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Topological band insulators and (semi-) metals can arise out of atomic insulators when the hopping strength between electrons increases. Such topological phases are separated from the atomic insulator by a bulk gap closing. In this work, we show that in many (magnetic) space groups, the crystals with certain Wyckoff positions and orbitals being occupied must be semimetal or metals in the atomic limit, e.g. the hopping strength between electrons is infinite weak but not vanishing, which then are termed atomic (semi-)metals (ASMs). We derive a sufficient condition for realizing ASMs in spinless and spinful systems. Remarkably, we find that increasing the hopping strength between electrons may transform an ASM into an insulator with both symmetries and electron fillings of crystal are preserved. The induced insulators inevitably are topologically non-trivial and at least are obstructed atomic insulators (OAIs) that are labeled as trivial insulator in topological quantum chemistry website. Particularly, using silicon as an example, we show ASM criterion can discover the OAIs missed by the recently proposed criterion of filling enforced OAI. Our work not only establishes an efficient way to identify and design non-trivial insulators but also predicts that the group-IV elemental semiconductors are ideal candidate materials for OAI.
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Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.
The three dimensional (3D) topological insulators are predicted to exhibit a 3D Dirac semimetal state in critical regime of topological to trivial phase transition. Here we demonstrate the first experimental evidence of 3D Dirac semimetal state in topological insulator Bi2Se3 with bulk carrier concentration of ~ 10^19 cm^{-3}, using magneto-transport measurements. At low temperatures, the resistivity of our Bi2Se3 crystal exhibits clear Shubnikov-de Haas (SdH) oscillations above 6T. The analysis of these oscillations through Lifshitz-Onsanger and Lifshitz-Kosevich theory reveals a non-trivial pi Berry phase coming from 3D bands, which is a decisive signature of 3D Dirac semimetal state. The large value of Dingle temperature and natural selenium vacancies in our crystal suggest that the observed 3D Dirac semimetal state is an outcome of enhanced strain field and weaker effective spin-orbit coupling.
The emergence of topological order in graphene is in great demand for the realization of quantum spin Hall states. Recently, it is theoretically proposed that the spin textures of surface states in topological insulator can be directly transferred to graphene by means of proximity effect. Here we report the observations of the topological proximity effect in the graphene-topological insulator Bi2Se3 heterojunctions via magnetotransport measurements. The coupling between the p_z orbitals of graphene and the p orbitals of surface states on the Bi2Se3 bottom surface can be enhanced by applying perpendicular negative magnetic field, resulting in a giant negative magnetoresistance at the Dirac point up to about -91%. An obvious resistivity dip in the transfer curve at the Dirac point is also observed in the hybrid devices, which is consistent with the theoretical predictions of the distorted Dirac bands with unique spin textures inherited from Bi2Se3 surface states.
We discuss the magnetic and topological properties of bulk crystals and quasi-two-dimensional thin films formed by stacking intrinsic magnetized topological insulator ( for example Mn(Sb$_{x}$Bi$_{1-x}$)$_2$X$_4$ with X = Se,Te, including MnBi$_2$Te$_4$) septuple layers and topological insulator quintuple layers in arbitrary order. Our analysis makes use of a simplified model that retains only Dirac-cone degrees of freedom on both surfaces of each septuple or quintuple layer. We demonstrate the models applicability and estimate its parameters by comparing with {it ab initio } density-functional-theory(DFT) calculations. We then employ the coupled Dirac cone model to provide an explanation for the dependence of thin-film properties, particularly the presence or absence of the quantum anomalous Hall effect, on film thickness, magnetic configuration, and stacking arrangement, and to comment on the design of Weyl superlattices.
Topological insulators are expected to be a promising platform for novel quantum phenomena, whose experimental realizations require sophisticated devices. In this Technical Review, we discuss four topics of particular interest for TI devices: topological superconductivity, quantum anomalous Hall insulator as a platform for exotic phenomena, spintronic functionalities, and topological mesoscopic physics. We also discuss the present status and technical challenges in TI device fabrications to address new physics.
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