Mechanical Analogue of a Majorana Bound State

The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well‐known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.     

A Single‐Electron Transistor Made of a 3D Topological Insulator Nanoplate

Quantum confined devices of 3D topological insulators are proposed to be promising and of great importance for studies of confined topological states and for applications in low‐energy‐dissipative spintronics and quantum information processing. The absence of energy gap on the topological insulator surface limits the experimental realization of a quantum confined system in 3D topological insulators. Here, the successful realization of single‐electron transistor devices in Bi₂Te₃ nanoplates using state‐of‐the‐art nanofabrication techniques is reported. Each device consists of a confined central island, two narrow constrictions that connect the central island to the source and drain, and surrounding gates. Low‐temperature transport measurements demonstrate that the two narrow constrictions function as tunneling junctions and the device shows well‐defined Coulomb current oscillations and Coulomb‐diamond‐shaped charge‐stability diagrams. This work provides a controllable and reproducible way to form quantum confined systems in 3D topological insulators, which should greatly stimulate research toward confined topological states, low‐energy‐dissipative devices, and quantum information processing.     

Van der Waals heterostructures based on three-dimensional topological insulators

Three-dimensional (3D) topological insulators (TIs) have generated tremendous research interest over the past decade due to their topologically-protected surface states with linear dispersion and helical spin texture. The topological surface states offer an important platform to realize topological phase transitions, topological magnetoelectric effects and topological superconductivity via 3D TI-based heterostructures. In this review, we summarize the key findings of magneto and quantum transport properties in 3D TIs and their related heterostructures with normal insulators, ferromagnets and superconductors. For intrinsic 3D TIs, the experimental evidences of the topological surface states and their coupling effects are reviewed. Whereas for 3D TI related heterostructures, we focus on some important phenomenological magnetotransport activities and provide explanations for the proximity-induced topological and quantum effects.     

Low‐Dimensional Topological Crystalline Insulators

Topological crystalline insulators (TCIs) are recently discovered topological phase with robust surface states residing on high‐symmetry crystal surfaces. Different from conventional topological insulators (TIs), protection of surface states on TCIs comes from point‐group symmetry instead of time‐reversal symmetry in TIs. The distinct properties of TCIs make them promising candidates for the use in novel spintronics, low‐dissipation quantum computation, tunable pressure sensor, mid‐infrared detector, and thermoelectric conversion. However, similar to the situation in TIs, the surface states are always suppressed by bulk carriers, impeding the exploitation of topology‐induced quantum phenomenon. One effective way to solve this problem is to grow low‐dimensional TCIs which possess large surface‐to‐volume ratio, and thus profoundly increase the carrier contribution from topological surface states. Indeed, through persistent effort, researchers have obtained unique quantum transport phenomenon, originating from topological surface states, based on controllable growth of low‐dimensional TCIs. This article gives a comprehensive review on the recent progress of controllable synthesis and topological surface transport of low‐dimensional TCIs. The possible future direction about low‐dimensional TCIs is also briefly discussed at the end of this paper.     

Adiabatic photo-steering theory in topological insulators

Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane–Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed.     

Density-Dependence of Surface Transport in Tellurium-Enriched Nanograined Bulk Bi2Te3

Three-dimensional topological insulators (3D TI) exhibit conventional parabolic bulk bands and protected Dirac surface states. A thorough investigation of the different transport channels provided by the bulk and surface carriers using macroscopic samples may provide a path toward accessing superior surface transport properties. Bi₂Te₃ materials make promising 3D TI models; however, due to their complicated defect chemistry, these materials have a high number of charge carriers in the bulk that dominate the transport, even as nanograined structures. To partially control the bulk charge carrier density, herein the synthesis of Te-enriched Bi₂Te₃ nanoparticles is reported. The resulting nanoparticles are compacted into nanograined pellets of varying porosity to tailor the surface-to-volume ratio, thereby emphasizing the surface transport channels. The nanograined pellets are characterized by a combination of resistivity, Hall- and magneto-conductance measurements together with (THz) time-domain reflectivity measurements. Using the Hikami-Larkin-Nagaoka (HLN) model, a characteristic coherence length of ≈200 nm is reported that is considerably larger than the diameter of the nanograins. The different contributions from the bulk and surface carriers are disentangled by THz spectroscopy, thus emphasizing the dominant role of the surface carriers. The results strongly suggest that the surface transport carriers have overcome the hindrance imposed by nanoparticle boundaries.     

Contrast Reversal in Scanning Tunneling Microscopy and Its Implications for the Topological Classification of SmB6

SmB₆ has recently attracted considerable interest as a candidate for the first strongly correlated topological insulator. Such materials promise entirely new properties such as correlation-enhanced bulk bandgaps or a Fermi surface from spin excitations. Whether SmB₆ and its surface states are topological or trivial is still heavily disputed however, and a solution is hindered by major disagreement between angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM) results. Here, a combined ARPES and STM experiment is conducted. It is discovered that the STM contrast strongly depends on the bias voltage and reverses its sign beyond 1 V. It is shown that the understanding of this contrast reversal is the clue to resolving the discrepancy between ARPES and STM results. In particular, the scanning tunneling spectra reflect a low-energy electronic structure at the surface, which supports a trivial origin of the surface states and the surface metallicity of SmB₆.     

Toward 2D Magnets in the (MnBi2Te4)(Bi2Te3)n Bulk Crystal

2D magnets and their engineered magnetic heterostructures are intriguing materials for both fundamental physics and application prospects. On the basis of the recently discovered intrinsic magnetic topological insulators (MnBi₂Te₄)(Bi₂Te₃)_n, here, a new type of magnet, in which the magnetic layers are separated by a large number of non-magnetic layers and become magnetically independent, is proposed. This magnet is named as a single-layer magnet, regarding the vanishing interlayer exchange coupling. Theoretical calculations and magnetization measurements indicate that, the decoupling of the magnetic layers starts to emerge from n = 2 and 3, as revealed by a unique slow-relaxation behavior below a ferromagnetic-type transition at T_c = 12–14 K. Magnetization data analysis shows that the proposed new magnetic states have a strong uniaxial anisotropy along the c-axis, forming an Ising-type magnetic structure, where T_c is the ordering temperature for each magnetic layer. The characteristic slow relaxation, which exists only along the c-axis but is absent along the ab plane, can be ascribed to interlayer coherent spin rotation and/or intralayer domain wall movement. The present results will stimulate further theoretical and experimental investigations for the prototypical magnetic structures, and their combination with the topological surface states may lead to exotic physical properties.     

Realization of Epitaxial Thin Films of the Topological Crystalline Insulator Sr3SnO

Topological materials are derived from the interplay between symmetry and topology. Advances in topological band theories have led to the prediction that the antiperovskite oxide Sr₃SnO is a topological crystalline insulator, a new electronic phase of matter where the conductivity in its (001) crystallographic planes is protected by crystallographic point group symmetries. Realization of this material, however, is challenging. Guided by thermodynamic calculations, a deposition approach is designed and implemented to achieve the adsorption-controlled growth of epitaxial Sr₃SnO single-crystal films by molecular-beam epitaxy (MBE). In situ transport and angle-resolved photoemission spectroscopy measurements reveal the metallic and electronic structure of the as-grown samples. Compared with conventional MBE, the used synthesis route results in superior sample quality and is readily adapted to other topological systems with antiperovskite structures. The successful realization of thin films of Sr₃SnO opens opportunities to manipulate topological states by tuning symmetries via strain engineering and heterostructuring.     

Indentation fracture toughness of single-crystal Bi<Subscript>2</Subscript>Te<Subscript>3</Subscript> topological insulators

Bismuth telluride (Bi₂Te₃) is one of the most important commercial thermoelectric materials. In recent years, the discovery of topologically protected surface states in Bi chalcogenides has paved the way for their application in nanoelectronics. Determination of the fracture toughness plays a crucial role for the potential application of topological insulators in flexible electronics and nanoelectromechanical devices. Using depth-sensing nanoindentation tests, we investigated for the first time the fracture toughness of bulk single crystals of Bi₂Te₃ topological insulators, grown using the Bridgman-Stockbarger method. Our results highlight one of the possible pitfalls of the technology based on topological insulators.

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Observation of Quantum Anomalous Hall Effect and Exchange Interaction in Topological Insulator/Antiferromagnet Heterostructure

Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically-doped topological insulator grown on the antiferromagnetic insulator Cr₂O₃. The exchange coupling between the two materials is investigated using field-cooling-dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr₂O₃ and the magnetic topological insulator, manifested as an exchange bias when the sample is field-cooled under an out-of-plane magnetic field, and an exchange spring-like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.     

Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators

Higher‐order topological insulators (HOTIs) belong to a new class of materials with unusual topological phases. They have garnered considerable attention due to their capabilities in confining energy at the hinges and corners, which is entirely protected by the topology, and have thus become attractive structures for acoustic wave studies and control. However, for most practical applications at audible and low frequencies, compact and subwavelength implementations are desirable in addition to providing robust guiding of sound beyond a single‐frequency operation. Here, a holey HOTI capable of sustaining deeply confined corner states 50 times smaller than the wavelength is proposed. A remarkable resilience of these surface‐confined acoustic states against defects is experimentally observed, and topologically protected sound is demonstrated in three different frequency regimes. Concerning this matter, the findings will thus have the capability to push forward exciting applications for robust acoustic imaging way beyond the diffraction limit.     

Ambipolar field effect in the ternary topological insulator (Bi(x)Sb(1-x))2Te3 by composition tuning

Topological insulators exhibit a bulk energy gap and spin-polarized surface states that lead to unique electronic properties, with potential applications in spintronics and quantum information processing. However, transport measurements have typically been dominated by residual bulk charge carriers originating from crystal defects or environmental doping, and these mask the contribution of surface carriers to charge transport in these materials. Controlling bulk carriers in current topological insulator materials, such as the binary sesquichalcogenides Bi2Te3, Sb2Te3 and Bi2Se3, has been explored extensively by means of material doping and electrical gating, but limited progress has been made to achieve nanostructures with low bulk conductivity for electronic device applications. Here we demonstrate that the ternary sesquichalcogenide (Bi(x)Sb(1-x))2Te3 is a tunable topological insulator system. By tuning the ratio of bismuth to antimony, we are able to reduce the bulk carrier density by over two orders of magnitude, while maintaining the topological insulator properties. As a result, we observe a clear ambipolar gating effect in (Bi(x)Sb(1-x))2Te3 nanoplate field-effect transistor devices, similar to that observed in graphene field-effect transistor devices. The manipulation of carrier type and density in topological insulator nanostructures demonstrated here paves the way for the implementation of topological insulators in nanoelectronics and spintronics.     

Engineering Second-Order Corner States in 2D Multiferroics

The understanding and manipulate of the second-order corner states are central to both fundamental physics and future topotronics applications. Despite the fact that numerous second-order topological insulators (SOTIs) are achieved, the efficient engineering in a given material remains elusive. Here, the emergence of 2D multiferroics SOTIs in SbAs and BP₅ monolayers is theoretically demonstrated, and an efficient and straightforward way for engineering the nontrivial corner states by ferroelasticity and ferroelectricity is remarkably proposed. With ferroelectric polarization of SbAs and BP₅ monolayers, the nontrivial corner states emerge in the mirror symmetric corners and are perpendicular to orientations of the in-plane spontaneous polarization. And remarkably the spatial distribution of the corner states can be effectively tuned by a ferroelastic switching. At the intermediate states of both ferroelectric and ferroelastic switchings, the corner states disappear. These finding not only combines exotic SOTIs with multiferroics but also pave the way for experimental discovery of 2D tunable SOTIs.     

Optically Unraveling the Edge Chirality‐Dependent Band Structure and Plasmon Damping in Graphene Edges

The nontrivial topological origin and pseudospinorial character of electron wavefunctions make edge states possess unusual electronic properties. Twenty years ago, the tight‐binding model calculation predicted that zigzag termination of 2D sheets of carbon atoms have peculiar edge states, which show potential application in spintronics and modern information technologies. Although scanning probe microscopy is employed to capture this phenomenon, the experimental demonstration of its optical response remains challenging. Here, the propagating graphene plasmon provides an edge‐selective polaritonic probe to directly detect and control the electronic edge state at ambient condition. Compared with armchair, the edge‐band structure in the bandgap gives rise to additional optical absorption and strongly absorbed rim at zigzag edge. Furthermore, the optical conductivity is reconstructed and the anisotropic plasmon damping in graphene systems is revealed. The reported approach paves the way for detecting edge‐specific phenomena in other van der Waals materials and topological insulators.     

Control over topological insulator photocurrents with light polarization

Three-dimensional topological insulators represent a new quantum phase of matter with spin-polarized surface states that are protected from backscattering. The static electronic properties of these surface states have been comprehensively imaged by both photoemission and tunnelling spectroscopies. Theorists have proposed that topological surface states can also exhibit novel electronic responses to light, such as topological quantum phase transitions and spin-polarized electrical currents. However, the effects of optically driving a topological insulator out of equilibrium have remained largely unexplored experimentally, and no photocurrents have been measured. Here, we show that illuminating the topological insulator Bi(2)Se(3) with circularly polarized light generates a photocurrent that originates from topological helical Dirac fermions, and that reversing the helicity of the light reverses the direction of the photocurrent. We also observe a photocurrent that is controlled by the linear polarization of light and argue that it may also have a topological surface state origin. This approach may allow the probing of dynamic properties of topological insulators and lead to novel opto-spintronic devices.     

Quantum Topological Boundary States in Quasi‐Crystals

Topological phases play a novel and fundamental role in matter and display extraordinary robustness to smooth changes in material parameters or disorder. A crossover between topological material and quantum information may lead to inherent fault‐tolerant quantum simulations and quantum computing. Quantum features may be preserved by being encoded among topological structures of physical evolution systems. This requires stimulation, manipulation, and observation of topological phenomena at the single quantum particle level, which has not, however, yet been realized. It is asked whether the quantum features of single photons can be preserved in topological structures. The boundary states are experimentally observed at the genuine single‐photon level and the performance of the topological phase is demonstrated to protect the quantum features against diffusion‐induced decoherence in coupled waveguides and noise decoherence from the ambient environment. Compatibility between macroscopic topological states and microscopic single photons in the ambient environment is thus confirmed, leading to a new avenue to “quantum topological photonics” and providing more new possibilities for quantum materials and quantum technologies.     

Topological Insulator Bi2Se3-Assisted Heterostructure for Ultrafast Charging Sodium-Ion Batteries

The development of fast charging materials offers a viable solution for large-scale and sustainable energy storage needs. However, it remains a critical challenge to improve the electrical and ionic conductivity for better performance. Topological insulator (TI), a topological quantum material that has attracted worldwide attention, hosts unusual metallic surface states and consequent high carrier mobility. Nevertheless, its potential in promising high-rate charging capability has not been fully realized and explored. Herein, a novel Bi₂Se₃-ZnSe heterostructure as excellent fast charging material for Na⁺ storage is reported. Ultrathin Bi₂Se₃ nanoplates with rich TI metallic surfaces are introduced as an electronic platform inside the material, which greatly reduces the charge transfer resistance and improves the overall electrical conductivity. Meanwhile, the abundant crystalline interfaces between these two selenides promote Na⁺ migration and provide additional active sites as well. As expected, the composite delivers the excellent high-rate performance of 360.5 mAh g⁻¹ at 20 A g⁻¹ and maintains its electrochemical stability of 318.4 mAh g⁻¹ after 3000 long cycles, which is the record high for all reported selenide-based anodes. This work is anticipated to provide alternative strategies for further exploration of topological insulators and advanced heterostructures.     

双拓扑绝缘体介质界面的反射波极化调控特性

本文对两种三维强拓扑绝缘体分界面的反射极化现象进行了研究,得到了线偏振光完全转化的普适性充要条件.通过分析分界面的直接反射率、交叉反射率以及极化转化率,发现该模型利用现有的拓扑绝缘体材料就可以实现线极化波的完全转变,突破了需要新的较小介电常数的拓扑绝缘体材料才能完全转化的限制.该转化过程可以利用克尔旋转角进行验证,并给...     

Epitaxial Growth of Ternary Topological Insulator Bi2Te2Se 2D Crystals on Mica

Nanostructures of ternary topological insulator (TI) Bi₂Te₂Se are, in principle, advantageous to the manifestation of topologically nontrivial surface states, due to significantly enhanced surface‐to‐volume ratio compared with its bulk crystals counterparts. Herein, the synthesis of 2D Bi₂Te₂Se crystals on mica via the van der Waals epitaxy method is explored and systematically the growth behaviors during the synthesis process are investigated. Accordingly, 2D Bi₂Te₂Se crystals with domain size up to 50 µm large and thickness down to 2 nm are obtained. A pronounced weak antilocalization effect is clearly observed in the 2D Bi₂Te₂Se crystals at 2 K. The method for epitaxial growth of 2D ternary Bi₂Te₂Se crystals may inspire materials engineering toward enhanced manifestation of the subtle surface states of TIs and thereby facilitate their potential applications in next‐generation spintronics.