Transport Properties and Electrical Field Effect Study of Topological Insulator (Bi,Sb)2Te3/Magnetic Insulator EuIG Heterostructures

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ISBN 13 :
Total Pages : 0 pages
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Book Synopsis Transport Properties and Electrical Field Effect Study of Topological Insulator (Bi,Sb)2Te3/Magnetic Insulator EuIG Heterostructures by : Wei-Jhih Zou

Download or read book Transport Properties and Electrical Field Effect Study of Topological Insulator (Bi,Sb)2Te3/Magnetic Insulator EuIG Heterostructures written by Wei-Jhih Zou and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Emergent Transport Properties of Magnetic Topological Insulator Heterostructures

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Publisher : Springer Nature
ISBN 13 : 981157183X
Total Pages : 109 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Emergent Transport Properties of Magnetic Topological Insulator Heterostructures by : Kenji Yasuda

Download or read book Emergent Transport Properties of Magnetic Topological Insulator Heterostructures written by Kenji Yasuda and published by Springer Nature. This book was released on 2020-09-07 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reveals unique transport phenomena and functionalities in topological insulators coupled with magnetism and superconductivity. Topological insulators are a recently discovered class of materials that possess a spin-momentum-locked surface state. Their exotic spin texture makes them an exciting platform for investigating emergent phenomena, especially when coupled with magnetism or superconductivity. Focusing on the strong correlation between electricity and magnetism in magnetic topological insulators, the author presents original findings on current-direction-dependent nonreciprocal resistance, current-induced magnetization reversal and chiral edge conduction at the domain wall. In addition, he demonstrates how the coupling between superconductivity and topological surface state leads to substantial nonreciprocal resistance. The author also elucidates the origins of these phenomena and deepens readers’ understanding of the topologically nontrivial electronic state. The book includes several works which are published in top journals and were selected for the President’s Award by the University of Tokyo and for the Ikushi Prize, awarded to distinguished Ph.D. students in Japan.

Transport Studies of the Electrical, Magnetic and Thermoelectric properties of Topological Insulator Thin Films

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Publisher : Springer
ISBN 13 : 3662499274
Total Pages : 128 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Transport Studies of the Electrical, Magnetic and Thermoelectric properties of Topological Insulator Thin Films by : Jinsong Zhang

Download or read book Transport Studies of the Electrical, Magnetic and Thermoelectric properties of Topological Insulator Thin Films written by Jinsong Zhang and published by Springer. This book was released on 2016-04-18 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the transport studies of topological insulator thin films grown by molecular beam epitaxy. Through band structure engineering, the ideal topological insulators, (Bi1−xSbx)2Te3 ternary alloys, are successfully fabricated, which possess truly insulating bulk and tunable conducting surface states. Further transport measurements on these ternary alloys reveal a disentanglement between the magnetoelectric and thermoelectric properties. In magnetically doped topological insulators, the fascinating quantum anomalous Hall effect was experimentally observed for the first time. Moreover, the topology-driven magnetic quantum phase transition was Systematically controlled by varying the strength of the spin-orbital coupling. Readers will not only benefit from the description of the technique of transport measurements, but will also be inspired by the understanding of topological insulators.

Transport Studies of Mesoscopic and Magnetic Topological Insulators

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Book Synopsis Transport Studies of Mesoscopic and Magnetic Topological Insulators by : Abhinav Kandala

Download or read book Transport Studies of Mesoscopic and Magnetic Topological Insulators written by Abhinav Kandala and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Insulators (TI) are a novel class of materials that are ideally insulating in the bulk, but have gapless, metallic states at the surface. These surface states have very exciting properties such as suppressed backscattering and spin-momentum locking, which are of great interest for research efforts towards dissipation-less electronics and spintronics. The popular thermo-electrics from the Bi chalcogenide family -- Bi2Se3 and Bi2Te3 -- have been experimentally demonstrated to be promising candidate TI materials, and form the chosen material system for this dissertation research. The first part of this dissertation research focuses on low temperature magneto-transport measurements of mesoscopic topological insulator devices (Chapter 3). The top-down patterning of epitaxial thin films of Bi2Se3 and Bi2Te3 (that are plagued with bulk conduction) is motivated, in part, by an effort to enhance the surface-to-volume ratio in mesoscopic channels. At cryogenic temperatures, transport measurements of these devices reveal periodic conductance fluctuations in straight channel devices, despite the lack of any explicit patterning of the TI film into a ring or a loop. A careful analysis of the surface morphology and comparison with the transport data then demonstrate that scattering off the edges of triangular plateaus at the surface leads to the creation of Aharonov-Bohm electronic orbits responsible for the periodicity. Another major focus of this dissertation work is on combining topological insulators with magnetism. This has been shown to open a gap in the surface states leading to possibilities of magnetic "gating" and the realization of dissipation-less transport at zero-field, amongst several other exotic quantum phenomena. In this dissertation, I present two different schemes for probing these effects in electrical transport devices -- interfacing with insulating ferromagnets (Chapter 4) and bulk magnetic doping (Chapter 5). In Chapter 4, I shall present the integration of GdN with Bi2Se3 thin films. Careful structural, magnetic and electrical characterization of the heterostructures is employed to confirm that the magnetic species is solely restricted to the surface, and that the ferromagnetic GdN layer to be insulating, ensuring current flow solely through the TI layer. We also devise a novel device geometry that enables direct comparison of the magneto-transport properties of TI films with and without proximate magnetism, all, in a single device. A comparative study of weak anti-localization suggested that the overlying GdN suppressed quantum interference in the top surface state. In our second generation hetero-structure devices, GdN is interfaced with low-carrier density, gate-tunable thin films of (Bi,Sb)2Te3 grown on SrTiO3 substrates. These devices enable us to map out the comparison of magneto-transport, as the chemical potential is tuned from the bulk conduction band into the bulk valence band.In a second approach to study the effects of magnetism on TI's, I shall present, in Chapter 5, our results from magnetic doping of (Bi,Sb)2Te3 thin films with Cr -- a system that was recently demonstrated to be a Quantum Anomalous Hall (QAH) insulator. In a Cr-rich regime, a highly insulating, high Curie temperature ferromagnetic phase is achieved. However, a careful, iterative process of tuning the composition of this complex alloy enabled access to the QAHE regime, with the observation of near dissipation-less transport and perfect Hall quantization at zero external field. Furthermore, we demonstrate a field tilt driven crossover between a quantum anomalous Hall phase and a gapless, ferromagnetic TI phase. This crossover manifests itself in an electrically tunable, giant anisotropic magneto-resistance effect that we employ as a quantitative probe of edge transport in this system.

Optical and electrical properties of topological insulator Bi2Se3

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Publisher : diplom.de
ISBN 13 : 3960676603
Total Pages : 88 pages
Book Rating : 4.9/5 (66 download)

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Book Synopsis Optical and electrical properties of topological insulator Bi2Se3 by : Jiajun Zhu

Download or read book Optical and electrical properties of topological insulator Bi2Se3 written by Jiajun Zhu and published by diplom.de. This book was released on 2017-07-12 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological insulator is one of the hottest research topics in solid state physics. This is the first book to describe the vibrational spectroscopies and electrical transport of topological insulator Bi2Se3, one of the most exciting areas of research in condensed matter physics. In particular, attempts have been made to summarize and develop the various theories and new experimental techniques developed over years from the studies of Raman scattering, infrared spectroscopy and electrical transport of topological insulator Bi2Se3. It is intended for material and physics researchers and graduate students doing research in the field of optical and electrical properties of topological insulators, providing them the physical understanding and mathematical tools needed to engage research in this quickly growing field. Some key topics in the emerging field of topological insulators are introduced.

Transport Property and Electrical Field Effect Study of Topological Insulator Thin Films

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (928 download)

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Book Synopsis Transport Property and Electrical Field Effect Study of Topological Insulator Thin Films by :

Download or read book Transport Property and Electrical Field Effect Study of Topological Insulator Thin Films written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topological Insulators

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Publisher : Materials Research Forum LLC
ISBN 13 : 1644902850
Total Pages : 195 pages
Book Rating : 4.6/5 (449 download)

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Book Synopsis Topological Insulators by : Inamuddin

Download or read book Topological Insulators written by Inamuddin and published by Materials Research Forum LLC. This book was released on 2024-01-15 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: A topological insulator is an area that has yet to be fully explored and developed. The charge-induced bandgap fluctuation in the best-known bismuth-chalcogenide-based topological insulators is approximately 10MeV in magnitude. The major focus has shifted to the investigation of the presence of high-symmetry electronic bands as well as the utilization of easily produced materials. As the subject of topological insulators is still in the nascent stage, there is growing research and knowledge in the emerging field. This book is intended to provide the readers with an understanding of the needs and application of these materials. Keywords: Topological Insulators, Insulators, One-Dimensional Topological Insulators, Graphene, Magnetic Topological Insulator, Antiferromagnetic Phase, Ferromagnetic Phase, Topological Superconductor, Nonlinear Optical Behavior, Saturable Absorber, Quantum, Band Gap, Photonic Topological Insulators.

Quantized Phenomena of Transport and Magneto-Optics in Magnetic Topological Insulator Heterostructures

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Publisher : Springer Nature
ISBN 13 : 9811921377
Total Pages : 120 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Quantized Phenomena of Transport and Magneto-Optics in Magnetic Topological Insulator Heterostructures by : Masataka Mogi

Download or read book Quantized Phenomena of Transport and Magneto-Optics in Magnetic Topological Insulator Heterostructures written by Masataka Mogi and published by Springer Nature. This book was released on 2022-05-07 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents experimental studies on emergent transport and magneto-optical properties in three-dimensional topological insulators with two-dimensional Dirac fermions on their surfaces. Designing magnetic heterostructures utilizing a cutting-edge growth technique (molecular beam epitaxy) stabilizes and manifests new quantization phenomena, as confirmed by low-temperature electrical transport and time-domain terahertz magneto-optical measurements. Starting with a review of the theoretical background and recent experimental advances in topological insulators in terms of a novel magneto-electric coupling, the author subsequently explores their magnetic quantum properties and reveals topological phase transitions between quantum anomalous Hall insulator and trivial insulator phases; a new topological phase (the axion insulator); and a half-integer quantum Hall state associated with the quantum parity anomaly. Furthermore, the author shows how these quantum phases can be significantly stabilized via magnetic modulation doping and proximity coupling with a normal ferromagnetic insulator. These findings provide a basis for future technologies such as ultra-low energy consumption electronic devices and fault-tolerant topological quantum computers.

Topological Insulators

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Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681745178
Total Pages : 216 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Topological Insulators by : Panagiotis Kotetes

Download or read book Topological Insulators written by Panagiotis Kotetes and published by Morgan & Claypool Publishers. This book was released on 2019-04-24 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to topological matter with a focus on insulating bulk systems. A number of prerequisite concepts and tools are first laid out, including the notion of symmetry transformations, the band theory of semiconductors and aspects of electronic transport. The main part of the book discusses realistic models for both time-reversal-preserving and -violating topological insulators, as well as their characteristic responses to external perturbations. Special emphasis is given to the study of the anomalous electric, thermal, and thermoelectric transport properties, the theory of orbital magnetisation, and the polar Kerr effect. The topological models studied throughout this book become unified and generalised by means of the tenfold topological-classification framework and the respective systematic construction of topological invariants. This approach is further extended to topological superconductors and topological semimetals. This book covers a wide range of topics and aims at the transparent presentation of the technical aspects involved. For this purpose, homework problems are also provided in dedicated Hands-on sections. Given its structure and the required background level of the reader, this book is particularly recommended for graduate students or researchers who are new to the field.

Transport Properties of Topological Insulator/Magnetic Insulator Heterostructures

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis Transport Properties of Topological Insulator/Magnetic Insulator Heterostructures by : Shang-Rong Yang

Download or read book Transport Properties of Topological Insulator/Magnetic Insulator Heterostructures written by Shang-Rong Yang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Transport Study of Three-dimensional Topological Insulators

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ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (914 download)

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Book Synopsis Transport Study of Three-dimensional Topological Insulators by : Murong Lang

Download or read book Transport Study of Three-dimensional Topological Insulators written by Murong Lang and published by . This book was released on 2015 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recently discovered time-reversal-invariant topological insulator (TI) has led to the flourishing of unique physics along with promises for innovative electronic and spintronic applications. However, the as-grown TI materials are not truly insulating but with a non-trivial bulk carrier density, which makes difficulties to the transport methods. In our work, we study the fundamental transport properties of TI and its heterostructure, in which various approaches are utilized to better reveal the surface state properties. In particular, in Chapter 2, in-situ Al surface passivation of Bi2Se3 inside MBE is investigated to inhibit the degradation process, reduce carrier density and reveal the pristine topological surface states. In contrast, we show the degradation of surface states for the unpassivated control samples, in which the 2D carrier density is increased by 39.2% due to ambient n-doping, the Shubnikov-de Hass oscillations are completely absent, and a deviation from WAL weak antilocalization is observed. In Chapter 3, through optimizing the material composition to achieve bulk insulating state, we present the ambipolar effect in 4-9 quintuple layers (Bi0.57Sb0.43)2Te3 thin films. We also demonstrate the evidence of a hybridized surface gap opening in (Bi0.57Sb0.43)2Te3 sample with thickness below six quintuple layers through transport and scanning tunneling spectroscopy measurements. By effective tuning the Fermi level via gate-voltage control, we unveil a striking competition between weak antilocalization and weak localization at low magnetic fields in nonmagnetic ultrathin films. In Chapter 4, we study the magnetic properties of Bi2Se3 surface states in the proximity of a high Tc ferrimagnetic insulator YIG. Proximity-induced magnetoresistance loops are observed by transport measurements with out-of-plane and in-plane magnetic fields applied. More importantly, a magnetic signal from the Bi2Se3 up to 130 K is clearly observed by magneto-optical Kerr effect measurements. Our results demonstrate the proximity-induced TI magnetism at higher temperatures, which is an important step toward room-temperature application of TI-based spintronic devices. The engineering of a TI and FMI heterostructure will open up numerous opportunities to study high temperature TI-based spintronic devices, in which the TI is controlled by breaking the TRS using a FMI with perpendicular magnetization component. A YIG film with out-of-plane anisotropy at> 300 K could potentially manipulate the magnetic properties of a TI may even above room temperature.

Advanced Topological Insulators

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Publisher : John Wiley & Sons
ISBN 13 : 1119407338
Total Pages : 431 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Advanced Topological Insulators by : Huixia Luo

Download or read book Advanced Topological Insulators written by Huixia Luo and published by John Wiley & Sons. This book was released on 2019-03-12 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for researchers and graduate students preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with the fundamental description on the topological phases of matter such as one, two- and three-dimensional topological insulators, and methods and tools for topological material's investigations, topological insulators for advanced optoelectronic devices, topological superconductors, saturable absorber and in plasmonic devices. Advanced Topological Insulators provides researchers and graduate students with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.

Topological Insulators

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Publisher : Elsevier Inc. Chapters
ISBN 13 : 0128086890
Total Pages : 48 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Topological Insulators by : Jeroen B. Oostinga

Download or read book Topological Insulators written by Jeroen B. Oostinga and published by Elsevier Inc. Chapters. This book was released on 2013-11-23 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of topological insulators as a new state of matter has generated immense interest in this new class of materials. Three-dimensional (3D) topological insulators are characterized by the presence of an odd number of families of Dirac fermions—ideally one- at each of their surfaces. Angle-resolved photoemission experiments have demonstrated the presence of the expected Dirac fermions, but it is clear that to explore the electronic properties of these systems, transport measurements in many different device geometries are called for, just as it has been the case for Dirac fermions in graphene. In this chapter we review the status of transport studies through 3D topological insulators as of early summer 2012, after that a first generation of experiments has been performed. The results provide many different indications of the presence of surface fermions, as well as evidence of their Dirac nature. However, no textbook “manifestation” of surface Dirac fermions has been reported so far in these materials. Indeed, experiments also show that investigations are severely hampered by the material quality in most cases, because of the effect of high conductivity in the bulk, of low carrier mobility, of technical difficulties hampering device fabrication, and other reasons. In this chapter, we attempt to give a balanced overview of the work done during this first period and of the results obtained, stressing the implications and the limits of many of the observations that have been reported in the literature.

Topological Insulators

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Publisher : Elsevier Inc. Chapters
ISBN 13 : 0128086831
Total Pages : 31 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Topological Insulators by : Joel E. Moore

Download or read book Topological Insulators written by Joel E. Moore and published by Elsevier Inc. Chapters. This book was released on 2013-11-23 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the topological insulator phase that emerges via spin-orbit coupling in three-dimensional materials is introduced, stressing its relationship to earlier topological phases in two dimensions. An unusual surface state with an odd number of “Dirac points” appears as a consequence of bulk topological invariants of the band structure. A different theoretical approach is then presented, based on the Berry phase of Bloch electrons, in order to illustrate a deep connection to the orbital contribution to the magnetoelectric polarizability in all materials. The unique features of transport in the topological insulator surface state are reviewed with an emphasis on possible experiments. The final section discusses briefly connections to interacting phases including topological superconductors and some recent efforts to construct fractional topological insulators in three dimensions.

Topological Insulators

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Publisher : Elsevier
ISBN 13 : 0444633189
Total Pages : 349 pages
Book Rating : 4.4/5 (446 download)

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Book Synopsis Topological Insulators by :

Download or read book Topological Insulators written by and published by Elsevier. This book was released on 2013-11-23 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was thought that all band insulators are essentially equivalent, the new theory predicts two distinct classes of band insulators in two spatial dimensions and 16 classes in three dimensions. These "topological" insulators exhibit a host of unusual physical properties, including topologically protected gapless surface states and exotic electromagnetic response, previously thought impossible in such systems. Within a short time, this new state of quantum matter, topological insulators, has been discovered experimentally both in 2D thin film structures and in 3D crystals and alloys. It appears that topological insulators are quite common in nature, and there are dozens of confirmed substances that exhibit this behavior. Theoretical and experimental studies of these materials are ongoing with the goal of attaining the fundamental understanding and exploiting them in future practical applications. - Usable as a textbook for graduate students and as a reference resource for professionals - Includes the most recent discoveries and visions for future technological applications - All authors are prominent in the field

Topological Insulator Systems with Magnetism

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (94 download)

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Book Synopsis Topological Insulator Systems with Magnetism by : Joon Lee

Download or read book Topological Insulator Systems with Magnetism written by Joon Lee and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation describes topological insulator systems hybridized with magnetism. The Dirac surface states induced by strong spin-orbit interaction can be modified by breaking time-reversal symmetry that protects the surface state. We study the modified surface states of topological insulators by introducing magnetism by doping magnetic atoms or interfacing a magnetic layer to the surface. Also, we explore potential spintronics applications of topological insulators by utilizing magnetic tunnel junctions to evidence the inherently spin-polarized texture of the topological insulator surface state. For this dissertation research, single crystalline topological insulator thin films grown by molecular beam epitaxy have been employed. From the motivation of breaking time-reversal symmetry in the surface state, the first experiments study the structural, magnetic, and magneto-transport properties of a magnetically doped, three-dimensional topological insulator, bismuth telluride doped with Mn. We observed ferromagnetism with a Curie temperature up to 17 K in films with ~2-10% Mn concentrations. The observed ferromagnetism is independent of carrier density in the Mn-doped bismuth telluride films, suggesting that it is not mediated by charge carriers. The next topological insulator system with magnetism is a hybrid topological insulator/ferromagnet heterostructure as a new approach for topological insulator hybrid systems using a dilute magnetic semiconductor Ga1-xMnxAs. A highly resistive Ga1-xMnxAs with out-of-plane magnetic anisotropy is cleanly interfaced with a topological insulator Bi2-xSbxTe3-ySey by molecular beam epitaxy. Magneto-transport measurements on a top-gated heterostructure device show a crossover from positive magneto-conductance to negative magneto-conductance as well as a systematic emergence of an anomalous Hall effect as the temperature is lowered or as the chemical potential approaches the Dirac point. The results are possibly interpreted as the modification of the surface state at the interface by the adjacent, ferromagnetic Ga1-xMnxAs layer. The last topological insulator system with magnetism is a topological insulator channel with a magnetic tunnel junction on it. We seek a potential role of topological insulators in spintronics as generators of carrier spin polarization. Electrical detection of the inherent spin polarization of the topological insulator surface state was demonstrated using a permalloy/Al2O3 magnetic tunnel junction on a (Bi,Sb)2Te3 channel. The observed hysteretic spin signals occurring at the magnetic switching field of the ferromagnet permalloy layer can be interpreted as the projection of the current-induced spin polarization on a topological insulator surface onto the magnetization of the ferromagnet via tunneling.

Numerical Study of Topological Insulators and Semi-Metals

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ISBN 13 : 9781361285282
Total Pages : pages
Book Rating : 4.2/5 (852 download)

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Book Synopsis Numerical Study of Topological Insulators and Semi-Metals by : Ruilin Chu

Download or read book Numerical Study of Topological Insulators and Semi-Metals written by Ruilin Chu and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Numerical Study of Topological Insulators and Semi-metals" by Ruilin, Chu, 储瑞林, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Topological insulators(TIs) constitute a novel state of quantum matter which possesses non-trivial topological properties. Although discovered only in the recent few years, TIs have attracted intensive interest among the community of condensed matter physics and material science. TIs are insulating in the bulk but have conductive gapless edge or surface states on the boundaries, which have their origin in the nontrivial bulk band topology that is induced by the strong spin-orbital interactions in the materials. Existing in all dimensions, TIs exhibit a variety of exotic physics such as quantum spin Hall effect, momentum-spin locked surface states, Dirac fermion transport, quantized anomalous Hall effect, Majorana fermions, etc. In this thesis, I study the transport properties of 2D and 3D TIs by numerical approaches. As an introduction, a brief review of TIs is given. A detailed description of the numerical methods is also presented. The results can be summarized in four aspects. First, disorder is found be able to induce a non-trivial TI from an originally trivial band insulator, where the conductance of a two terminal device drops to nearly zero and then rises to form an anomalous plateau as disorder strength is increased, and finally all the states become localized. The real space Chern number calculation as well as the effective medium theory suggests that disorder is fundamentally responsible for the emerging of the extended helical edge states in this system. We also present a levitation and pair annihilation picture of the extended states for this model. Second, by making the 2D TIs into singly connected quantum point contacts(QPCs), I show a coherent and fast Aharonov-Bohm oscillation of conductance caused by the quantum interference of the helical edge states. This oscillation not only happens against weak magnetic field but also against the gate voltage in the zero-field condition. This results in a giant edge magnetoresistance of the device in weak magnetic fields. The amplitude of the magnetoresistance is controllable by adjusting either the QPCs' slit width or the interference loop size in the device. The oscillation is found robust against disorder. Third, by applying a uniform spin-splitting Zeeman field in the bulk of the 3D TI whose surface states can be viewed as massless Dirac fermions, I find chiral edge states on the gapped surfaces of the 3D TI, which can be considered as interface states between domains of massive and massless Dirac fermions. Effectively these states are result of splitting of a perfect interface conducting channel. This picture is confirmed by the Landauer-B'ttiker calculations in four-terminal Hall bars. Finally, I propose the concept of topological semi-metals. By calculating the local density of states on the surfaces, I demonstrate that surface states and the gapless Dirac cone already exist in the system although the bulk is not gapped. We show how the uni-axial strain induces an insulating band gap and turn the semi-metal into true TI. We predict existence of quantum spin Hall effect in the thin films made of these materials, which can be significantly enhanced by disorders. DOI: 10.5353/th_b4716325 Subjects: Condensed matter Semimetals