Topological Surface States Research Articles

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.

On the topological surface states of the intrinsic magnetic topological insulator Mn-Bi-Te family.

We review recent progress in the electronic structure study of intrinsic magnetic topological insulators (MnBi2Te4) · (Bi2Te3)n ([Formula: see text]) family. Specifically, we focus on the ubiquitously (nearly) gapless behavior of the topological Dirac surface state observed by photoemission spectroscopy, even though a large Dirac gap is expected because of surface ferromagnetic order. The dichotomy between experiment and theory concerning this gap behavior is perhaps the most critical and puzzling question in this frontier. We discuss various proposals accounting for the lack of magnetic effect on the topological Dirac surface state, which are mainly categorized into two pictures, magnetic reconfiguration and topological surface state redistribution. Band engineering towards opening a magnetic gap of topological surface states provides great opportunities to realize quantized topological transport and axion electrodynamics at higher temperatures.

THz Generation from the Topological Nodal Line Semimetal Co2MnGa

Nonlinear optical spectroscopy is a fundamental probe for the investigation of topological effects in quantum materials. In this paper, we report on the terahertz (THz) emission from thin films at various thicknesses of the magnetic topological nodal semimetal Co2MnGa (CMG) when excited by femtosecond optical pulses. Experimental results suggest the presence of multiple THz generation mechanisms, originating from both bulk and surface states of CMG. The former is explained in terms of a photon-drag effect as induced by radiation pressure. The latter emission mechanism instead appears to be related to the photovoltaic effect coming from the topological surface states. This interplay between generation mechanisms indicates that Co2MnGa topological nodal semimetals are a valuable platform for THz emitter devices.

Topological states and competing magnetic fluctuations in iron germanides

The correlated multiorbital multiband electronic structures of iron-based superconductors harbor an abundance of exotic electronic states, such as spin density waves, superconductivity, topological surface states, and Majorana zero modes. In this paper, we carry out density functional theory combined with dynamical mean-field theory calculations of the electronic structures, spin dynamics, and topological properties in $\mathrm{Y}{\mathrm{Fe}}_{2}{\mathrm{Ge}}_{2}$ and MgFeGe and compare them with $\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ and LiFeAs. We find a coexistence of ferromagnetic and antiferromagnetic spin fluctuations in $\mathrm{Y}{\mathrm{Fe}}_{2}{\mathrm{Ge}}_{2}$ and MgFeGe, which are attributed to the weakly dispersive bands just below the Fermi level. Moreover, we demonstrate that MgFeGe is in a strong topological phase and has two sets of Dirac-cone-like topological surface states on the (001) surface. The coexistence of superconductivity and nontrivial band topology in these two compounds demonstrates that it is interesting to explore topological superconductivity and Majorana zero modes in iron germanides.

Crystallinity Control of the Topological-Insulator Surface Bi85Sb15(012) via Interfacial Engineering for Enhanced Spin-Orbit Torque

Topological insulators demonstrate high charge-spin conversion efficiency due to their spin-momentum locking at the Dirac surface states. However, the surface states are sensitive to disruption caused by exchange coupling when interfaced with a ferromagnet. Here, we demonstrate the use of various nonmagnetic insertion layer materials, $\mathrm{Ti},\phantom{\rule{0.2em}{0ex}}\mathrm{Cu},$ and $\mathrm{Pt}$, at the $\mathrm{Co}/\mathrm{Bi}$-$\mathrm{Sb}(012)$ interface to preserve the topological surface state and promote spin-orbit-torque efficiency through the crystallinity control of $\mathrm{Bi}$-$\mathrm{Sb}(012)$. For 20-nm-thick $\mathrm{Bi}$-$\mathrm{Sb}$, a spin Hall angle of up to 8.93 is observed with the use of a $\mathrm{Pt}$ insertion layer, while it is otherwise negligible for $\mathrm{Co}/\mathrm{Bi}$-$\mathrm{Sb}(012)$ interfaces. We further explore the enhancement of $\mathrm{Bi}$-$\mathrm{Sb}(012)$ crystallinity with increasing $\mathrm{Bi}$-$\mathrm{Sb}$ thickness, revealing a rapidly increasing spin-orbit-torque efficiency that gradually saturates above 30 nm. A clear correlation between spin-orbit-torque efficiency and $\mathrm{Bi}$-$\mathrm{Sb}(012)$ crystalline size is identified using x-ray diffractometry, establishing the origin of the high spin-orbit efficiency to be the $\mathrm{Bi}$-$\mathrm{Sb}(012)$ crystalline orientation. Our work demonstrates the spin-orbit-torque origin in $\mathrm{Bi}$-$\mathrm{Sb}$ experimentally and paves the way for the adaptation of topological insulators as a class of low-energy spin source material for spintronics applications.

Topological Nodal Surface and Quadratic Dirac Semimetal States and van Hove Singularities in ScH3 and LuH3 Superconductors.

The coexistence of non-trivial topology and superconductivity in a material may induce a novel physical phenomenon known as topological superconductivity. Topological superconductors have been the subject of intense research, yet there are severe limitations in their application due to a lack of suitable materials. Topological nodal surface semimetals with nearly flat nodal surfaces near the Fermi level can be promising materials to achieve topological superconductivity. Here, we use first-principles calculations to examine the topological electronic characteristics of two new superconductors, ScH3 and LuH3, at both ambient and high pressures. Our studies show that both ScH3 and LuH3 have van Hove singularities, which confirms their superconductivity. Interestingly, both materials host topological nodal surface states under the protection of time reversal and spatial inversion symmetries in the absence of spin-orbit coupling (SOC). These nodal surfaces are distinguished by a pair of unique drum-head-like surface states not previously observed in nodal surface semimetals. Moreover, the nodal surfaces transform into essential spin-orbit quadratic Dirac points when SOC is included. Our findings demonstrate that ScH3 and LuH3 are good candidates to investigate the exotic properties of both nodal surface semimetals (NSSMs) and quadratic Dirac semimetal states and also provide a platform to explore the coexistence of topology and superconductivity in NSSMs with promising applications in high-speed electronics and topological quantum computing.