Prototypical Topological Insulator Research Articles

Time-resolved ARPES with probe energy of 6.0 eV and tunable MIR pump at 250 kHz

In this paper, we present a laser source designed specifically for time- and angle-resolved photoemission spectroscopy (TR-ARPES) investigations of light-induced electron dynamics in quantum materials. Our laser source is based on a ytterbium-doped laser that seeds an optical parametric amplifier (OPA) followed by a difference frequency generation (DFG) stage. This configuration enables the generation of tunable near-infrared and mid-infrared laser pulses (1.5 to 8 μm - 0.82 to 0.15 eV) at 250 kHz of repetition rate, serving as the pump for TR-ARPES measurements. The remaining energy of the laser is used to generate the ultraviolet 6 eV probe pulses, which prompt the material to emit photoelectrons. We demonstrate the long-term stability of the source, as well as the characterization of the beam profiles and pulse durations. Additionally, we present preliminary TR-ARPES results obtained on Bi2Te3, a prototypical 3D topological insulator. This paper illustrates the capability of our laser source to probe electronic dynamics in quantum materials.

Electron-phonon interactions at the topological edge states in single bilayer Bi(111).

An intriguing feature of two-dimensional topological insulators is the topologically protected electronic edge state, which allows one-way carrier transport without backscattering. Although this feature has strong potential applications in lossless electronics, the ideal behavior of the edge states may be fragile due to electron-phonon (e-ph) interactions at room temperatures. Using density functional perturbation theory calculations for single bilayer Bi(111) as a prototypical 2D topological insulator, we show that e-ph scattering can be a significant source of backscattering at the topological edge states. We also show that e-ph interactions strongly correlate to the dispersions of the electronic edge states. In particular, the e-ph interactions increase significantly with temperature and are much stronger at the nonlinearly dispersed edge states of native edges compared to the linearly dispersed edge states of passivated edges, causing a significant energy dissipation in the temperature range of 200-400 K. Overall, we argue that the e-ph interactions can be a crucial factor at finite temperatures in controlling the electronic transport at the topologically protected edge states.

Exchange-Driven Intermixing of Bulk and Topological Surface States by Chiral Excitons in Bi2Se3

Topological surface states (TSS) in the prototypical topological insulator (TI) Bi_{2}Se_{3} are frequently characterized using optical probes, but electron-hole interactions and their effect on surface localization and optical response of the TSS remain unexplored. Here, we use ab initio calculations to understand excitonic effects in the bulk and surface of Bi_{2}Se_{3}. We identify multiple series of chiral excitons that exhibit both bulk and TSS character, due to exchange-driven mixing. Our results address fundamental questions about the degree to which electron-hole interactions can relax the topological protection of surface states and dipole selection rules for circularly polarized light in TIs by elucidating the complex intermixture of bulk and surface states excited in optical measurements and their coupling to light.

Development of a laser-based angle-resolved-photoemission spectrometer with sub-micrometer spatial resolution and high-efficiency spin detection.

Angle-resolved photoemission spectroscopy with sub-micrometer spatial resolution (μ-ARPES), has become a powerful tool for studying quantum materials. To achieve sub-micrometer or even nanometer-scale spatial resolution, it is important to focus the incident light beam (usually from synchrotron radiation) using x-ray optics, such as the zone plate or ellipsoidal capillary mirrors. Recently, we developed a laser-based μ-ARPES with spin-resolution (LMS-ARPES). The 177nm laser beam is achieved by frequency-doubling a 355nm beam using a KBBF crystal and subsequently focused using an optical lens with a focal length of about 16mm. By characterizing the focused spot size using different methods and performing spatial-scanning photoemission measurement, we confirm the sub-micron spatial resolution of the system. Compared with the μ-ARPES facilities based on the synchrotron radiation, our LMS-ARPES system is not only more economical and convenient, but also with higher photon flux (>5 × 1013 photons/s), thus enabling the high-resolution and high-statistics measurements. Moreover, the system is equipped with a two-dimensional spin detector based on exchange scattering at a surface-passivated iron film grown on a W(100) substrate. We investigate the spin structure of the prototype topological insulator Bi2Se3 and reveal a high spin-polarization rate, confirming its spin-momentum locking property. This lab-based LMS-ARPES will be a powerful research tool for studying the local fine electronic structures of different condensed matter systems, including topological quantum materials, mesoscopic materials and structures, and phase-separated materials.

Topological Surface State of Bi2Se3 Modified by Physisorption of n‐Alkane

AbstractRecently, the interface between an organic molecular layer and a topological insulator (TI) surface (Org./TI interface) has been studied to explore the possibility of multifunctional TI devices with organic molecules. Nevertheless, understanding of the electronic structure of Org./TI interfaces is insufficient. Especially, little is known about physisorption systems, where the interaction between adsorbed molecules and topological surface state (TSS) is weak. Here, we discuss an ideal physisorption system of an n‐alkane molecule, n‐tetratertacontane (TTC), and prototypical TI, Bi2Se3, in which the interaction between the molecule and TSS is the weakest one possible. Angle‐resolved photoemission spectroscopy results show that the energy of the Dirac cone (DC) energy band decreases by approximately 60 meV when the TTC layer is formed on Bi2Se3. The amount of energy reduction is consistent with the reduction in vacuum level at the TTC/Bi2Se3 interface, valence states of Bi2Se3 and the core levels of Bi2Se3 observed by ultraviolet‐ and X‐ray photoemission spectroscopy. Therefore, no chemical interactions, such as charge transfer, occur at the TTC/Bi2Se3 interface, but only a redistribution of charge density on the Bi2Se3 surface occurs due to the Pauli repulsion between the electrons of the adsorbed TTC molecule and TSS.

Ultrafast probes of photovoltage and two-dimensional electron gas in the topological insulator Bi2Te3 by angle-resolved photoemission and terahertz spectroscopy

Photoexcited carriers in three-dimensional topological insulators (3D TIs) decay rapidly through the electron-electron and electron-phonon scattering. While most studies focus on such fast dynamics, recent experiments find the slow photovoltage (PV) dynamics arising from the band-bending potentials, in which the optical transitions in two-dimensional electron gas (2DEG) are effective. Although early investigations speculated the existence of multiple band-bending structures from the TI surface to the TI bulk, how PV and 2DEG are correlated in the presence of such multiple band bendings has been less explored. Here, we employ the combination of time- and angle-resolved photoemission spectroscopy (tr-ARPES) and ultrafast time-resolved terahertz (tr-THz) spectroscopy to investigate the PV and 2DEG dynamics in the prototypical topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$. Our tr-ARPES analysis identifies two spatially separated PV dynamics associated with two types of band bending: one is the well-known surface PV, and another PV is formed deep within the bulk, which we call ``internal bulk PV.'' For the surface PV, our tr-THz spectra substantiate that the $\ensuremath{\mu}\mathrm{s}$-long transient signal arises from the surface-PV-induced increase of the TSS and 2DEG carrier density, which appears as a transient blueshift of a Fermi cutoff and an increased ARPES intensity in the tr-ARPES measurements. In contrast, the effect of the internal bulk PV shows only marginal changes in the 2DEG and TSS carrier densities but shifts the entire binding energy of the near-surface bands.

Occupancy of lattice positions probed by X-ray photoelectron diffraction: A case study of tetradymite topological insulators

Occupancy of different structural positions in a crystal lattice often seems to play a key role in material properties. Several experimental techniques have been developed to uncover this issue, all of them being mostly bulk sensitive. However, many materials including topological insulators (TIs), which are among the most intriguing modern materials, are intended to be used in devices as thin films, for which the sublattice occupancy may differ from the bulk. One of the possible approaches to occupancy analysis is X-ray Photoelectron Diffraction (XPD), a structural method in surface science with chemical sensitivity. We applied this method in a case study of Sb2(Te1-xSex)3 mixed crystals, which belong to prototypical TIs. We used high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) as a reference method to verify our analysis. We revealed that the XPD data for vacuum cleaved bulk crystals are in excellent agreement with the reference ones. Also, we demonstrate that the anion occupancy near a naturally formed surface can be rather different from that of the bulk. The present results are relevant for a wide range of compositions where the system remains a topological phase, as we ultimately show by probing the transiently occupied topological surface state above the Fermi level by ultrafast photoemission.

Spinor GW /Bethe-Salpeter calculations in BerkeleyGW: Implementation, symmetries, benchmarking, and performance

Computing the $GW$ quasiparticle bandstructure and Bethe-Salpeter Equation (BSE) absorption spectra for materials with spin-orbit coupling has commonly been done by treating $GW$ corrections and spin-orbit coupling as separate perturbations to density-functional theory. However, accurate treatment of materials with strong spin-orbit coupling often requires a fully relativistic approach using spinor wavefunctions in the Kohn-Sham equation and $GW$/BSE. Such calculations have only recently become available, in particular for the BSE. We have implemented this approach in the plane-wave pseudopotential $GW$/BSE code BerkeleyGW, which is highly parallelized and widely used in the electronic-structure community. We present reference results for quasiparticle bandstructures and optical absorption spectra of solids with different strengths of spin-orbit coupling, including Si, Ge, GaAs, GaSb, CdSe, Au, and Bi$_2$Se$_3$. The calculated quasiparticle band gaps of these systems are found to agree with experiment to within a few tens of meV. The absorption spectrum of GaSb calculated with the fully-relativistic $GW$-BSE captures the large spin-orbit splitting of peaks in the spectrum. For Bi$_2$Se$_3$, we find a drastic change in the low-energy bandstructure compared to that of DFT, with the fully-relativistic treatment of the $GW$ approximation correctly capturing the parabolic nature of the valence and conduction bands after including off-diagonal self-energy matrix elements. We present the detailed methodology, approach to spatial symmetries for spinors, comparison against other codes, and performance compared to spinless $GW$/BSE calculations and perturbative approaches to SOC. This work aims to spur further development of spinor $GW$/BSE methodology in excited-state research software.

Thermal topological phase transition in SnTe from ab initio calculations

One of the key issues in the physics of topological insulators is whether the topologically non-trivial properties survive at finite temperatures and, if so, whether they disappear only at the temperature of topological gap closing. Here, we study this problem, using quantum fidelity as a measure, by means of \emph{ab-initio} methods supplemented by an effective dissipative theory built on the top of the \emph{ab-initio} electron and phonon band structures. In the case of SnTe, the prototypical crystal topological insulator, we reveal the presence of a characteristic temperature, much lower than the gap-closing one, that marks a loss of coherence of the topological state. The transition is not present in a purely electronic system but it appears once we invoke coupling with a dissipative bosonic bath. Features in the dependence with temperature of the fidelity susceptibility can be related to changes in the band curvature, but signatures of a topological phase transition appear in the fidelity only though the non-adiabatic coupling with soft phonons. Our argument is valid for valley topological insulators, but in principle can be generalized to the broader class of topological insulators which host any symmetry-breaking boson.

Band structure and polarization effects in photothermoelectric spectroscopy of a Bi2Se3 device

Bi2Se3 is a prototypical topological insulator, which has a small bandgap (∼0.3 eV) and topologically protected conducting surface states. This material exhibits quite strong thermoelectric effects. Here, we show in a mechanically exfoliated thick (∼100 nm) nanoflake device that we can measure the energy dependent optical absorption through the photothermoelectric effect. Spectral signatures are seen for a number of optical transitions between the valence and conduction bands, including a broad peak at 1.5 eV, which is likely dominated by bulk band-to-band optical transitions but is at the same energy as the well-known optical transition between the two topologically protected conducting surface states. We also observe a surprising linear polarization dependence in the response of the device that reflects the influence of the metal contacts.

Excited electron and spin dynamics in topological insulator: A perspective from ab initio non-adiabatic molecular dynamics

We perform an ab initio non-adiabatic molecular dynamics simulation to investigate the non-equilibrium spin and electron dynamics in a prototypical topological insulator (TI) Bi2Se3. Different from the ground state, we reveal that backscattering can happen in an oscillating manner between time-reversal pair topological surface states (TSSs) in the non-equilibrium dynamics. Analysis shows the phonon excitation induces orbital composition change by electron-phonon interaction, which further stimulates spin canting through spin-orbit coupling. The spin canting of time-reversal pair TSSs leads to the non-zero non-adiabatic coupling between them and then issues in backscattering. Both the spin canting and backscattering result in ultrafast spin relaxation with a timescale around 100 fs. This study provides critical insights into the non-equilibrium electron and spin dynamics in TI at the ab initio level and paves a way for the design of ultrafast spintronic materials.

Real-space nanoimaging of THz polaritons in the topological insulator Bi2Se3

Plasmon polaritons in topological insulators attract attention from a fundamental perspective and for potential THz photonic applications. Although polaritons have been observed by THz far-field spectroscopy on topological insulator microstructures, real-space imaging of propagating THz polaritons has been elusive so far. Here, we show spectroscopic THz near-field images of thin Bi2Se3 layers (prototypical topological insulators) revealing polaritons with up to 12 times increased momenta as compared to photons of the same energy and decay times of about 0.48 ps, yet short propagation lengths. From the images we determine and analyze the polariton dispersion, showing that the polaritons can be explained by the coupling of THz radiation to various combinations of Dirac and massive carriers at the Bi2Se3 surfaces, massive bulk carriers and optical phonons. Our work provides critical insights into the nature of THz polaritons in topological insulators and establishes instrumentation and methodology for imaging of THz polaritons.

Designing Sb<sub>2</sub>Te<sub>3</sub> heterophase homostructure

<p indent="0mm">Antimony sesquitelluride (Sb₂Te₃) is the most important hosting material for the development of high-performance phase-change memory and brain-like computing technology. This material has two crystalline phases, namely, the metastable cubic rock-salt structure with 1/6 atomic sites taken by randomly distributed vacancies, and the stable rhombohedral phase with layered structures and vacant gaps in hexagonal stacking. The former is an Anderson insulator (AI) and serves as the key ingredient for memory applications, while the latter is a prototypical topological insulator (TI). In this work, we propose a new heterophase homostructure concept for Sb₂Te₃, which in principle could utilize both the topologically protected surface state of the rhombohedral phase and the Anderson localization features of the cubic phase in the bulk interior to achieve ultralow-loss electron transport. To sustain the topological surface state, the edges of the device should be kept in rhombohedral phase with the thickness larger than <sc>~4 nm.</sc> The bulk interior of the sample should be transformed into cubic phase with strong electron localization. According to our density functional theory (DFT) results, the layered atomic building blocks for the two phases are quite similar, though their stacking sequence and degree of structural disorder are different. Thanks to the similar structure and mass density of the two phases, lattice mismatch is not expected to be present at the interface of the heterophase homostructure, superior to heterostructures made of different materials. To lend support to this heterophase homostructure concept, we have prepared a <sc>~500 nm</sc> thick rhombohedral Sb₂Te₃ thin film on a silicon substrate via molecular beam epitaxy (MBE) and made an attempt to induce the phase transition in its bulk interior. A cross-sectional specimen for transmission electron microscopy (TEM) experiments was prepared by a dual beam focused ion beam (FIB) system. The TEM specimen along the electron beam direction was <sc>~80 nm.</sc> For standard TEM observation in short time, the damage brought by electron beam is very limited. However, when the electron beam was focused in an exposure area of <sc>~120 nm</sc> or below inside an electron microscope with a fixed accelerating voltage of <sc>200 keV,</sc> visible structural changes in the Sb₂Te₃ specimen were observed. A gradual structural transition from the stable rhombohedral phase to the metastable cubic phase was observed under extensive electron beam irradiation over <sc>90 min.</sc> The<italic> in situ </italic>high-resolution TEM experiments revealed a clear vacancy disordering induced metastabilization process in the Sb₂Te₃ specimen, where Sb atoms from the atomic stacks diffused into the vacant gap layers in Sb₂Te₃ and eventually triggered a structural change from rhombohedral to cubic Sb₂Te₃. Our DFT calculations corroborated this picture, which showed a systematic increase in total energy as the vacant gap was gradually filled in rhombohedral Sb₂Te₃. The bonding environment of the Sb atoms in the gap for the two phases is entirely different. For the cubic phase, the Sb atoms in the gap are located as the center of octahedral structures with the bond angle of ~90°, which is consistent with the Sb atoms in the original rhombohedral and cubic phase. In stark contrast, the Sb atoms in the gap layers of rhombohedral phase are in a distorted bonding environment with bond angles of both ~110° and ~90°, leading to a large energy penalty for the rhombohedral phase. When the concentration of vacancies in the target layers reached 50%–70%, a change in stacking sequence from rhombohedral to cubic stacking was triggered. The critical vacancy concentration was mainly affected by the degree of compressive strain perpendicular to the target layers. In summary, we have discussed the design concept of a Sb₂Te₃ based heterophase homostructure and demonstrated that this structure could be free of lattice mismatch via <italic>in situ</italic> TEM experiments and DFT calculations. Finally, we provided some guidelines for practical synthesis of Sb₂Te₃ heterophase homostructure samples to explore the interaction between topological physics and Anderson localization of electrons, and to fabricate potential electronic devices of ultra-low power consumption.

All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser Fields.

We report the observation of an anomalous nonlinear optical response of the prototypical three-dimensional topological insulator bismuth selenide through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes maximum for circular polarization. With the aid of a microscopic theory and a detailed analysis of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topology of the band structure that originates from the interplay of strong spin-orbit coupling and time-reversal symmetry protection. The implications are in ultrafast probing of topological phase transitions, light-field driven dissipationless electronics, and quantum computation.

An STM Perspective on Hexaborides: Surface States of the Kondo Insulator SmB6

AbstractCompounds within the hexaboride class of materials exhibit a wide variety of interesting physical phenomena, including polaron formation and quadrupolar order. In particular, SmB6 has recently drawn attention as it is considered a prototypical topological Kondo insulator. Evidence in favor of this concept, however, has proven experimentally difficult and controversial, partly because of the required temperatures and energy resolution. Here, a powerful tool is scanning tunneling microscopy (STM) with its unique ability to give local, microscopic information that directly relates to the one‐particle Green's function. Yet, STM on hexaborides is met with its own set of challenges. This article attempts to review the progress in STM investigations on hexaborides, with emphasis on SmB6 and its intriguing properties.

Growth of topological insulator Bi2Se3 particles on GaAs via droplet epitaxy

The discovery of topological insulators (TIs) and their unique electronic properties has motivated research into a variety of applications, including quantum computing. It has been proposed that TI surface states will be energetically discretized in a quantum dot nanoparticle. These discretized states could then be used as basis states for a qubit that is more resistant to decoherence. In this work, prototypical TI Bi2Se3 nanoparticles are grown on GaAs (001) using the droplet epitaxy technique, and we demonstrate the control of nanoparticle height, area, and density by changing the duration of bismuth deposition and substrate temperature. Within the growth window studied, nanoparticles ranged from 5 to 15 nm in height with an 8–18 nm equivalent circular radius, and the density could be relatively well controlled by changing the substrate temperature and bismuth deposition time.

Dielectric relaxation in amorphous and crystalline Sb2Te3 thin films

Sb2Te3 is an endpoint of the GeTe-Sb2Te3 quasi-binary tie-line that represents phase-change alloys widely used in optical and non-volatile phase-change memory devices. In the crystalline form it is also a prototypical topological insulator with a layered structure where covalently bonded quintuple layers are held together by weak van der Waals forces. One of the ways to fabricate a crystalline phase is solid-state crystallization of an amorphous film, whereby the three-dimensional (3D) structure relaxes to the two-dimensional (2D) crystalline phase. The mechanism of the 3D-2D transformation remains unclear. In this work, we performed a study of relaxation processes in thin Sb2Te3 films in both amorphous and crystalline phases. We found that both phases possess two kinds of relaxators (type I and type II), where the type I fragments are identical in the two phases, while the relaxation of type II fragments are shifted to lower temperature in the amorphous phases. The activation energies of the associated relaxation processes and the values of the Havriliak–Negami parameters were determined. The differences between the relaxation processes in the two phases are discussed. The obtained result will contribute to better understanding of the 3D-2D transformation during the crystallization of van der Waals solids.

Engineering topological phases guided by statistical and machine learning methods

The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method, supported by machine learning techniques, that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram. By sampling tight-binding parameter vectors from a random distribution, we obtain data sets that we label with the corresponding topological index. This labeled data is then analyzed to extract those parameters most relevant for the topological classification and to find their most likely values. We find that the marginal distributions of the parameters already define a topological model. Additional information is hidden in correlations between parameters. Here we present as a proof of concept the prediction of the Haldane model as the prototypical topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class A. The algorithm is straightforwardly applicable to any other AZ class or lattice, and could be generalized to interacting systems.4 MoreReceived 16 September 2020Accepted 12 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013132Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsChern insulatorsTopological insulatorsTechniquesMachine learningMonte Carlo methodsTight-binding modelCondensed Matter, Materials & Applied Physics

The AiiDA-KKR plugin and its application to high-throughput impurity embedding into a topological insulator

The ever increasing availability of supercomputing resources led computer-based materials science into a new era of high-throughput calculations. Recently, Pizzi et al. introduced the AiiDA framework that provides a way to automate calculations while allowing to store the full provenance of complex workflows in a database. We present the development of the AiiDA-KKR plugin that allows to perform a large number of ab initio impurity embedding calculations based on the relativistic full-potential Korringa-Kohn-Rostoker Green function method. The capabilities of the AiiDA-KKR plugin are demonstrated with the calculation of several thousand impurities embedded into the prototypical topological insulator Sb2Te3. The results are collected in the JuDiT database which we use to investigate chemical trends as well as Fermi level and layer dependence of physical properties of impurities. This includes the study of spin moments, the impurity’s tendency to form in-gap states or its effect on the charge doping of the host-crystal. These properties depend on the detailed electronic structure of the impurity embedded into the host crystal which highlights the need for ab initio calculations in order to get accurate predictions.

Crystalline Sb2Te3: Side Surfaces and Disappearance of Dirac Cones

Sb2Te3 is an end point of quasibinary GeTe–Sb2Te3 phase‐change alloys and also a prototypical topological insulator (TI). TIs are materials that behave like insulators in their interior but whose surfaces are characterized by metallic states with linear dispersion, the so‐called Dirac cones. Such surface states are symmetry protected, robust, and are maintained even in the presence of surface defects. It has been tacitly implied that any surfaces of a TI possess this property. Herein, using ab initio simulations, it is demonstrated that cleaving Sb2Te3 along certain side surfaces may lead to the disappearance of Dirac surface states. In particular, it is shown that the (110) surface of the typical TI Sb2Te3 is slightly gapped, whereas the () surface is metallic. The significance and potential benefits of the obtained results for practical applications in planar devices and memory cells are discussed.