Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap of such systems are protected by time-reversal symmetry. The study of such states was originally inspired by the robustness to scattering of conducting edge states in quantum Hall systems. Recently, such analogies have resulted in the discovery of topologically protected states in two-dimensional and three-dimensional band insulators with large spin-orbit coupling. So far, the only known three-dimensional topological insulator is Bi R ecently, the subject of time-reversal-invariant topological insulators has attracted great attention in condensed-matter physics  . Topological insulators in two or three dimensions have insulating energy gaps in the bulk, and gapless edge or surface states on the sample boundary that are protected by time-reversal symmetry. The surface states of a three-dimensional (3D) topological insulator consist of an odd number of massless Dirac cones, with a single Dirac cone being the simplest case. The existence of an odd number of massless Dirac cones on the surface is ensured by the Z 2 topological invariant 7-9 of the bulk. Furthermore, owing to the Kramers theorem, no time-reversalinvariant perturbation can open up an insulating gap at the Dirac point on the surface. However, a topological insulator can become fully insulating both in the bulk and on the surface if a timereversal-breaking perturbation is introduced on the surface. In this case, the electromagnetic response of three-dimensional (3D) topological insulators is described by the topological θ term of the form S θ = (θ /2π)(α/2π) d 3 x dt E · B, where E and B are the conventional electromagnetic fields and α is the fine-structure constant 10 . θ = 0 describes a conventional insulator, whereas θ = π describes topological insulators. Such a physically measurable and topologically non-trivial response originates from the odd number of Dirac fermions on the surface of a topological insulator.Soon after the theoretical prediction 5 , the 2D topological insulator exhibiting the quantum spin Hall effect was experimentally observed in HgTe quantum wells 6 . The electronic states of the 2D HgTe quantum wells are well described by a 2 + 1-dimensional Dirac equation where the mass term is continuously tunable by the thickness of the quantum well. Beyond a critical thickness, the Dirac mass term of the 2D quantum well changes sign from being positive to negative, and a pair of gapless helical edge states appears inside the bulk energy gap. This microscopic mechanism for obtaining topological insulators by inverting the bulk Dirac gap spectrum can also be generalized to other 2D and 3D systems. The guiding principle is to search for insulators where the
The anomalous Hall effect is a fundamental transport process in solids arising from the spin-orbit coupling. In a quantum anomalous Hall insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically nontrivial electronic structure, leading to the quantized Hall effect without an external magnetic field. Based on first-principles calculations, we predict that the tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in contrast to conventional dilute magnetic semiconductors where free carriers are necessary to mediate the magnetic coupling. In two-dimensional thin films, this magnetic order gives rise to a topological electronic structure characterized by a finite Chern number, with the Hall conductance quantized in units of e2/h (where e is the charge of an electron and h is Planck's constant).
In this paper we give the full microscopic derivation of the model Hamiltonian for the three dimensional topological insulators in the Bi2Se3 family of materials (Bi2Se3, Bi2T e3 and Sb2T e3). We first give a physical picture to understand the electronic structure by analyzing atomic orbitals and applying symmetry principles. Subsequently, we give the full microscopic derivation of the model Hamiltonian introduced by Zhang et al  based both on symmetry principles and the k · p perturbation theory. Two different types of k 3 terms, which break the in-plane full rotation symmetry down to three fold rotation symmetry, are taken into account. Effective Hamiltonian is derived for the topological surface states. Both the bulk and the surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For more quantitative fitting to the first principle calculations, we also present a new model Hamiltonian including eight energy bands.
The search for large-gap quantum spin Hall (QSH) insulators and effective approaches to tune QSH states is important for both fundamental and practical interests. Based on first-principles calculations we find two-dimensional tin films are QSH insulators with sizable bulk gaps of 0.3 eV, sufficiently large for practical applications at room temperature. These QSH states can be effectively tuned by chemical functionalization and by external strain. The mechanism for the QSH effect in this system is band inversion at the Γ point, similar to the case of a HgTe quantum well. With surface doping of magnetic elements, the quantum anomalous Hall effect could also be realized.
Background: Faced with the coronavirus disease 2019 (COVID-19) pandemic, the development of COVID-19 vaccines has been progressing at an unprecedented rate. This study aimed to evaluate the acceptance of COVID-19 vaccination in China and give suggestions for vaccination strategies and immunization programs accordingly. Methods: In March 2020, an anonymous cross-sectional survey was conducted online among Chinese adults. The questionnaire collected socio-demographic characteristics, risk perception, the impact of COVID-19, attitudes, acceptance and attribute preferences of vaccines against COVID-19 during the pandemic. Multivariate logistic regression was performed to identify the influencing factors of vaccination acceptance. Results: Of the 2058 participants surveyed, 1879 (91.3%) stated that they would accept COVID-19 vaccination after the vaccine becomes available, among whom 980 (52.2%) wanted to get vaccinated as soon as possible, while others (47.8%) would delay the vaccination until the vaccine’s safety was confirmed. Participants preferred a routine immunization schedule (49.4%) to emergency vaccination (9.0%) or either of them (41.6%). Logistic regression showed that being male, being married, perceiving a high risk of infection, being vaccinated against influenza in the past season, believing in the efficacy of COVID-19 vaccination or valuing doctor’s recommendations could increase the probability of accepting COVID-19 vaccination as soon as possible, while having confirmed or suspected cases in local areas, valuing vaccination convenience or vaccine price in decision-making could hinder participants from immediate vaccination. Conclusion: During the pandemic period, a strong demand for and high acceptance of COVID-19 vaccination has been shown among the Chinese population, while concerns about vaccine safety may hinder the promotion of vaccine uptake. To expand vaccination coverage, immunization programs should be designed to remove barriers in terms of vaccine price and vaccination convenience, and health education and communication from authoritative sources are important ways to alleviate public concerns about vaccine safety.
The discovery of the quantum Hall (QH) effect led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two dimensional electron layer under a strong magnetic field. 1,2 The quantum anomalous Hall (QAH) effect shares a similar physical phenomenon as the QH effect, whereas its physical origin relies on the intrinsic spin-orbit coupling and ferromagnetism.
We report direct imaging of standing waves of the nontrivial surface states of topological insulator Bi2Te3 using a scanning tunneling microscope. The interference fringes are caused by the scattering of the topological states off Ag impurities and step edges on the Bi2Te3(111) surface. By studying the voltage-dependent standing wave patterns, we determine the energy dispersion E(k), which confirms the Dirac cone structure of the topological states. We further show that, very different from the conventional surface states, backscattering of the topological states by nonmagnetic impurities is completely suppressed. The absence of backscattering is a spectacular manifestation of the time-reversal symmetry, which offers a direct proof of the topological nature of the surface states.
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