Topological Insulator State Research Articles

High photodetection performance on vertically oriented topological insulator Sb2Te3/Silicon heterostructure

The coexistence of bulk electronic band gap and gapless surface states of topological insulators (TIs) opens up many new opportunities in optoelectronic devices. Here we demonstrate the synthesis and photodetection response of vertical Sb2Te3 nanoplate film grown on n-type Si substrates. The small bulk bandgap of Sb2Te3 and surface states conduction lead to effective light absorption and photocarrier transport. The device exhibits a significant photoresponse over a broad spectral range between 350 and 1400 ​nm. The switching speed and on/off ratio Iph/Id are estimated to be 3 ​ms and 5900, respectively, which are much better than those of other TI-based photodetectors. Given the simple device preparation and compatibility with silicon technology, the unconventional structure Sb2Te3/Si heterostructure holds great promise for high-performance optoelectronic applications.

Formation of bound states from the edge states of 2D topological insulator by macroscopic magnetic barriers

A model of bound state formation from the delocalized edge states of 2D topological insulator (TI) is derived by considering the effects of magnetic barriers attached to the edge of the HgTe/CdTe quantum well. The resulting structure has a spatial form of 1D quantum dot (QD) with variable number of bound states depending on barrier parameters. The spatial profile of exchange interaction between the edge states and barriers is derived from the interaction with single impurity magnetic moment and is generalized for the barrier bulk structure formed by ensemble of impurities. The resulting Hamiltonian is studied as a function of barrier parameters including their strength and orientation of the magnetic moments. It is shown that for parallel magnetization of two barriers at least two discrete levels are formed regardless of the barrier strength. For antiparallel magnetization at least a single bound state is formed for any strength of the barriers. Our results may help in design of novel types of QDs based on TIs.

Sub- to super-Poissonian crossover of current noise in helical edge states coupled to a spin impurity in a magnetic field

Edge states of two-dimensional topological insulators are helical and single-particle backscattering is prohibited by time-reversal symmetry. In this paper, we show that an isotropic exchange coupling of helical edge states (HES) to a spin 1/2 impurity subjected to a magnetic field results in characteristic backscattering current noise (BCN) as a function of bias voltage and tilt angle between the direction of the magnetic field and the quantization axis of the HES. In particular, we find transitions from sub-Poissonian (antibunching) to super-Poissonian (bunching) behavior as a direct consequence of the helicity of the edge state electrons. We use the method of full counting statistics within a master equation approach treating the exchange coupling between the spin-1/2 impurity and the HES perturbatively. We express the BCN via coincidence correlation functions of scattering processes between the HES, which gives a precise interpretation of the Fano factor in terms of bunching and antibunching behavior of electron jump events. We also investigate the effect of electron-electron interactions in the HES in terms of the Tomonaga-Luttinger liquid theory.

Chiral hinge transport in disordered non-Hermitian second-order topological insulators

The generalized bulk-boundary correspondence predicts the existence of the chiral hinge states in three-dimensional second-order topological insulators (3DSOTIs), resulting in a quantized Hall effect in three dimensions. Chiral hinge states in Hermitian 3DSOTIs are characterized by the quantized transmission coefficients with zero fluctuations, even in the presence of disorders. Here, we show that chiral hinge transport in disordered non-Hermitian systems deviates from the paradigm of the Hermitian case. Our numerical calculations prove the robustness of hinge states of disordered non-Hermitian 3DSOTIs. The mean transmission coefficients may or may not equal the number of chiral hinge channels, depending on the Hermiticity of the chiral hinge states, while the fluctuations of transmission coefficients are always nonzero. Such fluctuations are not due to the broken chirality of hinge states but the incoherent scatterings of non-Hermitian potentials. The physics revealed here should also be true for one-dimensional chiral channels in topological materials that support chiral boundary states, such as Chern insulators, three-dimensional anomalous Hall insulators, and Weyl semimetals.

Topological states and topological phase transition in Cu2SnS3 and Cu2SnSe3

Based on the first-principles calculations and model analysis, we propose that the isostructural compounds ${\mathrm{Cu}}_{2}{\mathrm{SnS}}_{3}$ and ${\mathrm{Cu}}_{2}{\mathrm{SnSe}}_{3}$ are both the simplest nodal-line semimetals with only one nodal line in their crystal momentum space when spin-orbit coupling (SOC) is ignored. The inclusion of SOC drives ${\mathrm{Cu}}_{2}{\mathrm{SnS}}_{3}$ into a Weyl semimetal (WSM) state with only two pairs of Weyl nodes, the minimum number required for a WSM with time-reversal symmetry. In contrast, SOC leads ${\mathrm{Cu}}_{2}{\mathrm{SnSe}}_{3}$ to a strong topological insulator (STI) state. This difference can be well understood as there is a topological phase transition (TPT). In it, the Weyl nodes are driven by tunable SOC and annihilate in a mirror plane, resulting in a STI. This TPT, together with the evolution of Weyl nodes, the changing of mirror Chern numbers of the mirror plane, and the ${Z}_{2}$ indices protected by time-reversal symmetry, has been demonstrated by the calculation of ${\mathrm{Cu}}_{2}\mathrm{Sn}{({\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$ within virtual crystal approximation and an effective $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model analysis. Though our first-principles calculations have overestimated the topological states in both compounds, we believe that the theoretical demonstration of controlling the TPT and the evolution of Weyl nodes will stimulate further efforts to explore them.

Electrochemical biosensor based on topological insulator Bi2Se3 tape electrode for HIV-1 DNA detection.

A large-size Bi2Se3 tape electrode (BTE) was prepared by peeling off a 2 × 1 × 0.5cm high-quality single crystal. The feasibility of using the flexible BTE as an efficient bioplatform to load Au nanoparticles and probe DNA for HIV-1 DNA electrochemical sensing was explored. Differential pulse voltammetry (DPV) and electrochemical impedance spectroscopy (EIS) show that the resultant biosensor has a wide linear range from 0.1 fM to 1pM, a low detection limit of 50 aM, excellent selectivity, reproducibility and stability, and is superior to the pM DNA detection level of Pt-Au, graphene-AuNPs hybrid biosensors. This outstanding performance is attributed to the intrinsic surface state of Bi2Se3 topological insulator in facilitating electron transfer. Therefore, BTE electrochemical biosensor platform has great potential in the application for sensitive detection of DNA biomarkers.

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics1,2. The quantum spin Hall phase3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi4Br4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z2 topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

Magnetic moiré surface states and flat Chern bands in topological insulators

We propose the magnetic moir\'e surface states of topological insulators as a platform for time-reversal symmetry breaking flat Chern bands. We construct a generic continuum model of Dirac electrons with a single Dirac cone moving in a time-reversal symmetry breaking periodic potential containing minimal parameters. The Zeeman-type moir\'e potentials generically gap out the moir\'e surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\ifmmode\pm\else\textpm\fi{}1$. Interestingly, the bandwidth of such isolated flat minibands is insensitive to the twisting angle, which originates from the completely flat band of the $p$ orbitals on the honeycomb lattice. This result provides a promising platform for realizing time-reversal breaking correlated topological phases and circumvents two main experimental difficulties in correlated states with twisted graphene: that the bandwidth varies rapidly with angle as well as the moir\'e disorder. Furthermore, in a ${C}_{6}$ periodic potential, with the interplay of the scalar potential and the Zeeman moir\'e potential, the $\mathrm{\ensuremath{\Gamma}}$-valley moir\'e surface electrons simulate two-dimensional honeycomb lattice physics, leading to emergent moir\'e surface Dirac cones as well as the Haldane model.

Dual topological states in the layered titanium-based oxypnictide superconductor BaTi2Sb2O

Topological superconductors have long been predicted to host Majorana zero modes which obey non-Abelian statistics and have potential for realizing non-decoherence topological quantum computation. However, material realization of topological superconductors is still a challenge in condensed matter physics. Utilizing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations, we predict and then unveil the coexistence of topological Dirac semimetal and topological insulator states in the vicinity of Fermi energy (EF) in the titanium-based oxypnictide superconductor BaTi2Sb2O. Further spin-resolved measurements confirm its spin-helical surface states around EF, which are topologically protected and give an opportunity for realization of Majorana zero modes and Majorana flat bands in one material. Hosting dual topological states, the intrinsic superconductor BaTi2Sb2O is expected to be a promising platform for further investigation of topological superconductivity.

Topological states in a dimerized system with staggered magnetic fluxes

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional first-order and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At $\frac{1}{2}$-filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the $\mathcal{C}=2$ Chern insulator states. At $\frac{1}{4}$-filling, we find a $\mathcal{C}=0$ topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.

Robust topological one-way edge states in radius-fluctuated photonic Chern topological insulators.

Recent developments in topological photonics have shown that the introduction of disorders can yield the innovative and striking transport phenomena. Here, we theoretically investigate topological one-way edge states in radius-fluctuated photonic Chern topological insulators (PCTIs), which are composed of two-dimensional gyromagnetic photonic crystals with cylinder site fixed but with cylinder radius fluctuated. We use a fluctuation index to characterize the degree of radius fluctuation, employ two empirical parameters to inspect the evolution of topological one-way edge states, and verify the stability of topological one-way edge states by calculating massive samples with various random numbers. We find that as the radius-fluctuation strength increases, there arises a competition between topological one-way edge state, Anderson localization state and trivial bulk state. We reveal that the Anderson localization state appears far more easily in the radius-fluctuation PCTI with even a weak strength compared with the position-perturbed PCTI with a strong randomness. We also demonstrate that the topological one-way edge states are protected against a strong fluctuation much larger than the fabrication errors in practical experiments. Our results show that the PCTIs consisting of gyromagnetic photonic crystals have a high-tolerance for the material and sample fabrication errors, and this would provide a deeper understanding of fundamental topology physics.

Topological acoustic tweezer and pseudo-spin states of acoustic topological insulators

Topological protection wave engineering in artificially structured media is at the forefront of metamaterials research. Acoustic analogs of electronic topological insulators have brought a lot of new opportunities for manipulating sound propagation and have attracted the attention of many scholars. A variety of artificial acoustic systems hosting topological edge states have been proposed. However, the pseudo-spin edge states at a boundary have not been clearly and intuitively characterized. In this article, we provide experimental verification of pseudo-spin states by the method of acoustic particle manipulation by using the rotation of the particle to describe the pseudo-spin sound field characteristics at the boundary of the acoustic topological insulator in detail. It indicates the existence of pseudo-spin–orbit coupling effects and pseudo-spin-related acoustic unidirectional transmission even if the defect exists. Furthermore, the pseudo-spin sound field can be used to control the rotation of multiple particles and droplets. This kind of topological acoustic tweezer with defect immunity has great application potential in the fields of biomedicine and materials science.

Emergent optical plasmons at the surface of a doped three-dimensional topological insulator

The conduction electrons in the topologically nontrivial surface states of three-dimensional topological insulators have been actively exploited to exhibit emergent exotic properties and functionalities. The existence of a trivial two-dimensional electron gas near the surface has also been widely established, stemming from surface carrier doping of the topological insulators. Here we investigate theoretically the coupling between the electrons in the topological surface states and two-dimensional electron gas, and reveal that the helical nature of the former can be effectively shared with the latter through proximity effect. Next we examine the collective modes of the combined system and predict an optical plasmon mode rooted in the enhanced interband transitions of the nontrivial bands with the same helicity. The emergence of the interband transitions also introduce pronounced variations in the Dirac plasmon mode of the topological surface states, characterized by its gapped feature. These findings may find important applications in plasmonic and spintronic devices.

Coherent interaction of a quantum emitter and the edge states in two-dimensional optical topological insulators

The two-dimensional optical topological insulators have exhibited a series of novel optical behaviors, especially the topologically protected edge states. We theoretically locate an initial excited quantum emitter (QE) in the two-dimensional ring resonator array and analyze the evolution of the QE in three kinds structures, i.e., topologically nontrivial, trivial, and graphene structure. We found that the dynamic evolution in the nontrivial topological structure is much different from that in the trivial and the graphene structures. When the QE excites edge states in nontrivial structures, the excited edge states can detour along the boundary and re-interact coherently with the QE, resulting in the recovery of the QE population. However, this repeated energy exchange is incomplete, depending on the coupling $g$ between the QE and the resonator. More importantly, we check the influence of the QE's position and the coupling $g$ (between the QE and the resonator) on dynamic evolution of the whole system. For the nontrivial structure, the effective excitation of edge states by the QE requires that: (1) the QE is located in the resonator in boundary and (2) $g$ is much less than coupling coefficient $J$ (between neighbor resonators). When $g$ is much larger than $J$, the QE cannot excite edge states anymore. We give the critical value ${g}_{\mathrm{c}}$ and find that it relates to band gap and size. Our paper is conducive to an in-depth understanding of the interaction between light and matter in optical topological insulators and provides a useful reference for quantum communication and quantum computing mediated by topological photonics.

Anomalous flux periodicity in proximitised quantum spin Hall constrictions

We theoretically analyse a long constriction between the helical edge states of a two-dimensional topological insulator. The constriction is laterally tunnel-coupled to two superconductors and a magnetic field is applied perpendicularly to the plane of the two-dimensional topological insulator. The Josephson current is calculated analytically up to second order in the tunnel coupling both in the absence and in the presence of a bias (DC and AC Josephson currents). We show that in both cases the current acquires an anomalous 4π-periodicity with respect to the magnetic flux that is absent if the two edges are not tunnel-coupled to each other. The result, that provides at the same time a characterisation of the device and a possible experimental signature of the coupling between the edges, is stable against temperature. The processes responsible for the anomalous 4π-periodicity are the ones where, within the constriction, one of the two electrons forming a Cooper pair tunnels between the two edges.

Magnetically tunable Dirac and Weyl fermions in the Zintl materials family

Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solid-state systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here, we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ is a dual topological insulator with ${Z}_{2}=(1;000)$ and mirror Chern number ${C}_{M}=\ensuremath{-}1$. Its isostructural and isovalent antiferromagnetic cousin ${\mathrm{EuIn}}_{2}{\mathrm{As}}_{2}$ is found to be an axion insulator with ${Z}_{4}=2$. The broken time-reversal symmetry via Eu doping in ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{\mathrm{As}}_{2}$ results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic ${\mathrm{EuIn}}_{2}{\mathrm{P}}_{2}$ is a trivial insulator with ${Z}_{4}=0$, and that it undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state with ${Z}_{4}=1$ with applied magnetic field. Our study identifies ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{(\text{As},\mathrm{P})}_{2}$ as a tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states.

Topological transitions and Anderson localization of light in disordered atomic arrays

We explore the interplay of disorder and topological phenomena in honeycomb lattices of atoms coupled by the electromagnetic field. On the one hand, disorder can trigger transitions between distinct topological phases and drive the lattice into the topological Anderson insulator state. On the other hand, the nontrivial topology of the photonic band structure suppresses Anderson localization of modes that disorder introduces inside the band gap of the ideal lattice. Furthermore, we discover that disorder can both open a topological pseudogap in the spectrum of an otherwise topologically trivial system and introduce spatially localized modes inside it.

Ultrafast dynamics of Dirac surface and bulk photocarriers in topological-insulator bismuth telluride nanocrystals using terahertz spectroscopy

Unlike conventional semiconductors, Dirac fermions in surface states of topological insulators (TIs) exhibit many fascinating electronic properties relevant for several optoelectronic and spintronic applications. We investigate the relaxation dynamics of photoexcited carriers in bismuth telluride (${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$) nanocrystals---a prominent candidate among the three-dimensional (3D) topological insulators, using ultrafast time resolved terahertz (THz) spectroscopy. Upon photoexcitation using an 800 nm pump pulse, we observe a decrease in the THz transmission due to the absorption of THz radiation by the photoexcited carriers. The time evolution of the real part of pump induced conductivity [$\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})=\phantom{\rule{4pt}{0ex}}{\ensuremath{\sigma}}_{\text{pump}}{\phantom{\rule{4pt}{0ex}}}_{\text{on}}({\ensuremath{\tau}}_{\text{pp}})\ensuremath{-}{\ensuremath{\sigma}}_{\text{pump}}{\phantom{\rule{4pt}{0ex}}}_{\text{off}}$] with respect to the pump-probe delay time (${\ensuremath{\tau}}_{\text{pp}}$), exhibits a sign change from positive to negative as carriers relax back to their equilibrium distribution, which is also evident from the spectral signatures of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sigma}(\ensuremath{\omega})$, measured at various ${\ensuremath{\tau}}_{\text{pp}}$. While the positive sign of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$ is attributed to the contribution from the semiconducting bulk states, the negative sign of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$ at longer delay times is shown to arise from the Dirac surface states of TIs due to increased scattering rate of photoexcited charge carriers. We model the differential conductivity spectrum [$\mathrm{\ensuremath{\Delta}}\ensuremath{\sigma}(\ensuremath{\omega})$] and the transient dynamics [$\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$] quantitatively using the Boltzmann transport equation applied to the surface and bulk states. This includes the energy dependence of scattering rates along with the dynamics of hot electron temperature (${T}_{e}$) evaluated in a self-consistent manner. Such an approach enables us to understand various scattering mechanisms associated with the photoexcited carriers both in Dirac surface as well as in bulk electronic states.

Nonlinear optical absorption and photocurrents in topological insulators

Theory of optical absorption of linearly and circularly polarized light in surface and edge states in topological insulators is developed for a nonlinear in light intensity regime. The absorbance for surface states and the absorption width for the edge states both decease as $1/\sqrt{I}$ at high light intensity $I$. Elastic scattering of the photoexcited electrons and holes is taken into account. The absorption bleaching at high intensity is shown to be strongly suppressed by the elastic scattering. The linear-circular dichroism of one- and two-photon absorption in surface states, emerging in the nonlinear in intensity regime, decreases due to the elastic scattering of photocarriers. Absorption in the edge states of two-dimensional topological insulators also depends on the elastic scattering rate being suppressed when it is stronger that the energy relaxation rate. The linear dichroism - a dependence of the absorption length on the polarization plane orientation - is studied at arbitrary light intensities. We show that a degree of the linear dichroism is governed by the ratio of the elastic and inelastic relaxation times. The photocurrents generated in the edge states by both linearly and circularly polarized light change their intensity dependencies from the linear one at low $I$ to the $\propto \sqrt{I}$ at high intensities. The variation of the photocurrents with both polarization and intensity are strongly dependent on the elastic scattering rate. The considered effects can be observed in THz frequency range at laser intensities used in modern experiments.

Coexisting valley and pseudo-spin topological edge states in photonic topological insulators made of distorted Kekulé lattices

Photonic topological insulators protected by the lattice spatial symmetry (e.g., inversion and rotation symmetry) mainly support single type edge state, interpreted by either valley or pseudo-spin. Here, we demonstrate theoretically, numerically, and experimentally that a type of judiciously designed two-dimensional Kekulé photonic crystal with time reversal symmetry can possess topological valley and pseudo-spin edge states in different frequency bands. Topologically robust transportation of both the valley and pseudo-spin edge states was confirmed by measuring the transmission of straight and z-shaped interface supported edge mode and comparing with bulk modes in the microwave frequency regime. In addition, we show that due to the distinct topological origins, valley and pseudo-spin edge states can be distinguished by examining their end-scattering into the free space. Our system provides an alternative way in manipulating electromagnetic waves with additional degree-of-freedom, which has potential applications for robust and high-capacity waveguiding and multi-mode dividing.