and thus restrict potential applications of natural materials. The discovery and subsequent development of novel materials regularly boost the standards of living through new technological progress and cutting-edge research. One of the very recent and promising discoveries is related to the field of metamaterials - artificially structured media with subwavelength patterning. These artificial materials offer a unique platform with large flexibility and unusual properties for tailoring acoustic and electromagnetic waves, including novel ways for the manipulation of light. In this thesis, I employed the concept of metamaterials for both the study of new physical phenomena related to the emerging field of topological photonics and also develop innovative applications of specific metamaterials for the advancing the magnetic resonance imaging (MRI) machines. Chapter 1 provides an introduction to the field of metamaterials and their unusual properties, starting from the definition of meta-atoms and expanding to more complex structures, including one-dimensional meta-chains and metasurfaces. This is followed by an introduction to the fields of topological photonics and magnetic resonance imaging techniques. The experimental approaches based on a microwave platform are also described. Finally, the thesis motivation and structure are summarized. Chapter 2 presents experimental studies of topological features of zigzag arrays of dielectric particles. It includes the first experimental observation of the subwavelength photonic topological edge states, topological phase transition in the chains of dielectric particles, as well as, the study of the specific features of the photonic spin Hall effect mediated by the excitation of the subwavelength topological edge states. Chapter 3 describes the study of bianisotropic metasurfaces and metamaterials. The experimental designs of bianisotropic metallic and dielectric metasurfaces are presented, with a direct observation of topologically nontrivial edge states. Further, it is revealed how to couple topologically protected metasurfaces to form three-dimensional all-dielectric topologically nontrivial bianisotropic metamaterials and metacrystals. Chapter 4 focuses on the study metasurfaces based on resonant arrays of metallic wires used for advancing magnetic resonance imaging (MRI) characteristics. A new conceptual idea for the substantial enhancement of signal-to-noise ratio of a 1.5T MRI is presented. This approach is further developed and extended to ultra-high field MRI (7T) where a direct evaluation of the metasurface properties is examined during in-vivo human brain imaging. Chapter 5 summarizes the results and concludes the thesis.

碩士
國立清華大學
材料科學工程學系
105
The optical responses of one dimensional hyperbolic metamaterials (1DHMMs) are usually determined by effective medium theory based on the long wavelength approximation. However, the long wavelength approximation shows significant deviation when the wavelength of the incident light is comparable with the unit cell of HMMs. Therefore, plasmonic band theory have been suggested to analyze the 1DHMMs recently and the existence of the interface state has been proposed. The requirement for the existence of the interface state is determined by the admittance matching condition. Furthermore, the interface state formation in the plasmonic band gap can be related to the properties of the plasmonic band in terms of the wave admittance, so called “bulk-interface correspondence”. In this work, we experimentally identify the existence of the interface state of 1DHMM by the Kretschmann and the Otto configurations. By varying the metallic filling ratio in the 1DHMMs, we successfully demonstrate the disappearance and reappearance of the interface state which indicates the optical topological phase transition of 1DHMMs.

Tesis (Doctor en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2017.
Los descubrimientos experimentales del grafeno y de los materiales aislantes topológicos han suscitado un gran interés en la comunidad científica. El objetivo de la presente tesis es estudiar los estados topológicos de borde del grafeno y otros materiales de baja dimensión, y analizar diferentes formas de manipulación y dirección de los mismos para obtener sistemas con nuevas propiedades. Para ello, empleamos como base el modelo SSH para polímeros conductores (presenta carácter topológico nativo), y el grafeno. A este último se le inducen propiedades topológicas a partir de perturbaciones externas como ser campos magnéticos, términos de acoplamiento de tipo Haldane o irradiación con luz láser (teoría de Floquet). Entre los resultados encontrados podemos destacar la posibilidad de destruir y crear selectivamente estados de borde topológicos, y de dirigir la corriente eléctrica a través de los mismos. Estos efectos resultan atractivos para el diseño de futuros nanodispositivos y sus posteriores aplicaciones.
The experimental discoveries of graphene and topological insulator materials have aroused great interest in the scientific community. The aim of this thesis is to study the topological edge states of graphene and others low dimensional materials, and to analyze different ways of manipulating and directing them to achieve systems with new properties. In order to do this, we employ the SSH model for conducting polymers (it has a native topological character) and graphene as a base. Topological properties are induced to the latter through external perturbations such as magnetic fields, Haldane coupling terms or irradiation with laser light (Floquet theory). Among the results found we can highlight the possibility of selectively destroying and creating topological edge states, and of directing the electrical current through them. These effects are attractive for the design of future nanodevices and their subsequent applications.

The demand for the faster information transport and better computational abilities is ever increasing. In the last few decades, the electronic industry has met this requirement by increasing the number of transistors per square inch. This lead to the scaling of devices to tens of nm. However, the speed of the electronics is limited to few GHz. Using light, the operating speed of photonic devices can be much larger than GHz. But the photonic devices are diffraction limited and hence the size of photonic device is much larger than the electronic components. Plasmonics is an emerging field with light-induced surface excitations, and can manipulate the light at nanoscale. It can bridge the gap between electronics and photonics.

With the present scaling of devices to few nm, the scientific community is looking for alternatives for continued progress. This has opened up several promising routes recently, including two-dimensional materials, quantum computing, topological computing, spintronics and valleytronics. The discovery of graphene has led to the immense interest in the field of two-dimensional materials. Two dimensional-materials have extraordinary properties compared to its bulk. This work discusses the applications of plasmonics in this emerging field of two-dimensional materials and for heat assisted magnetic recording.

Black phosphorus is an emerging low-direct bandgap two-dimensional semiconductor, with anisotropic optical and electronic properties. It has high mobility and is promising for photo detection at infrared wavelengths due to its low band gap. We demonstrate two different plasmonic designs to enhance the photo responsivity of black phosphours by localized surface plasmons. We use bowtie antenna and bowtie apertures to increase the absorption and polarization selectivity respectively. Plasmonic structures are designed by numerical electromagnetic simulations, and are fabricated to experimentally demonstrate the enhanced photo responsivity of black phosphorus.

Next, we look at another emerging two-dimensional material, bismuth telluride selenide (Bi₂Te₂Se). It is a topological insulator with an insulating bulk but conducting electronic surface states. These surface states are Dirac like, similar to graphene and can lead to exotic plasmonic phenomena. We investigated the optical properties of Bi₂Te₂Se and found that the bulk is plasmonic below 650 nm wavelength. We study the distinct surface plasmons arising from the bulk and surface state of the topological insulator, Bi₂Te₂Se. The propagating surface plasmons at a nanoscale slit in Bi₂Te₂Se are imaged using near-field scanning optical microscopy. The surface state plasmons are studied with a below band gap excitation of 10.6 µm wavelength and the surface plasmons of the bulk are studied with a visible wavelength of 633 nm. The surface state plasmon wavelength is 100 times shorter than the incident wavelength in sharp contrast to the plasmon wavelength of the bulk.

Next, we look at the application of plasmonics in heat assisted magnetic recording (HAMR). HAMR is one of the next generation data storage technology that can increase the areal density to beyond 1 Tb/in². Near-field transducer (NFT) is a key component of the HAMR system that locally heats the recording medium by concentrating light below the diffraction limit using surface plasmons. In this work, we use density-based topology optimization for inverse design of NFT for a desired temperature profile in the recording medium. We first perform an inverse thermal calculation to obtain the required volumetric heat generation (electric field) for a desired temperature profile. Then an inverse electromagnetic design of NFT is performed for achieving the desired electric field. NFT designs for both generating a small heated spot size and a heated spot with desired aspect ratio in recording medium are demonstrated. The effect of waveguide, write pole and moving recording medium on the heated spot size is also investigated.