Magnetic Topological Insulator And Quantum Anomalous Hall Effect
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Quantum Anomalous Hall Effect In Magnetic Topological Insulators
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Author :
language : en
Publisher:
Release Date : 2015
Quantum Anomalous Hall Effect In Magnetic Topological Insulators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We present the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.
Theoretical Study Of Magnetic Topological Insulators
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Author : An Zhao
language : en
Publisher: Open Dissertation Press
Release Date : 2017-01-26
Theoretical Study Of Magnetic Topological Insulators written by An Zhao and has been published by Open Dissertation Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with categories.
This dissertation, "Theoretical Study of Magnetic Topological Insulators" by An, Zhao, 赵安, 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: In recent years, the discovery of topological insulators brought a topological classification of materials and opened a new field in condensed matter physics. Due to the nontrivial topological properties, the topological insulators have insulating bulk and metallic edge/surface relating to some exotic physics such as quantum anomalous Hall effect, quantum spin Hall effect, and magneto-electric effect. Followed realizations of the Z2 topological insulators in two and three dimensions, the quantum anomalous Hall effect was realized in the magnetic-doped topological insulators very recently, which attracts intensive interest. In this thesis, the magnetic topological insulators as a consequence of time-reversal symmetry breaking in the Z2 topological insulators in two or three dimensions are studied. As an introduction, a review of the topological insulators including some relevant theories is given. The approaches involved in this study are also presented. The results can be summarized in two parts. First, the quantum anomalous Hall effect can be found on the two-dimensional decorated lattice with spin-orbit coupling and electron-electron interaction. Without interaction, this model exhibits the quantum spin Hall effect and has at bands in the middle of the spectra. A at-band ferrimagnetism which breaks the time-reversal symmetry and a charge-density wave can be induced by the electron-electron interaction. Altogether they can modulate the Chern number of the system and give rise to the quantum anomalous Hall effect. In the second part, the realization of the quantum anomalous Hall effect in magnetic-doped topological insulator thin films is investigated. With an effective Hamiltonian of the surface states of a topological insulator thin _lm, the condition of the quantum anomalous Hall effect and the behavior of the longitudinal and Hall conductivity is given, which agrees with the experimental results. The effects of the structural inversion asymmetry potential and the particle-hole symmetry breaking term are studied. With a thin _lm model of the three-dimensional topological insulator, it is shown that the lateral surface states account for the non-quantized value of the Hall conductance and the nonzero longitudinal conductance. The quantized Hall conductance restores when the lateral surface state electrons are thoroughly localized by disorder. The quantum anomalous Hall phase in magnetic topological insulator thin film in the present of disorder is also studied. The disorder will shrink the regime of the quantum anomalous Hall effect in a thick film and becomes an obstacle to the realization of the quantum anomalous Hall effect. DOI: 10.5353/th_b5194784 Subjects: Condensed matter
Magnetic Topological Insulator And Quantum Anomalous Hall Effect
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Author : Xufeng Kou
language : en
Publisher:
Release Date : 2015
Magnetic Topological Insulator And Quantum Anomalous Hall Effect written by Xufeng Kou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
The engineering of topological surface states is a key to realize applicable devices based on topological insulators (TIs). Among various proposals, introducing magnetic impurities into TIs has been proven to be an effective way to open a surface gap and integrate additional ferromagnetism with the original topological order. In this Dissertation, we study both the intrinsic electrical and magnetic properties of the magnetic TI thin films grown by molecular beam epitaxy. By doping transition element Cr into the host tetradymite-type V-VI semiconductors, we achieve robust ferromagnetic order with a strong perpendicular magnetic anisotropy. With additional top-gating capability, we realize the electric-field-controlled ferromagnetism in the magnetic TI systems, and demonstrate such magneto-electric effects can be effectively manipulated, depending on the interplays between the band topology, magnetic exchange coupling, and structural engineering. Most significantly, we report the observation of quantum anomalous Hall effect (QAHE) in the Cr-doped (BiSb)2Te3 samples where dissipationless chiral edge conduction is realized in the macroscopic millimeter-size devices without the presence of any external magnetic field, and the stability of the quantized Hall conductance of e2/h is well-maintained as the film thickness varies across the 2D hybridization limit. With additional quantum confinement, we discover the metal-to-insulator switching between two opposite QAHE states, and reveal the universal QAHE phase diagram in the thin magnetic TI samples. In addition to the uniform magnetic TIs, we further investigate the TI/Cr-doped TI bilayer structures prepared by the modulation-doped growth method. By controlling the magnetic interaction profile, we observe the Dirac hole-mediated ferromagnetism and develop an effective way to manipulate its strength. Besides, the giant spin-orbit torque in such magnetic TI-based heterostructures enables us to demonstrate the current-induced magnetization switching with the critical current density much lower than other heavy metal/magnet systems. Our work on the magnetic TIs and their heterostructures thus unfolds new avenues for novel multifunctional nano-electronics and non-volatile spintronic applications.
Topological Insulators
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Author : Inamuddin
language : en
Publisher: Materials Research Forum LLC
Release Date : 2024-01-15
Topological Insulators written by Inamuddin and has been published by Materials Research Forum LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-15 with Technology & Engineering categories.
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.
Exploring The Three Dimensional Quantum Anomalous Hall Effect And Topological Superconductivity In Topological Insulator Heterostructures
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Author : Ruoxi Zhang
language : en
Publisher:
Release Date : 2023
Exploring The Three Dimensional Quantum Anomalous Hall Effect And Topological Superconductivity In Topological Insulator Heterostructures written by Ruoxi Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Topological materials exhibit unique properties that make them robust against local defects and perturbations. These properties stem from the distinctive band structure compared to conventional materials, which are characterized by different topological invariants. In this thesis, we study two phenomena that arise in epitaxial topological insulator (TIs) films/heterostructures. The first phenomenon is the quantum anomalous Hall (QAH) effect. The QAH effect requires no external magnetic field and possesses non-dissipative chiral edge states that are resistant to local disorders. The second phenomenon is the topological superconducting (TSC) states. The TSC state hosts quasiparticle excitations, including Majorana zero modes (MZMs) and chiral Majorana edge modes (CMEMs). These excitations have potential applications in fault-tolerant topological quantum computations. The first experimental observation of the QAH effect was realized in molecular beam epitaxy (MBE)-grown magnetically doped TI thin films, which offer the advantages of scalability and reproducibility. However, the introduction of magnetic dopants also leads to higher disorder density in TI thin films. To overcome this limitation, we employed MBE-grown magnetically doped TI/TI/magnetically doped TI sandwich heterostructures to separate the magnetic dopants from the TI bulk. By employing this method, we successfully realized high Chern number QAH states, Chern domain walls, and hundred-nanometer-thick QAH samples. These results reveal new phases of matter and the underlying physics of the QAH phase transition induced by interlayer coupling. The second half of the thesis describes our effort in the TSC state in QAH insulators and TIs with induced superconductivity. The first project in this effort focuses on the search for CMEMs, which are predicted to emerge in QAH/superconductor hybrid structures. We examined a prior transport experiment that claimed the realization of CMEMs by measuring the two-terminal resistance. We improved the experimental design by fabricating Josephson junction and tunneling junction devices based on Bi2Te3 and (Bi,Sb)2Te3, and obtained transport results that suggest the dominance of Dirac surface states in vortex generation in the junction area.
Emergent Transport Properties Of Magnetic Topological Insulator Heterostructures
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Author : Kenji Yasuda
language : en
Publisher: Springer Nature
Release Date : 2020-09-07
Emergent Transport Properties Of Magnetic Topological Insulator Heterostructures written by Kenji Yasuda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-07 with Computers categories.
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.
Quantized Phenomena Of Transport And Magneto Optics In Magnetic Topological Insulator Heterostructures
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Author : Masataka Mogi
language : en
Publisher: Springer Nature
Release Date : 2022-05-07
Quantized Phenomena Of Transport And Magneto Optics In Magnetic Topological Insulator Heterostructures written by Masataka Mogi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-07 with Computers categories.
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.
Transport Studies Of The Electrical Magnetic And Thermoelectric Properties Of Topological Insulator Thin Films
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Author : Jinsong Zhang
language : en
Publisher: Springer
Release Date : 2016-04-18
Transport Studies Of The Electrical Magnetic And Thermoelectric Properties Of Topological Insulator Thin Films written by Jinsong Zhang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Science categories.
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.
Tuning Magnetism And Band Topology In Intrinsic Magnetic Topological Insulators Mnbi2nte3n 1
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Author : Chaowei Hu
language : en
Publisher:
Release Date : 2022
Tuning Magnetism And Band Topology In Intrinsic Magnetic Topological Insulators Mnbi2nte3n 1 written by Chaowei Hu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Topological materials are materials whose electronic band structures are described by certain non-trivial topological invariants. Forty years ago the importance of band topology in condensed matter physics was first recognized when the quantum Hall effect (QHE) was found to be related with the integer Chern number in two-dimensional (2D) electron gas. Since 2008, the discovery of three-dimensional (3D) topological insulators (TI) with a non-trivial topological invariant and gapless surface state has taken the field into a new era. Various new topological phases were proposed and band topology has become a new way to classify the state of matter. The design, synthesis and characterization of new topological materials pave essential basis to uncovering novel physics arising from non-trivial band topology and its interplay with various degrees of freedom such as spin, orbital and charge. Today, with more sought-after novel topological phases, emergent phenomena such as surface Fermi arcs, chiral anomaly, quantum anomalous Hall effect were discovered and enable future technological advances including topological quantum computation. A new topological phase can be created when additional symmetry breaking is introduced into an existing topological phase. For example, by breaking the time reversal symmetry of a 3D TI through ferromagnetism (FM), one can get a Chern insulator in its 2D limit, where QHE can be realized without external magnetic field and gives topologically-protected dissipationless chiral edge states. This phenomenon, the so-called quantum anomalous Hall effect (QAHE), has been long sought since its early proposal in the yet-to-be-realized Haldane model for graphene lattice with opposite magnetic field at neighboring atoms in 1988. Therefore, the realization of QAHE in magnetically-doped TI Cr0.15(Bi0.1Sb0.9)1.85Te3 thin films in 2013 was revolutionary. However, the unavoidable sample inhomogeneity in doped materials restrains the investigation of associated emergent phenomena in mK-regime. Ideally, magnetism from intrinsic magnetic atoms in a crystal can provide more homogeneous electronic and magnetic properties than the magnetism from dopants. To realize QAHE at higher temperatures, the intrinsic magnetic TIs with only clean topological bands but no other bands at the Fermi level are strongly desired. In 2018, MnBi2Te4 was discovered to be the first of such kinds, as an antiferromagnetic (AFM) TI with intrinsic magnetic Mn site. It is a layered van der Waals (vdW) material. When the magnetism orders below 24 K, the spins are FM aligned in the ab plane but AFM coupled along the c axis. In 2D limit, MnBi2Te4 films can have a net magnetization either in odd-layer devices, or when the even-layer devices are in the spin-flop state above ~ 3.5 T and the forced FM state above ~ 8 T. These time-reversal-symmetry breaking states are ideal for realizing the Chern insulator state. Indeed, QAHE was experimentally observed at 0 T and 1.6 K in a 5-layer device and quantized Hall conductance was realized when the even-layer devices enter the forced FM state above the saturation field of 8 T. Following this line, for QAHE to be realized at zero field and higher temperature, it is strongly desirable if the FM alignment of Mn spins can be accessed at a lower or even zero field. To do so, one must weaken the interlayer AFM interactions between [MnBi2Te4] layers. We thus propose to introduce n-1 nonmagnetic TI [Bi2Te3] layers between [MnBi2Te4] layers to get natural heterostructures of MnBi2nTe3n+1. By this rational design, we can increase the distance between the neighboring [MnBi2Te4] layers and thus reduce the interlayer AFM interaction. Under such a design principle we successfully grew single crystals of MnBi4Te7 (n=2), MnBi6Te10 (n=3) and MnBi8Te13 (n=4). Then with the physical property characterization, first-principles calculations and angle-resolved photoemission spectroscopy measurements, for the first time, we demonstrated that MnBi4Te7 is an intrinsic AFM TI with saturation field 40 times smaller than that of MnBi2Te4, and that MnBi8Te13 is the first realization of an intrinsic FM axion insulator, proving the success of our material design principle. The manipulation of magnetism is crucial to access different magnetic topological phase and novel physics. In MnBi2nTe3n+1, the control of the magnetism from AFM to FM by n is only discrete. To achieve a fine and continuous control of the magnetic transition, we doped Sb to MnBi4Te7 where the interlayer AFM coupling is weak and more tunable. Through single crystal growth, transport, thermodynamic, neutron diffraction measurements, we show that under Sb doping, MnBi4Te7 evolves from AFM to FM and then ferrimagnetic. We attribute this to the formation of Mn_(Bi, Sb) antisites upon doping, which results in additional Mn sublattices that modify the delicate interlayer magnetic interactions and changes the overall magnetism. We further investigate the effect of antisites on the band topology using the first-principles calculations. Without considering antisites, the series evolves from AFM topological insulator (x = 0) to FM axion insulators. In the exaggerated case of 16.7\% of periodic antisites, the band topology is modified and type-I magnetic Weyl semimetal phase can be realized at intermediate doping. Therefore, this doping series provides a fruitful platform with rich and continuously tunable magnetism and topology. After we achieve FM in MnBi2nTe3n+1, for practical applications especially in the pursuit of high temperature QAHE when fluctuations become important, the study on magnetic dynamics is indispensable too. We investigated the magnetic dynamics in FM MnBi8Te13 and Sb doped MnBi4Te7 and MnBi6Te10 using AC susceptibility and magneto-optical imaging. Slow relaxation behavior is observed in all three compounds, suggesting its universality among FM MnBi2nTe3n+1. The origin of the relaxation behavior is attributed to the irreversible domain movements since they only appear below the saturation fields when FM domains form and evolve. These FM domains are very soft, as revealed by the low-field fine-structured domains and high-field sea-urchin-shaped remnant-state domains imaged via the magneto-optical measurements. Finally, we attribute the rare "double-peak" behavior observed in the AC susceptibility under small DC bias fields to the very soft FM domain formations. This study provides a thorough understanding of the soft FM in highly anisotropic magnets. As the first intrinsic antiferromagnetic topological insulator, MnBi2Te4 is still the major material platform to search for QAHE, so its material optimization is very urged. We develop the chemical-vapor-transport (CVT) growth for of MnBi2Te4, which has a higher success rate in observation of the field-induced quantized Hall conductance in 6-layer devices. Through comparative studies between our CVT-grown and flux-grown MnBi2Te4, we find that CVT-grown MnBi2Te4 is marked with higher Mn occupancy on the Mn site, slightly higher Mn_Bi antisites and smaller carrier concentration. On the device end, thin film from CVT-grown sample shows by far the highest mobility of 2500 cm2 V s in MnBi2Te4 devices with the quantized Hall conductance appearing at 1.8 K and 8 T. This study provides a route to obtain high-quality single crystals of MnBi2Te4 that are promising to make superior devices and realize emergent phenomena. In summary, we have discovered and established MnBi4Te7 and MnBi8Te13 as new intrinsic magnetic topological insulators. In particular, we provide deep understanding of the importance of material design, synthesis and chemical doping to the magnetism and topology in the series. The growths of high-quality single crystals and the study of magnetic dynamics provide essential basis for the search of QAHE in MnBi2nTe3n+1. Our works will shed light on future endeavors in finding novel magnetic topological materials as well as searching for QAHE and the associated emergent phenomena in the condensed matter field
Quantized Topological Magnetoelectric Effect Of The Zero Plateau Quantum Anomalous Hall State
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Author :
language : en
Publisher:
Release Date : 2015
Quantized Topological Magnetoelectric Effect Of The Zero Plateau Quantum Anomalous Hall State written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
The topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in units of $e2/2h$. Here in this paper, we propose that the topological magnetoelectric effect can be realized in the zero-plateau quantum anomalous Hall state of magnetic topological insulators or a ferromagnet-topological insulator heterostructure. The finite-size effect is also studied numerically, where the magnetoelectric coefficient is shown to converge to a quantized value when the thickness of the topological insulator film increases. We further propose a device setup to eliminate nontopological contributions from the side surface.