Optical study of magnetic topological insulator MnBi_(4)Te_7

We present an infrared spectroscopy study of the magnetic topological insulator MnBi_(4)Te_7 with antiferromagnetic(AFM) order below the Neel temperature TN= 13 K. Our investigation reveals that the low-frequency optical conductivity consists of two Drude peaks, indicating a response of free carriers involving multiple bands. Interestingly, the narrow Drude peak grows strongly as the temperature decreases, while the broad Drude peak remains relatively unchanged. The onset of interband transitions starts around 2000 cm^(-1), followed by two prominent absorption peaks around 10000 cm^(-1) and 20000 cm^(-1). Upon cooling, there is a notable transfer of spectral weight from the interband transitions to the Drude response. Below TN, the AFM transition gives rise to small anomalies of the charge response due to a band reconstruction.These findings provide valuable insights into the interplay between magnetism and the electronic properties in MnBi_(4)Te_7.

Transport properties of topological insulators films and nanowires

The last several years have witnessed the rapid developments in the study and understanding of topological insulators. In this review, after a brief summary of the history of topological insulators, we focus on the recent progress made in transport experiments on topological insulator films and nanowires. Some quantum phenomena, including the weak antilocalization, the Aharonov-Bobm effect, and the Shubnikov-de Haas oscillations, observed in these nanostructures are described. In addition, the electronic transport evidence of the superconducting proximity effect as well as an anomalous resistance enhancement in topological insulator/superconductor hybrid structures is included.

Molecular-beam epitaxy of topological insulator Bi_2Se_3(111) and (221) thin films

This paper presents an overview of the growth of Bi2Se3, a prototypical three-dimensional topological insulator, by molecular-beam epitaxy on various substrates. Comparison is made between the growth of Bi2 Se3 （111） on van der Waals （vdW） and non-vdW substrates, with attention paid to twin suppression and strain. Growth along the [221] direction of Bi2Se3 on InP （001） and GaAs （001） substrates is also discussed.

MoS_(2) on topological insulator Bi_(2)Te_(3) thin films:Activation of the basal plane for hydrogen reduction

2H-MoS_(2) is a well-studied and promising non-noble metal electrocatalyst for heterogeneous reactions,such as the hydrogen evolution reaction(HER).The performance is largely limited by the chemically inert basal plane,which is unfavorable for surface adsorption and reactions.Herein,we report a facile method to boost the HER activities of 2H-MoS_(2) by coupling with epitaxial Bi2Te3 topological insulator films.The as-obtained MoS_(2)/Bi2Te3/SrTiO3 catalyst exhibits prominent HER catalytic activities compared to that of pure MoS_(2) structures,with a 189 mV decrease in the overpotential required to reach a current density of 10 mA cm^(−2) and a low Tafel slope of 58 mV dec−1.Theoretical investigations suggest that the enhanced catalytic activity originates from the charge redistribution at the interface between the Bi2Te3topological insulator films and the MoS_(2) layer.The delocalized sp-derived topological surface states could denote electrons to the MoS_(2) layer and activate the basal plane for hydrogen adsorption.This study demonstrates the potential of manipulating topological surface states to design high-performance electrocatalysts.

Topological edge states and electronic structures of a 2D topological insulator: Single-bilayer Bi (111)

Providing the strong spin-orbital interaction, Bismuth is the key element in the family of three-dimensional topological insulators. At the same time, Bismuth itself also has very unusual behavior, existing from the thinnest unit to bulk crystals. Ultrathin Bi （111） bilayers have been theoretically proposed as a two-dimensional topological insulator. The related experimental realization achieved only recently, by growing Bi （111） ultrathin bilayers on topological insulator Bi2Te3 or Bi2Se3 substrates. In this review, we started from the growth mode of Bi （111） bilayers and reviewed our recent progress in the studies of the electronic structures and the one-dimensional topological edge states using scanning tunneling microscopy/spectroscopy （STM/STS）, angle-resolved photoemission spectroscopy （ARPES）, and first principles calculations.

Probing the minigap in topological insulator-based Josephson junctions under radio frequency irradiation

Recently,a contact-resistance-measurement method was developed to detect the minigap,hence the Andreev bound states(ABSs),in Josephson junctions constructed on the surface of three-dimensional topological insulators(3D TIs).In this work,we further generalize that method to the circumstance with radio frequency(rf)irradiation.We find that with the increase of the rf power,the measured minigap becomes broadened and extends to higher energies in a way similar to the rf power dependence of the outer border of the Shapiro step region.We show that the corresponding data of contact resistance under rf irradiation can be well interpreted by using the resistively shunted Josephson junction(RSJ)model and the Blonder–Tinkham–Klapwijk(BTK)theory.Our findings could be useful when using the contact-resistancemeasurement method to study the Majorana-related physics in topological insulator-based Josephson junctions under rf irradiation.

The preparation process and feature of the topological insulator Bi_2Te_3

Topological insulators are insulating in the bulkbut have metallic surface states. Its unique physicochemicalproperties can find numerous applications in electronics,spintronics, photonics, the energy sciences, and thesignal control of transportation. We report an experimentalapproach to synthesize the high-quality single crystal oftopological insulator Bi2Te3 by using self-flux method. Weobtained the optimal preparation conditions by adjustingthe parameters of heat treatment, and successfully preparedthe single-crystal Bi2Te3 sample. The as-grown sampleshave a surface with bright metallic luster and are soft andfragile. Furthermore, Bi2Te3 has the obvious layer structurefrom SEM results. The data of X-ray diffraction andscanning electron microscope show that Bi2Te3 singlecrystal grows along the c-axis with the order of Te（1）–Bi–Te（2）–Bi–Te（1） and crystallizes in the hexagonal systemwith space group of R/3 m. The q–T curve shows that qdecreases with temperature, showing metallic behaviorover the whole temperature range.

Low-Frequency Noise in Gate Tunable Topological Insulator Nanowire Field Emission Transistor near the Dirac Point

Low-frequency flicker noise is usually associated with material defects or imperfection of fabrication procedure. Up to now, there is only very limited knowledge about flicker noise of the topological insulator, whose topologically protected conducting surface is theoretically immune to back scattering. To suppress the bulk conductivity we synthesize antimony doped Bi2Se3 nanowires and conduct transport measurements at cryogenic temperatures. The low-frequency current noise measurement shows that the noise amplitude at the high-drain current regime can be described by Hooge＇s empirical relationship, while the noise level is significantly lower than that predicted by Hooge＇s model near the Dirac point. Furthermore, different frequency responses of noise power spectrum density for specific drain currents at the low drain current regime indicate the complex origin of noise sources of topological insulator.

Electron-Elastic-Wave Interaction in a Two-Dimensional Topological Insulator

The interaction between an electron and an elastic wave is investigated for HgTe and InAs-GaSb quantum wells. The well-known Bernevig Hughes-Zhang model, i.e., the 4 × 4 model for a two-dimensional （2D） topological insulator （TI）, is extended to include the terms that describe the coupling between the electron and the elastic wave. The influence of this interaction on the transport properties of the 2DTI and of the edge states is discussed. As the electron-like and hole-like carriers interact with the elastic wave differently due to the crystal symmetry of the 2DTI, one may utilize the elastic wave to tune^control the transport property of charge carriers in the 2DTI. The extended 2DTI model also provides the possibility to investigate the backscattering of edge states of a 2DTI more realistically.

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z_2 Topological Insulator

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator（TI） and topological crystalline insulator（TCI） in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.

Proximity effects in topological insulator heterostructures

Topological insulators （Tls） are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to TI-based heterostructures, in which con- ventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent studies on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insu- lator or other topologically trivial systems. Using first-principles approaches, we have realized the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topo- logical helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath, These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI- based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications.

Topological insulator nanostructures and devices

Topological insulators＇ properties and their potential device applications are reviewed. We also explain why topologi- cal insulator （TI） nanostructnres are an important avenue for research and discuss some methods by which TI nanostructures are produced and characterized. The rapid development of high-quality TI nanostructures provides an ideal platform to ex- ploit salient physical phenomena that have been theoretically predicted but not yet experimentally realized.

Thermoelectric Transport by Surface States in Bi2Se3-Based Topological Insulator Thin Films

We develop a tractable theoretical model to investigate the thermoelectric （TE） transport properties of surface states in topological insulator thin films （TITFs） of Bi2Sea at room temperature. The hybridization between top and bottom surface states in the TITF plays a significant role. With the increasing hybridization-induced surface gap, the electrical conductivity and electron thermal conductivity decrease while the Seebeck coefficient increases. This is due to the metal-semiconductor transition induced by the surface-state hybridization. Based on these TE transport coefficients, the TE figure-of-merit ZT is evaluated. It is shown that ZT can be greatly improved by the surface-state hybridization. Our theoretical results are pertinent to the exploration of the TE transport properties of surface states in TITFs and to the potential application of Bi2Sea-based TITFs as high-performance TE materials and devices.

Electrostatic field effects on three-dimensional topological insulators

Three-dimensional topological insulators are a new class of quantum matter which has interesting connections to nearly all main branches of condensed matter physics. In this article, we briefly review the advances in the field effect control of chemical potential in three-dimensional topological insulators. It is essential to the observation of many exotic quantum phenomena predicted to emerge from the topological insulators and their hybrid structures with other materials. We also describe various methods for probing the surface state transport. Some challenges in experimental study of electron transport in topological insulators will also be briefly discussed.

Elastic scattering of surface states on three-dimensional topological insulators

Topological insulators as a new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states protected by the time-reversal symmetry. We propose that the interference patterns caused by the elastic scattering of defects or impurities are dominated by the surface states at the extremal points on the constant energy contour. Within such a formalism, we summarize our recent theoretical investigations on the elastic scattering of topological surface states by various imperfections, including non-magnetic impurities, magnetic impurities, step edges, and various other defects, in comparison with the recent related experiments in typical topological materials such as BiSb alloys, Bi2Te3, and Bi2Se3 crystals.

Confined states and spin polarization on a topological insulator thin film modulated by an electric potential

We study the electronic structure and spin polarization of the surface states of a three-dimensional topological insulator thin film modulated by an electrical potential well. By routinely solving the low-energy surface Dirac equation for the system, we demonstrate that confined surface states exist, in which the electron density is almost localized inside the well and exponentially decayed outside in real space, and that their subband dispersions are quasilinear with respect to the propagating wavevector. Interestingly, the top and bottom surface confined states with the same density distribution have opposite spin polarizations due to the hybridization between the two surfaces. Along with the mathematical analysis, we provide an intuitive, topological understanding of the effect.

Ferromagnetic-insulators-modulated transport properties on the surface of a topological insulator

Transport properties on the surface of a topological insulator （TI） under the modulation of a two-dimensional （2D） ferromagnet/ferromagnet junction are investigated by the method of wave function matching. The single ferromagnetic barrier modulated transmission probability is expected to be a periodic function of the polarization angle and the planar rotation angle, that decreases with the strength of the magnetic proximity exchange increasing. However, the transmission probability for the double ferromagnetic insulators modulated n-n junction and n-p junction is not a periodic function of polarization angle nor planar rotation angle, owing to the combined effects of the double ferromagnetic insulators and the barrier potential. Since the energy gap between the conduction band and the valence band is narrowed and widened respectively in ranges of 0 ≤ 0 〈π/2 and r/2 〈 0 ≤ π, the transmission probability of the n-n junction first increases rapidly and then decreases slowly with the increase of the magnetic proximity exchange strength. While the transmission probability for the n-p junction demonstrates an opposite trend on the strength of the magnetic proximity exchange because the band gaps contrarily vary. The obtained results may lead to the possible realization of a magnetic/electric switch based on TIs and be useful in further understanding the surface states of TIs.

Electronic states and spin-filter effect in three-dimensional topological insulator Bi_2Se_3 nanoribbons

We study the electronic band structure, density distribution, and transport of a Bi2Se3 nanoribbon, We find that the density distribution of the surface states is dependent on not only the shape and size of the transverse cross section of the nanoribbon, but also the energy of the electron. We demonstrate that a transverse electric field can eliminate the coupling between surface states on the walls of the nanoribbon, remove the gap of the surface states, and restore the quantum spin Hall effects. In addition, we study the spin-dependent transport property of the surface states transmitting from top and bottom surfaces （x-y plane） to the side surfaces （z-x plane） of a Bi2Se3 nanoribbon. We find that transverse electric fields can open two surface channels for spin-up and -down Dirac electrons, and then switch off one channel for the spin-up Dirac electron. Our results may provide a simple way for the design of a spin filter based on topological insulator nanostructures.

Femtosecond Tm-Ho co-doped fiber laser using a bulk-structured Bi2Se3 topological insulator

We experimentally demonstrate a femtosecond mode-locked thulium-holmium（Tm-Ho） co-doped fiber laser incorporating a saturable absorber（SA） based on a bulk-structured bismuth selenide（Bi2Se3） topological insulator（TI）. The SA was prepared by depositing a mechanically exfoliated Bi2Se3 TI layer onto a side-polished optical fiber platform. Unlike high-quality nano-structured Bi2Se3 TI-based SA, bulk-structured Bi2Se3 with non-negligible oxidation was used as a saturable absorption material for this experimental demonstration due to its easy fabrication process. The saturation power and modulation depth of the prepared SA were measured to be -28.6 W and -13.4%, respectively. By incorporating the prepared SA into a Tm-Ho co-doped fiber ring cavity, stable soliton pulses with a temporal width of - 853 fs could be generated at 1912.12 nm. The 3-dB bandwidth of the mode-locked pulse was measured to be -4.87 nm. This experimental demonstration reaffirms that Bi2Se3 is a superb base material for mid-infrared passive mode-locking even under oxidation.