Topological Surface States Research Articles

Bulk-surface coupling in dual topological insulator Bi1Te1 and Sb-doped Bi1Te1 single crystals via electron-phonon interaction

Recently, has been proved to be a dual topological insulator (TI), a new subclass of symmetry-protected topological phases, and predicted to be higher order topological insulator (HOTI). Being a dual TI (DTI), Bi1Te1 is said to host quasi-1D surface states (SSs) due to weak TI phase and topological crystalline insulating SSs at the same time. On the other hand, HOTI supports topologically protected hinge states. So, is a unique platform to study the electrical signature of topological SS (TSS) of fundamentally different origins. Though there is a report of magneto-transport measurements on large-scale Bi1Te1 thin films, the Bi1Te1 single crystal is not studied experimentally to date. Even the doping effect in a DTI Bi1Te1 is missing in the literature. In this regard, we performed the perpendicular and parallel field magneto-transport measurement on the exfoliated microflake of Bi1Te1 and Sb-doped Bi1Te1 single crystals, grown by the modified Bridgmann method. Our metallic sample shows the weak anti-localization behavior analyzed by the multi-channel Hikami-Larkin-Nagaoka equation. We observed the presence of a pair of decoupled TSS. Further, we extracted the dephasing index (β) from temperature (T)-dependence of phase coherence length (L), following the power law equation (L). The thickness-dependent value of β indicates the transition in the dephasing mechanism from electron-electron to electron-phonon interaction with the increase in thickness, indicating the enhancement in the strength of bulk-surface coupling. Sb-doped system shows weakened bulk-surface coupling, hinted by the reduced dephasing indices.

Spin pumping through nanocrystalline topological insulators

The topological surface states (TSSs) in topological insulators (TIs) offer exciting prospects for dissipationless spin transport. Common spin-based devices, such as spin valves, rely on trilayer structures in which a non-magnetic layer is sandwiched between two ferromagnetic (FM) layers. The major disadvantage of using high-quality single-crystalline TI films in this context is that a single pair of spin-momentum locked channels spans across the entire film, meaning that only a very small spin current can be pumped from one FM to the other, along the side walls of the film. On the other hand, using nanocrystalline TI films, in which the grains are large enough to avoid hybridization of the TSSs, will effectively increase the number of spin channels available for spin pumping. Here, we used an element-selective, x-ray based ferromagnetic resonance technique to demonstrate spin pumping from a FM layer at resonance through the TI layer and into the FM spin sink.

Ultrafast electron dynamics in a topological surface state observed in two-dimensional momentum space

We study ultrafast population dynamics in the topological surface state of Sb_2Te_3 in two-dimensional momentum space with time- and angle-resolved two-photon photoemission spectroscopy. Linearly polarized mid-infrared pump pulses are used to permit a direct optical excitation across the Dirac point. We show that this resonant excitation is strongly enhanced within the Dirac cone along three of the six {bar{Gamma }}–{bar{M}} directions and results in a macroscopic photocurrent when the plane of incidence is aligned along a {bar{Gamma }}–{bar{K}} direction. Our experimental approach makes it possible to disentangle the decay of transiently excited population and photocurent by elastic and inelastic electron scattering within the full Dirac cone in unprecedented detail. This is utilized to show that doping of Sb_2Te_3 by vanadium atoms strongly enhances inelastic electron scattering to lower energies, but only scarcely affects elastic scattering around the Dirac cone.

Topological antichiral surface states in a magnetic Weyl photonic crystal

Chiral edge states that propagate oppositely at two parallel strip edges are a hallmark feature of Chern insulators which were first proposed in the celebrated two-dimensional (2D) Haldane model. Subsequently, counterintuitive antichiral edge states that propagate in the same direction at two parallel strip edges were discovered in a 2D modified Haldane model. Recently, chiral surface states, the 2D extension of one-dimensional (1D) chiral edge states, have also been observed in a photonic analogue of a 3D Haldane model. However, despite many recent advances in antichiral edge states and chiral surface states, antichiral surface states, the 2D extension of 1D antichiral edge states, have never been realized in any physical system. Here, we report the experimental observation of antichiral surface states by constructing a 3D modified Haldane model in a magnetic Weyl photonic crystal with two pairs of frequency-shifted Weyl points (WPs). The 3D magnetic Weyl photonic crystal consists of gyromagnetic cylinders with opposite magnetization in different triangular sublattices of a 3D honeycomb lattice. Using microwave field-mapping measurements, unique properties of antichiral surface states have been observed directly, including the antichiral robust propagation, tilted surface dispersion, a single open Fermi arc connecting two projected WPs and a single Fermi loop winding around the surface Brillouin zone (BZ). These results extend the scope of antichiral topological states and enrich the family of magnetic Weyl semimetals.

Moiré Pattern Formation in Epitaxial Growth on a Covalent Substrate: Sb on InSb(111)A.

Structural moiré superstructures arising from two competing lattices may lead to unexpected electronic behavior. Sb is predicted to show thickness-dependent topological properties, providing potential applications for low-energy-consuming electronic devices. Here we successfully synthesize ultrathin Sb films on semi-insulating InSb(111)A. Despite the covalent nature of the substrate, which has dangling bonds on the surface, we prove by scanning transmission electron microscopy that the first layer of Sb atoms grows in an unstrained manner. Rather than compensating for the lattice mismatch of -6.4% by structural modifications, the Sb films form a pronounced moiré pattern as we evidence by scanning tunneling microscopy. Our model calculations assign the moiré pattern to a periodic surface corrugation. In agreement with theoretical predictions, irrespective of the moiré modulation, the topological surface state known on a thick Sb film is experimentally confirmed to persist down to small film thicknesses, and the Dirac point shifts toward lower binding energies with a decrease in Sb thickness.

Linear photogalvanic effect in surface states of topological insulators

The theory of the linear photogalvanic effect is developed for direct optical transitions between surface states of three-dimensional topological insulators. The photocurrent governed by the orientation of the polarization plane of light and caused by the warping of the energy dispersion of two-dimensional carriers is calculated. It is shown that both the shift contribution caused by coordinate shifts of the particle wave packets during the optical transitions and the ballistic contribution caused by interference of the optical absorption and scattering by disorder have generally the same order of magnitude. The ballistic contribution is present owing to electron-hole asymmetry of topological surface states and has a frequency dependence in contrast to the shift photocurrent. In the nonlinear-in-the-light-intensity regime appearing due to saturation of the direct optical transitions, the ballistic contribution dominates. The nontrivial dependence of the photocurrent on the polarization plane orientation in the nonlinear regime appears solely due to the ballistic contribution. Our findings allow separating the ballistic and shift contributions to the Linear photogalvanic current in experiments.

Bulk and surface electronic structure of NiBi3

We present a high-resolution, angle-resolved photoemission spectroscopy study of the normal electronic state of the superconducting ${\mathrm{NiBi}}_{3}$. Our experimental results show a complex Fermi surface structure with many sheets along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}X$ and $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}Y$ directions of the Brillouin zone. The band structure presents a topological surface state (TSS) at the high symmetry $\mathrm{\ensuremath{\Gamma}}$ point with a surface Dirac point at the energy $\ensuremath{-}0.185$ eV. The Dirac-like cone presents a linear dispersion along ${\mathrm{k}}_{x}$ while it presents saddle-like states along ${\mathrm{k}}_{y}$ located in the vicinity of the surface Dirac point. Our results are in good agreement with results of density functional theory band structure calculations. We also discuss the topological band structure of the ${\mathrm{NiBi}}_{3}$ compound.

Tuning Multiple Landau Quantization in Transition-Metal Dichalcogenide with Strain.

Landau quantization associated with the quantized cyclotron motion of electrons under magnetic field provides the effective way to investigate topologically protected quantum states with entangled degrees of freedom and multiple quantum numbers. Here we report the cascade of Landau quantization in a strained type-II Dirac semimetal NiTe2 with spectroscopic-imaging scanning tunneling microscopy. The uniform-height surfaces exhibit single-sequence Landau levels (LLs) at a magnetic field originating from the quantization of topological surface state (TSS) across the Fermi level. Strikingly, we reveal the multiple sequence of LLs in the strained surface regions where the rotation symmetry is broken. First-principles calculations demonstrate that the multiple LLs attest to the remarkable lifting of the valley degeneracy of TSS by the in-plane uniaxial or shear strains. Our findings pave a pathway to tune multiple degrees of freedom and quantum numbers of TMDs via strain engineering for practical applications such as high-frequency rectifiers, Josephson diode and valleytronics.

Investigation of topological regime in Bi2Se3 thin films through low-frequency electric noise

Topological insulators are considered new states of quantum matter that cannot be systematically related to conventional insulators and semiconductors. Among them, Bi2Se3 has attracted an increasing interest due to a simple surface band structure and due to a strong contribution of the surface to transport. While the dc electric transport properties have been extensively studied, intrinsic fluctuations and their effect on the surface conduction have received less attention. In order to better investigate these aspects, a detailed characterization of the low-frequency noise, also known as noise spectroscopy, has been made in Bi2Se3 thin films. The experimental results have been obtained for different samples thickness and geometry, in a temperature range from 300 down to 8 K, and as a function of dc bias current and gate voltage. While the observed spectral noise shows a typical thermal and shot noise part, an unusual reduction of the 1/f noise component is found, especially in the low-temperature region. A correlation of this behavior with structural and dc electric transport investigations suggests that it could be an indication of the occurrence of the topological regime. Flicker noise measurements, therefore, could be considered as a valid alternative technique to standard topological surface state spectroscopy.

Superconductivity by alloying the topological insulator SnBi2Te4

Alloying indium into the topological insulator ${\mathrm{SnBi}}_{2}{\mathrm{Te}}_{4}$ induces bulk superconductivity with critical temperatures ${T}_{c}$ up to 1.85 K and upper critical fields up to about 14 kOe. This is confirmed by electrical resistivity, heat capacity, and magnetic susceptibility measurements. The heat capacity shows a discontinuity at ${T}_{c}$ and temperature dependence below ${T}_{c}$ consistent with weak coupling BCS theory, and suggests a superconducting gap near 0.25 meV. The superconductivity is type-II and the topological surface states have been verified by photoemission. A simple picture suggests analogies with the isostructural magnetic topological insulator ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$, in which a natural heterostructure hosts complementary properties on different sublattices, and motivates new interest in this large family of compounds. The existence of both topological surface states and superconductivity in ${\mathrm{Sn}}_{1\ensuremath{-}\mathrm{x}}{\mathrm{In}}_{\mathrm{x}}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ identifies these materials as promising candidates for the study of topological superconductivity.

Top-Down Fabrication of Bulk-Insulating Topological Insulator Nanowires for Quantum Devices

In a nanowire (NW) of a three-dimensional topological insulator (TI), the quantum confinement of topological surface states leads to a peculiar sub-band structure that is useful for generating Majorana bound states. Top-down fabrication of TINWs from a high-quality thin film would be a scalable technology with great design flexibility, but there has been no report on top-down-fabricated TINWs where the chemical potential can be tuned to the charge neutrality point (CNP). Here we present a top-down fabrication process for bulk-insulating TINWs etched from high-quality (Bi1-xSbx)2Te3 thin films without degradation. We show that the chemical potential can be gate-tuned to the CNP, and the resistance of the NW presents characteristic oscillations as functions of the gate voltage and the parallel magnetic field, manifesting the TI-sub-band physics. We further demonstrate the superconducting proximity effect in these TINWs, preparing the groundwork for future devices to investigate Majorana bound states.

Multi‐Dimensional Topological Fermions in Electrides

AbstractTopological electrides have attracted extensive attention in various fields, for example, electrocatalysis, spintronics, electron emitters, etc., due to their non‐trivial topological surface states and unique electronic properties. It is well known that topologically protected nontrivial surface states are not broken by external perturbations and further exhibit high carrier mobility and high electron density on some specific surfaces. In addition, electrides usually possess a lower work function due to the presence of approximately loose excess electrons. In this case, topological electrides not only build a bridge between topological materials and electrides, but also couple various excellent properties of these two materials. Since the concept of topological electrides was first proposed, several novel types of topological electrides have been reported in the last few years. Therefore, it is necessary to give a comprehensive review of these topological electrides. In this review, the history of the development of topological electrides and their current status is systematically summarized. In addition, relevant insights into the challenges and opportunities facing topological materials are provided.

Top-down patterning of topological surface and edge states using a focused ion beam

The conducting boundary states of topological insulators appear at an interface where the characteristic invariant ℤ2 switches from 1 to 0. These states offer prospects for quantum electronics; however, a method is needed to spatially-control ℤ2 to pattern conducting channels. It is shown that modifying Sb2Te3 single-crystal surfaces with an ion beam switches the topological insulator into an amorphous state exhibiting negligible bulk and surface conductivity. This is attributed to a transition from ℤ2 = 1 → ℤ2 = 0 at a threshold disorder strength. This observation is supported by density functional theory and model Hamiltonian calculations. Here we show that this ion-beam treatment allows for inverse lithography to pattern arrays of topological surfaces, edges and corners which are the building blocks of topological electronics.

Evidence for surface spin structures from first order reversal curves in Co[formula omitted]Sn[formula omitted]S[formula omitted] and Fe[formula omitted]GeTe[formula omitted] magnetic topological semimetals

We study magnetization reversal and first order reversal curves for two different magnetic topological semimetals, Co3Sn2S2 and Fe3GeTe2, in a wide temperature range. For the magnetization reversal, we observe strong temperature dependence of the initial (low-temperature) step-like magnetization switchings, so the inverted hysteresis appears at high temperatures. Usually, the inverted hysteresis is a fingerprint of material with two independent magnetic phases, the inversion reflects the phase interaction. First order reversal curve analysis confirms the two-phase behavior even at the lowest temperatures of the experiment. While the bulk ferromagnetic magnetization shows strong temperature dependence, one of the observed phases demonstrates perfect stability below the Curie temperature. The obtained hysteresis loops are of the bow-tie type, which is usually ascribed to appearance of the skyrmionic phase. The described two-phase behavior is mostly identical for Co3Sn2S2 and Fe3GeTe2 magnetic topological semimetals, only the characteristic temperatures differ for these materials. The specifics of our experiment is the excellent temperature stability of the second phase, while the skyrmions are usually observed near the Curie temperature. On the other hand, temperature stability can be expected for surface-state induced spin textures due to the topological protection of surface states in topological semimetals. This also explains the universal behavior of the second phase for two different topological semimetals Co3Sn2S2 and FGT. Both these materials have strongly different bulk properties, the only similarity is the presence of the topological surface states. Thus, we can ascribe the second, temperature-stable magnetic phase to the surface states in topological semimetals.

Extended terahertz valley-locked surface waves in designer surface plasmon crystals

Topological valley-locked edge states have been attracting much attention in terahertz (THz) and optical regimes due to their unique unidirectional backscattering-immune feature. However, these one-dimensional edge transports are essentially not compatible to traditional waveguides or devices. In this work, we propose a THz topological waveguide supporting two dimensional valley-locked surface waves based on designer surface plasmon crystals. The waveguide is implemented by designing a sandwich-like A|C|B heterostructure with three domains. The central domain C carrying a Dirac cone in the band structure is topologically trivial. The A and B domains consist of two distinct topological structures with opposite valley-Chern numbers. Unlike topological edge states existing only at the interface of conventional A|B domain wall structure, extended topological valley-locked surface states propagating along the whole B domain are observed in our proposed structure. This heterostructure with designable waveguide width is more flexible for interfacing with existing THz devices, and is quite suitable for high-throughput and high-power-capacity applications. Besides, the unique features of momentum-valley locking and immunity against sharp bends are reserved. This work may promote future topological and traditional integrated functional devices in THz and optical regimes.

Consequences of average time-reversal symmetry in disordered antiferromagnetic topological insulators

Average symmetry protects the topological surface states of topological (crystalline) insulators with time-reversal symmetry from disorder-induced localization. However, the nature of such average symmetry for magnetic topological insulators and, in particular, its connection to surface transport await inspection. Here, we investigate the impact of imperfect magnetic order on an antiferromagnetic topological insulator, which is a solid with a bulk axion field $\ensuremath{\theta}=\ensuremath{\pi}$. We find that the disordered topological surfaces of an antiferromagnetic topological insulator can be generally gapped and localized. The behavior of topological surfaces is now controlled by a mesoscopic average time-reversal symmetry that requires a magnetically imperfect system to be divisible into finite and magnetically neutral slabs. In the presence of this mesoscopic average time-reversal symmetry, the topological surface states will be gapless in the thermodynamic limit and tend to delocalize at a single energy similar to the delocalization transition in the chiral universality class. The notion of average-symmetry-induced delocalization is thus extended to account for magnetic topological insulators, and the spectroscopic and transport signatures clarified herein are relevant to future experimental investigations.

Highly active hydrogen evolution facilitated by topological surface states on a Pd/SnTe heterostructure

Highly active hydrogen evolution facilitated by topological surface states on a Pd/SnTe heterostructure

Topological band inversion in HgTe(001): Surface and bulk signatures from photoemission

HgTe is a prime example of a topological material that exhibits a range of topological phases based on its dimensionality and lattice strain. The key to its topological properties lies in the band inversion between the Hg 6$s$ and Te 5$p$ valence levels, leading to the emergence of surface states. In this study, the authors present an in-depth examination of the electronic structure of strained HgTe films using angle-resolved photoelectron spectroscopy and density functional theory. The results offer a direct visualization of the topological band inversion and surface states present in HgTe.

Antiferromagnetic topological insulating state in Tb0.02Bi1.08Sb0.9Te2S single crystals

Topological insulators are emerging materials with insulating bulk and symmetry protected nontrivial surface states. One of the most fascinating transport behaviors in a topological insulator is the quantized anomalous Hall insulator, which has been observed in magnetic-topological-insulator-based devices. In this work, we report a successful doping of rare earth element Tb into ${\mathrm{Bi}}_{1.08}{\mathrm{Sb}}_{0.9}{\mathrm{Te}}_{2}\mathrm{S}$ topological insulator single crystals, in which the Tb moments are antiferromagnetically ordered below $\ensuremath{\sim}10$ K. Benefiting from the in-bulk-gap Fermi level, transport behavior dominant by the topological surface states is observed below $\ensuremath{\sim}150$ K. At low temperatures, strong Shubnikov--de Haas oscillations are observed, which exhibit 2D-like behavior. The topological insulator with long range magnetic ordering in rare earth doped ${\mathrm{Bi}}_{1.08}{\mathrm{Sb}}_{0.9}{\mathrm{Te}}_{2}\mathrm{S}$ single crystal provides an ideal platform for quantum transport studies and potential applications.

Vacancy‐Defect Topological Insulators Bi2Te3−x Embedded in N and B Co‐Doped 1D Carbon Nanorods Using Ionic Liquid Dopants for Kinetics‐Enhanced Li–S Batteries

AbstractLithium–sulfur (Li–S) batteries are hindered by the shuttle effect and the sluggish redox kinetics of polysulfides. In this study, topological insulators (TIs) Bi2Te3−x with abundant Te vacancies embedded in N and B co‐doped carbon nanorods (Bi2Te3−x@NBCNs) are synthesized and used as sulfur host composites for high‐performance Li–S batteries. Bi2Te3−x@NBCNs effectively enhance the intrinsic conductivity, strengthened the chemical affinity, and accelerated the redox kinetics of polysulfides. 1D carbon nanorods with N and B co‐doped heteroatoms endowed with abundant polar sites improve the chemical affinity of polysulfides, while the embedded Bi2Te3−x nanoparticles further promote the nucleation and electrodeposition of Li2S2/Li2S. In situ Raman spectroscopy confirms that Bi2Te3−x@NBCNs effectively reduced cathode‐side accumulation of polysulfides and suppressed the shuttle effect. Owing to the extraordinary synergistic effects of rich heteroatom polar sites and conductive topological surface states, Bi2Te3−x@NBCN‐based cells exhibit a high initial specific capacity of 1264 mAh g−1 at 0.2 C and ultra‐long lifetime (>1000 cycles, with a degradation rate of 0.02% per cycle at 1.0 C). The fundamental insights offered by this work are likely to enable improvement of the electrochemical performance of Li–S batteries based on TI materials.