STM imaging of electronic waves on the surface of Bi2Te3: topologically protected surface states and hexagonal warping effects

Phase Separation of Dirac Electrons in Topological Insulators at the Spatial Limit

In this work we present unique signatures manifested by the local electronic properties of the topological surface state in Bi₂Te₃ nanostructures as the spatial limit is approached. We concentrate on the pure nanoscale limit (nanoplatelets) with spatial electronic resolution down to 1 nm. The highlights include strong dependencies on nanoplatelet size: (1) observation of a phase separation of Dirac electrons whose length scale decreases as the spatial limit is approached, and (2) the evolution from heavily n-type to lightly n-type surface doping as nanoplatelet thickness increases. Our results show a new approach to tune the Dirac point together with reduction of electronic disorder in topological insulator (TI) nanostructured systems. We expect our work will provide a new route for application of these nanostructured Dirac systems in electronic devices.

Probing the Nodal Structure of Landau Level Wave Functions in Real Space

The inversion layer of p-InSb(110) obtained by Cs adsorption of 1.8% of a monolayer is used to probe the Landau level wave functions within smooth potential valleys by scanning tunneling spectroscopy at 14 T. The nodal structure becomes apparent as a double peak structure of each spin polarized first Landau level, while the zeroth Landau level exhibits a single peak per spin level only. The real space data show single rings of the valley-confined drift states for the zeroth Landau level and double rings for the first Landau level. The result is reproduced by a recursive Green function algorithm using the potential landscape obtained experimentally. We show that the result is generic by comparing the local density of states from the Green function algorithm with results from a well-controlled analytic model based on the guiding center approach.

Enhanced Mobility of Spin-Helical Dirac Fermions in Disordered 3D Topological Insulators

The transport length l_tr and the mean free path l_e are determined for bulk and surface states in a Bi₂Se₃ nanoribbon by quantum transport and transconductance measurements. We show that the anisotropic scattering of spin-helical Dirac fermions results in a strong enhancement of l_tr (≈ 200 nm) and of the related mobility μ_tr (≈ 4000 cm² V^-1 s^-1), which confirms theoretical predictions.1 Despite strong disorder, the long-range nature of the scattering potential gives a large ratio l_tr/l_e ≈ 8, likely limited by bulk/surface coupling. This suggests that the spin-flip length l_sf ≈ l_tr could reach the micron size in materials with a reduced bulk doping and paves the way for building functionalized spintronic and ballistic electronic devices out of disordered 3D topological insulators.

Quasiparticle Scattering in the Rashba Semiconductor BiTeBr: The Roles of Spin and Defect Lattice Site

Observations of quasiparticle interference have been used in recent years to examine exotic carrier behavior at the surfaces of emergent materials, connecting carrier dispersion and scattering dynamics to real-space features with atomic resolution. We observe quasiparticle interference in the strongly Rashba split 2DEG-like surface band found at the tellurium termination of BiTeBr and examine two mechanisms governing quasiparticle scattering: We confirm the suppression of spin-flip scattering by comparing measured quasiparticle interference with a spin-dependent elastic scattering model applied to the calculated spectral function. We also use atomically resolved STM maps to identify point defect lattice sites and spectro-microscopy imaging to discern their varying scattering strengths, which we understand in terms of the calculated orbital characteristics of the surface band. Defects on the Bi sublattice cause the strongest scattering of the predominantly Bi 6p derived surface band, with other defects causing nearly no scattering near the conduction band minimum.

Annealing-Induced Bi Bilayer on Bi2Te3 Investigated via Quasi-Particle-Interference Mapping

Topological insulators (TIs) are renowned for their exotic topological surface states (TSSs) that reside in the top atomic layers, and hence, detailed knowledge of the surface top atomic layers is of utmost importance. Here we present the remarkable morphology changes of Bi2Te3 surfaces, which have been freshly cleaved in air, upon subsequent systematic annealing in ultrahigh vacuum and the resulting effects on the local and area-averaging electronic properties of the surface states, which are investigated by combining scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and Auger electron spectroscopy (AES) experiments with density functional theory (DFT) calculations. Our findings demonstrate that the annealing induces the formation of a Bi bilayer atop the Bi2Te3 surface. The adlayer results in n-type doping, and the atomic defects act as scattering centers of the TSS electrons. We also investigated the annealing-induced Bi bilayer surface on Bi2Te3 via voltage-dependent quasi-particle-interference (QPI) mapping of the surface local density of states and via comparison with the calculated constant-energy contours and QPI patterns. We observed closed hexagonal patterns in the Fourier transform of real-space QPI maps with secondary outer spikes. DFT calculations attribute these complex QPI patterns to the appearance of a "second" cone due to the surface charge transfer between the Bi bilayer and the Bi2Te3. Annealing in ultrahigh vacuum offers a facile route for tuning of the topological properties and may yield similar results for other topological materials.

Tailoring Kinetics on a Topological Insulator Surface by Defect-Induced Strain: Pb Mobility on Bi2Te3

Heteroepitaxial structures based on Bi2Te3-type topological insulators (TIs) exhibit exotic quantum phenomena. For optimal characterization of these phenomena, it is desirable to control the interface structure during film growth on such TIs. In this process, adatom mobility is a key factor. We demonstrate that Pb mobility on the Bi2Te3(111) surface can be modified by the engineering local strain, ε, which is induced around the point-like defects intrinsically forming in the Bi2Te3(111) thin film grown on a Si(111)-7 × 7 substrate. Scanning tunneling microscopy observations of Pb adatom and cluster distributions and first-principles density functional theory (DFT) analyses of the adsorption energy and diffusion barrier Ed of Pb adatom on Bi2Te3(111) surface show a significant influence of ε. Surprisingly, Ed reveals a cusp-like dependence on ε due to a bifurcation in the position of the stable adsorption site at the critical tensile strain εc ≈ 0.8%. This constitutes a very different strain-dependence of diffusivity from all previous studies focusing on conventional metal or semiconductor surfaces. Kinetic Monte Carlo simulations of Pb deposition, diffusion, and irreversible aggregation incorporating the DFT results reveal adatom and cluster distributions compatible with our experimental observations.

2D layered transport properties from topological insulator Bi2Se3 single crystals and micro flakes

Low-field magnetotransport measurements of topological insulators such as Bi2Se3 are important for revealing the nature of topological surface states by quantum corrections to the conductivity, such as weak-antilocalization. Recently, a rich variety of high-field magnetotransport properties in the regime of high electron densities (∼10(19) cm(-3)) were reported, which can be related to additional two-dimensional layered conductivity, hampering the identification of the topological surface states. Here, we report that quantum corrections to the electronic conduction are dominated by the surface states for a semiconducting case, which can be analyzed by the Hikami-Larkin-Nagaoka model for two coupled surfaces in the case of strong spin-orbit interaction. However, in the metallic-like case this analysis fails and additional two-dimensional contributions need to be accounted for. Shubnikov-de Haas oscillations and quantized Hall resistance prove as strong indications for the two-dimensional layered metallic behavior. Temperature-dependent magnetotransport properties of high-quality Bi2Se3 single crystalline exfoliated macro and micro flakes are combined with high resolution transmission electron microscopy and energy-dispersive x-ray spectroscopy, confirming the structure and stoichiometry. Angle-resolved photoemission spectroscopy proves a single-Dirac-cone surface state and a well-defined bulk band gap in topological insulating state. Spatially resolved core-level photoelectron microscopy demonstrates the surface stability.

Nanoscale electron transport at the surface of a topological insulator

The use of three-dimensional topological insulators for disruptive technologies critically depends on the dissipationless transport of electrons at the surface, because of the suppression of backscattering at defects. However, in real devices, defects are unavoidable and scattering at angles other than 180° is allowed for such materials. Until now, this has been studied indirectly by bulk measurements and by the analysis of the local density of states in close vicinity to defect sites. Here, we directly measure the nanoscale voltage drop caused by the scattering at step edges, which occurs if a lateral current flows along a three-dimensional topological insulator. The experiments were performed using scanning tunnelling potentiometry for thin Bi₂Se₃ films. So far, the observed voltage drops are small because of large contributions of the bulk to the electronic transport. However, for the use of ideal topological insulating thin films in devices, these contributions would play a significant role.

Topological insulators offer lossless surface transport because of the suppression of conduction-electron backscattering from defect sites. Here, the authors show that the nanoscale voltage drops caused by such scattering can be directly measured using scanning tunnelling potentiometry.

Kondo-like zero-bias conductance anomaly in a three-dimensional topological insulator nanowire

Zero-bias anomalies in topological nanowires have recently captured significant attention, as they are possible signatures of Majorana modes. Yet there are many other possible origins of zero-bias peaks in nanowires--for example, weak localization, Andreev bound states, or the Kondo effect. Here, we discuss observations of differential-conductance peaks at zero-bias voltage in non-superconducting electronic transport through a 3D topological insulator (Bi(1.33)Sb(0.67))Se3 nanowire. The zero-bias conductance peaks show logarithmic temperature dependence and often linear splitting with magnetic fields, both of which are signatures of the Kondo effect in quantum dots. We characterize the zero-bias peaks and discuss their origin.

Dirac fermions at high-index surfaces of bismuth chalcogenide topological insulator nanostructures

Binary bismuth chalcogenides Bi₂Se₃, Bi₂Te₃, and related materials are currently being extensively investigated as the reference topological insulators (TIs) due to their simple surface-state band dispersion (single Dirac cone) and relatively large bulk band gaps. Nanostructures of TIs are of particular interest as an increased surface-to-volume ratio enhances the contribution of surfaces states, meaning they are promising candidates for potential device applications. So far, the vast majority of research efforts have focused on the low-energy (0001) surfaces, which correspond to natural cleavage planes in these layered materials. However, the surfaces of low-dimensional nanostructures (nanoplatelets, nanowires, nanoribbons) inevitably involve higher-index facets. We perform a systematic ab initio investigation of the surfaces of bismuth chalcogenide TI nanostructures characterized by different crystallographic orientations, atomic structures and stoichiometric compositions. We find several stable terminations of high-index surfaces, which can be realized at different values of the chemical potential of one of the constituent elements. For the uniquely defined stoichiometric termination, the topological Dirac fermion states are shown to be strongly anisotropic with a clear dependence of Fermi velocities and spin polarization on the surface orientation. Self-doping effects and the presence of topologically trivial mid-gap states are found to characterize the non-stoichiometric surfaces. The results of our study pave the way towards experimental control of topologically protected surface states in bismuth chalcogenide nanostructures.

Spatial potential ripples of azimuthal surface modes in topological insulator Bi2Te3 nanowires

Topological insulators (TI) nanowires (NW) are an emerging class of structures, promising both novel quantum effects and potential applications in low-power electronics, thermoelectrics and spintronics. However, investigating the electronic states of TI NWs is complicated, due to their small lateral size, especially at room temperature. Here, we perform scanning probe based nanoscale imaging to resolve the local surface potential landscapes of Bi₂Te₃ nanowires (NWs) at 300 K. We found equipotential rings around the NWs perimeter that we attribute to azimuthal 1D modes. Along the NW axis, these modes are altered, forming potential ripples in the local density of states, due to intrinsic disturbances. Potential mapping of electrically biased NWs enabled us to accurately determine their conductivity which was found to increase with the decrease of NW diameter, consistent with surface dominated transport. Our results demonstrate that TI NWs can pave the way to both exotic quantum states and novel electronic devices.

Surface Collective Modes in the Topological Insulators Bi_{2}Se_{3} and Bi_{0.5}Sb_{1.5}Te_{3-x}Se_{x}

We used low-energy, momentum-resolved inelastic electron scattering to study surface collective modes of the three-dimensional topological insulators Bi_{2}Se_{3} and Bi_{0.5}Sb_{1.5}Te_{3-x}Se_{x}. Our goal was to identify the "spin plasmon" predicted by Raghu and co-workers [Phys. Rev. Lett. 104, 116401 (2010)]. Instead, we found that the primary collective mode is a surface plasmon arising from the bulk, free carriers in these materials. This excitation dominates the spectral weight in the bosonic function of the surface χ^{"}(q,ω) at THz energy scales, and is the most likely origin of a quasiparticle dispersion kink observed in previous photoemission experiments. Our study suggests that the spin plasmon may mix with this other surface mode, calling for a more nuanced understanding of optical experiments in which the spin plasmon is reported to play a role.

Spin-orbit coupling at surfaces and 2D materials

Spin-orbit interaction gives rise to a splitting of surface states via the Rashba effect, and in topological insulators it leads to the existence of topological surface states. The resulting k(//) momentum separation between states with the opposite spin underlies a wide range of new phenomena at surfaces and interfaces, such as spin transfer, spin accumulation, spin-to-charge current conversion, which are interesting for fundamental science and may become the basis for a breakthrough in the spintronic technology. The present review summarizes recent theoretical and experimental efforts to reveal the microscopic structure and mechanisms of spin-orbit driven phenomena with the focus on angle and spin-resolved photoemission and scanning tunneling microscopy.

Unconventional band structure for a periodically gated surface of a three-dimensional topological insulator

The surface states of the three-dimensional (3D) topological insulators are described by a two-dimensional (2D) massless dirac equation. A gate-voltage-induced one-dimensional potential barrier on such surfaces creates a discrete bound state in the forbidden region outside the dirac cone. Even for a single barrier it is shown that such a bound state can create an electrostatic analogue of Shubnikov de Haas oscillation which can be experimentally observed for relatively smaller size samples. However, when these surface states are exposed to a periodic arrangement of such gate-voltage-induced potential barriers, the band structure of the same was significantly modified. This is expected to significantly alter the properties of the macroscopic system. We also suggest that, within suitable limits, the system may offer ways to control electron spin electrostatically, which may be practically useful.

Scanning tunneling microscopy study of the possible topological surface states in BiTeCl

Recently, the non-centrosymmetric bismuth tellurohalides such as BiTeCl are being studied as possible candidates for topological insulators. While some photoemission studies showed that BiTeCl is an inversion asymmetric topological insulator, others showed that it is a normal semiconductor with Rashba splitting. Meanwhile, first-principle calculations have failed to confirm the existence of topological surface states in BiTeCl so far. Therefore, the topological nature of BiTeCl requires further investigation. Here we report a low-temperature scanning tunneling microscopy study on the surface states of BiTeCl single crystals. On the tellurium (Te) -terminated surfaces with relatively low defect density, evidence for topological surface states is observed in the quasi-particle interference patterns, both in the anisotropy of the scattering vectors and the fast decay of the interference near the step edges. Meanwhile, on the samples with much higher defect densities, we observed surface states that behave differently. Our results may help to resolve the current controversy on the topological nature of BiTeCl.

High mobility, large linear magnetoresistance, and quantum transport phenomena in Bi2Te3 films grown by metallo-organic chemical vapor deposition (MOCVD)

We investigated the magnetotransport properties of Bi2Te3 films grown on GaAs (001) substrate by a cost-effective metallo-organic chemical vapor deposition (MOCVD). We observed the remarkably high carrier mobility and the giant linear magnetoresistance (carrier mobility ∼ 22 000 cm(2) V(-1) s(-1), magnetoresistance ∼ 750% at 1.8 K and 9 T for a 100 nm thick film) that depends on the film thickness. In addition, the Shubnikov-de Haas oscillation was observed, from which the effective mass was calculated to be consistent with the known value. From the thickness dependence of the Shubnikov-de Haas oscillation, it was found that a two dimensional electron gas with the conventional electron nature coexists with the topological Dirac fermion states and dominates the carrier transport in the Bi2Te3 film with thickness higher than 300 nm. These results are attributed to the intrinsic nature of Bi2Te3 in the high-mobility transport regime obtained by a deliberate choice of the substrate and the growth conditions.

Scattering times and surface conductivity of Dirac fermions in a 3D topological insulator film with localised impurities

The zero gap surface states of a 3D-topological insulator host highly mobile Dirac fermions with spin locked to the momentum. The high mobility attributed to the absence of back scattering is reduced in the presence of impurities on the surface. In particular, we discuss and compare scattering times for localised impurities on the surface, scattering between states of opposite helicity located on different surfaces coupled through a hybridisation potential and the role of magnetic impurities. Magnetic impurities give rise to an additional spin suppression factor. The role of warped bands and their influence on topological factors that can enhance the overall surface mobility is examined. Finally, employing a linearised Boltzmann equation approach, surface conductivity calculations for Dirac fermions in a 3D TI is outlined.

Polarization dependent photocurrent in the Bi2Te3 topological insulator film for multifunctional photodetection

Three dimensional Z₂ Topological insulator (TI) is an unconventional phase of quantum matter possessing insulating bulk state as well as time-reversal symmetry-protected Dirac-like surface state, which is demonstrated by extensive experiments based on surface sensitive detection techniques. This intriguing gapless surface state is theoretically predicted to exhibit many exotic phenomena when interacting with light, and some of them have been observed. Herein, we report the first experimental observation of novel polarization dependent photocurrent of photodetectors based on the TI Bi₂Te₃ film under irradiation of linearly polarized light. This photocurrent is linearly dependent on both the light intensity and the applied bias voltage. To pursue the physical origin of the polarization dependent photocurrent, we establish the basic TI surface state model to treat the light irradiation as a perturbation, and we adopt the Boltzmann equation to calculate the photocurrent. It turns out that the theoretical results are in nice qualitative agreement with the experiment. These findings show that the polycrystalline TI Bi₂Te₃ film working as a multifunctional photodetector can not only detect the light intensity, but also measure the polarization state of the incident light, which is remarkably different from conventional photodetectors that usually only detect the light intensity.

Manifestation of a Second Dirac Surface State and Bulk Bands in THz Radiation from Topological Insulators

Topological insulators (TIs) are interesting quantum matters that have a narrow bandgap for bulk and a Dirac-cone-like conducting surface state (SS). The recent discovered second Dirac surface state (SS) and bulk bands (BBs) located ~1.5 eV above the first SS are important for optical coupling in TIs. Here, we report on the time-domain measurements of THz radiation generated from TIs n-type Cu(0.02)Bi2Se3 and p-type Bi2Te3 single crystals by ultrafast optical pulse excitation. The observed polarity-reversal of the THz pulse originated from transient current is unusual, and cannot be reconciled with the photo-Dember effect. The second SS and BBs are found to be indispensable for the explanation of the unusual phenomenon. Thanks to the existence of the second SS and BBs, TIs manifest an effective wide band gap in THz generation. The present study demonstrates that time-domain THz spectroscopy provide rich information of the optical coupling and the electronic structure of TIs.

The evaluation of non-topological components in Berry phase and momentum relaxation time in a gapped 3D topological insulator

The zero gap surface states of a 3D-topological insulator host Dirac fermions with spin locked to the momentum. The gap-less Dirac fermions exhibit electronic behaviour different from those predicted in conventional materials. While calculations based on a simple linear dispersion can account for observed experimental patterns, a more accurate description of the physics of these systems and a better agreement between experimental data theoretical results can be obtained by including higher order k terms in the Hamiltonian. In this work, in presence of a time reversal symmetry breaking external magnetic field and higher order warping term, alteration to the topologically ordained Berry phase of (2n + 1)π, momentum relaxation time, and the magneto-conductivity tensors is established. The relation between scattering times and the deviations to topological Berry phase of π is also emphasized.

Ultra-broadband and high response of the Bi2Te3-Si heterojunction and its application as a photodetector at room temperature in harsh working environments

Broadband photodetection is central to various technological applications including imaging, sensing and optical communications. On account of their Dirac-like surface state, Topological insulators (TIs) are theoretically predicted to be promising candidate materials for broadband photodetection from the infrared to the terahertz. Here, we report a vertically-constructed ultra-broadband photodetector based on a TI Bi2Te3-Si heterostructure. The device demonstrated room-temperature photodetection from the ultraviolet (370.6 nm) to terahertz (118 μm) with good reproducibility. Under bias conditions, the visible responsivity reaches ca. 1 A W(-1) and the response time is better than 100 ms. As a self-powered photodetector, it exhibits extremely high photosensitivity approaching 7.5 × 10(5) cm(2) W(-1), and decent detectivity as high as 2.5 × 10(11) cm Hz(1/2) W(-1). In addition, such a prototype device without any encapsulation suffers no obvious degradation after long-time exposure to air, high-energy UV illumination and acidic treatment. In summary, we demonstrate that TI-based heterostructures hold great promise for addressing the long lasting predicament of stable room-temperature high-performance broadband photodetectors.

Nanoscale Probing of Local Electrical Characteristics on MBE-Grown Bi₂Te₃ Surfaces under Ambient Conditions

The local electrical characteristics on the surface of MBE-grown Bi2Te3 are probed under ambient conditions by conductive atomic force microscopy. Nanoscale mapping reveals a 10-100× enhancement in current at step-edges compared to that on terraces. Analysis of the local current-voltage characteristics indicates that the transport mechanism is similar for step-edges and terraces. Comparison of the results with those for control samples shows that the current enhancement is not a measurement artifact but instead is due to local differences in electronic properties. The likelihood of various possible mechanisms is discussed. The absence of enhancement at the step-edges for graphite terraces is consistent with the intriguing possibility that spin-orbit coupling and topological effects play a significant role in the step-edge current enhancement in Bi2Te3.

Vertical twinning of the Dirac cone at the interface between topological insulators and semiconductors

Topological insulators are a new class of matter characterized by the unique electronic properties of an insulating bulk and metallic boundaries arising from non-trivial bulk band topology. While the surfaces of topological insulators have been well studied, the interface between topological insulators and semiconductors may not only be more technologically relevant, but the interaction with non-topological states may fundamentally alter the physics. Here, we present a general model to show that this type of interaction can lead to vertical twinning of the Dirac cone, whereby the hybridized non-spin-degenerate interfacial states cross twice as they span the bulk bandgap. This hybridization leads to spin-momentum locking of non-topological states with either helical (clockwise or anticlockwise) or even anti-helical (negative winding number) spin orientation depending on the parametization of the interaction. Model results are corroborated by first-principles calculations of the technologically relevant Bi2Se3 film van der Waals bound to a Se-treated GaAs substrate.

Probing Dirac fermion dynamics in topological insulator Bi2Se3 films with a scanning tunneling microscope

Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi2Se3 ultrathin films. At the two-dimensional limit, bulk electrons become quantized and the quantization can be controlled by the film thickness at a single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of the phase relaxation length lϕ and inelastic scattering lifetime τ of topological surface-state electrons. We find that τ exhibits a remarkable (E - EF)(-2) energy dependence and increases with film thickness. We show that the features revealed are typical for electron-electron scattering between surface and bulk states.

Anisotropic conductivity in magnetic topological insulators

We study the surface conductivity of a three dimensional topological insulator doped with magnetic impurities. The spin-momentum locking of surface electrons makes their scattering from magnetic impurities anisotropic and the standard relaxation time approximation is not applicable. Using the semiclassical Boltzmann approach together with a generalized relaxation time scheme, we obtain closed forms for the relaxation times and analytic expressions for the surface conductivities of the system as functions of the bulk magnetization and the orientation of the aligned surface magnetic impurities. We show that the surface conductivity is anisotropic, and strongly depends both on the direction of the spins of magnetic impurities and on the magnitude of the bulk magnetization. In particular, we find that the surface conductivity has its minimum value when the spin of surface impurities are aligned perpendicular to the surface of TI, and therefore the backscattering probability is enhanced due to the magnetic torque exerted by impurities on the surface electrons.

Substitution-induced spin-splitted surface states in topological insulator (Bi 1-x Sbx)2Te3

We present a study on surface states of topological insulator (Bi 1-x Sbx)2Te3 by imaging quasiparticle interference patterns (QPI) using low temperature scanning tunneling microscope. Besides the topological Dirac state, we observed another surface state with chiral spin texture within the conduction band range. The quasiparticle scattering in this state is selectively suppressed. Combined with first-principles calculations, we attribute this state to a spin-splitted band induced by the substitution of Bi with Sb atoms. Our results demonstrate that the coexistence of topological order and alloying may open wider tunability in quantum materials.

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2-xTe3

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr0.08(Bi0.1Sb0.9)1.92Te3. Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship [Formula: see text] is confirmed throughout and exhibits an electron-dopant interaction energy J* = 145 meV·nm(2). These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.

Surface-dominated transport and enhanced thermoelectric figure of merit in topological insulator Bi(1.5)Sb(0.5)Te(1.7)Se(1.3)

We report the observation of an order of magnitude enhancement of the thermoelectric figure of merit (ZT = 0.36) in topological insulator Bi1.5Sb0.5Te1.7Se1.3 nanowires at 300 K as compared with the bulk specimen (ZT = 0.028). The enhancement was primarily due to an order of magnitude increase in the electrical conductivity of the surface-dominated transport and thermally activated charge carriers in the nanowires. Magnetoresistance analysis revealed the presence of Dirac electrons and determined that the Fermi level was near the conduction band edge. This may be the first thermoelectric measurement of samples with a chemical potential in the gap of a topological insulator without gate tuning, and provides an opportunity to study the contribution of surface states to the Seebeck coefficient and resistivity without concern for the complex effect of band bending.

Kondo effect mediated topological protection: Co on Sb(111)

We report on a Kondo effect on Co/Sb(111) mediating topological protection of the surface states against local magnetic perturbations. A sharp scanning tunneling spectroscopic peak near the Fermi energy is interpreted as a fingerprint of the Kondo resonance with a high Kondo temperature of about 200 K. Density function theory calculations reveal that the protruding Co adatoms are responsible for the Kondo peak, while the Co atoms underneath present as nonmagnetic impurities. By identifying the quasiparticle interference wavevectors, we demonstrate that only scattering channels related to backscattering confinements are observed for surfaces with and without the Co adsorption. It suggests that the Kondo effect suppresses the backscattering of the topological surface states and may help to expand the functionality of magnetically coupled topological materials for spintronics applications.

Evaluation of mobility in thin Bi2Se3 topological insulator for prospects of local electrical interconnects

Three-dimensional (3D) topological insulator (TI) has been conjectured as an emerging material to replace copper (Cu) as an interconnect material because of the suppression of elastic scattering from doping and charge impurities for carrier transport on TI surface. We, therefore via full real-space simulation, examine the feasibility of using thin 3D-TI (Bi₂Se₃) wire for the local electrical interconnects in the presence of edge roughness, vacancies, acoustic phonons and charge impurities across temperature and Fermi-level by simulating quantum transport through Non-Equilibrium Green Function algorithm. We found that because of the scattering induced by the acoustic phonons, the mobility reduces considerably at the room temperature which complemented with the low density of states near Dirac-point does not position Bi₂Se₃ 3D-TI as a promising material to replace Cu for local interconnects. Properties required in suitable TI material for this application have also been discussed.

Intrinsic conduction through topological surface states of insulating Bi2Te3 epitaxial thin films

Topological insulators represent a novel state of matter with surface charge carriers having a massless Dirac dispersion and locked helical spin polarization. Many exciting experiments have been proposed by theory, yet their execution has been hampered by the extrinsic conductivity associated with the unavoidable presence of defects in Bi2Te3 and Bi2Se3 bulk single crystals, as well as impurities on their surfaces. Here we present the preparation of Bi2Te3 thin films that are insulating in the bulk and the four-point probe measurement of the conductivity of the Dirac states on surfaces that are intrinsically clean. The total amount of charge carriers in the experiment is of the order of 10(12) cm(-2) only, and mobilities up to 4,600 cm(2)/Vs have been observed. These values are achieved by carrying out the preparation, structural characterization, angle-resolved and X-ray photoemission analysis, and temperature-dependent four-point probe conductivity measurement all in situ under ultra-high-vacuum conditions. This experimental approach opens the way to prepare devices that can exploit the intrinsic topological properties of the Dirac surface states.

Scanning tunneling microscopy studies of topological insulators

Scanning tunneling microscopy (STM), with surface sensitivity, is an ideal tool to probe the intriguing properties of the surface state of topological insulators (TIs) and topological crystalline insulators (TCIs). We summarize the recent progress on those topological phases revealed by STM studies. STM observations have directly confirmed the existence of the topological surface states and clearly revealed their novel properties. We also discuss STM work on magnetic doped TIs, topological superconductors and crystalline symmetry-protected surface states in TCIs. The studies have greatly promoted our understanding of the exotic properties of the new topological phases, as well as put forward new challenges. STM will continue to play an important role in this rapidly growing field from the point view of both fundamental physics and applications.

Tuning the Dirac point position in Bi(2)Se(3)(0001) via surface carbon doping

Angular resolved photoemission spectroscopy in combination with ab initio calculations show that trace amounts of carbon doping of the Bi_{2}Se_{3} surface allows the controlled shift of the Dirac point within the bulk band gap. In contrast to expectation, no Rashba-split two-dimensional electron gas states appear. This unique electronic modification is related to surface structural modification characterized by an expansion of the top Se-Bi spacing of ≈11% as evidenced by surface x-ray diffraction. Our results provide new ways to tune the surface band structure of topological insulators.

Anisotropic Fabry-Pérot resonant states confined within nano-steps on the topological insulator surface

The peculiar nature of topological surface states, such as absence of backscattering, weak anti-localization, and quantum anomalous Hall effect, has been demonstrated mainly in bulk and film of topological insulator (TI), using surface sensitive probes and bulk transport probes. However, it is equally important and experimentally challenging to confine massless Dirac fermions with nano-steps on TI surfaces. This potential structure has similar ground with linearly-dispersed photons in Fabry-Pérot resonators, while reserving fundamental differences from well-studied Fabry-Pérot resonators and quantum corrals on noble metal surfaces. In this paper, we study the massless Dirac fermions confined within steps along the x (Γ–K) or y (Γ–M) direction on the TI surface, and the Fabry-Pérot-like resonances in the electronic local density of states (LDOS) between the steps are found. Due to the remarkable warping effect in the topological surface states, the LDOS confined in the step-well running along Γ-M direction exhibit anisotropic resonance patterns as compared to those in the step-well along Γ-K direction. The transmittance properties and spin orientation of Dirac fermion in both cases are also anisotropic in the presence of warping effect.

Atomic and electronic structure of an alloyed topological insulator, Bi1.5Sb0.5Te1.7Se1.3

Bi2-xSbxTe3-ySey has been argued to exhibit both topological surface states and insulating bulk states, but has not yet been studied with local probes on the atomic scale. Here we report on the atomic and electronic structures of Bi1.5Sb0.5Te1.7Se1.3 studied using scanning tunnelling microscopy (STM) and spectroscopy (STS). Although there is significant surface disorder due to alloying of constituent atoms, cleaved surfaces of the crystals present a well-ordered hexagonal lattice with 10 Å high quintuple layer steps. STS results reflect the band structure and indicate that the surface state and Fermi energy are both located inside the energy gap. In particular, quasi-particle interference patterns from electron scattering demonstrate that the surface states possess linear dispersion and chirality from spin texture, thus verifying its topological nature. This finding demonstrates that alloying is a promising route to achieve full suppression of bulk conduction in topological insulators whilst keeping the topological surface state intact.

One-dimensional helical transport in topological insulator nanowire interferometers

The discovery of three-dimensional (3D) topological insulators opens a gateway to generate unusual phases and particles made of the helical surface electrons, proposing new applications using unusual spin nature. Demonstration of the helical electron transport is a crucial step to both physics and device applications of topological insulators. Topological insulator nanowires, of which spin-textured surface electrons form 1D band manipulated by enclosed magnetic flux, offer a unique nanoscale platform to realize quantum transport of spin-momentum locking nature. Here, we report an observation of a topologically protected 1D mode of surface electrons in topological insulator nanowires existing at only two values of half magnetic quantum flux (±h/2e) due to a spin Berry's phase (π). The helical 1D mode is robust against disorder but fragile against a perpendicular magnetic field breaking-time-reversal symmetry. This result demonstrates a device with robust and easily accessible 1D helical electronic states from 3D topological insulators, a unique nanoscale electronic system to study topological phenomena.

Warping effect-induced optical absorbance increment of topological insulator films for THz photodetectors with high signal-to-noise ratio

Strong optical absorbance makes topological insulator (TI) surfaces a promising high-performance photodetector in the terahertz (THz) to infrared frequency range. Here, we study the optical absorbance of more realistic TI films with hexagonal warping effect using the Fermi's golden rules. It was found that when the warping term is λ ≠ 0, the absorbance is no longer a universal value as that of graphene or ideal Dirac cone, but increases monotonously with the photon energy. The increment is positively correlated with the parameter λ/vF(3) where vF is the Fermi velocity. The relative signal-to-noise ratio (SNR) of the TI film working as a photoresistor-type photodetector is significantly enhanced by the warping effect-induced absorbance increment. These investigations provide useful information for developing TI-based photodetectors with high SNR in the range of THz to infrared frequency.

Emergence of a coherent in-gap state in the SmB6 Kondo insulator revealed by scanning tunneling spectroscopy

We use scanning tunneling microscopy to investigate the (001) surface of a cleaved SmB6 Kondo insulator. Variable temperature dI/dV spectroscopy up to 60 K reveals a gaplike density of state suppression around the Fermi level, which is due to the hybridization between the itinerant Sm 5d band and localized Sm 4f band. At temperatures below 40 K, a sharp coherence peak emerges within the hybridization gap near the lower gap edge. We propose that the in-gap resonance state is due to a collective excitation in magnetic origin with the presence of spin-orbital coupling and mixed valence fluctuations. These results shed new light on the electronic structure evolution and transport anomaly in SmB6.

Robust protection from backscattering in the topological insulator Bi1.5Sb0.5Te1.7Se1.3

Electron scattering in the topological surface state (TSS) of the topological insulator Bi1.5Sb0.5Te1.7Se1.3 was studied using quasiparticle interference observed by scanning tunneling microscopy. It was found that not only the 180° backscattering but also a wide range of backscattering angles of 100°-180° are effectively prohibited in the TSS. This conclusion was obtained by comparing the observed scattering vectors with the diameters of the constant-energy contours of the TSS, which were measured for both occupied and unoccupied states using time- and angle-resolved photoemission spectroscopy. The robust protection from backscattering in the TSS is good news for applications, but it poses a challenge to the theoretical understanding of the transport in the TSS.

A quantum dot in topological insulator nanofilm

We introduce a quantum dot in topological insulator nanofilm as a bump at the surface of the nanofilm. Such a quantum dot can localize an electron if the size of the dot is large enough, ≳5 nm. The quantum dot in topological insulator nanofilm has states of two types, which belong to two ('conduction' and 'valence') bands of the topological insulator nanofilm. We study the energy spectra of such defined quantum dots. We also consider intraband and interband optical transitions within the dot. The optical transitions of the two types have the same selection rules. While the interband absorption spectra have multi-peak structure, each of the intraband spectra has one strong peak and a few weak high frequency satellites.

High-performance Bi(2)Te(3)-based topological insulator film magnetic field detector

Topological insulators with the nanoscaled metallic surface state (3-5 nm) are actually of typical functional nanostructures. Significant efforts have been devoted to study new families of topological insulators and identifications of topological surface state, as well as fundamental physics issues relating to spin-polarized surface electronic states in the past few years. However, transport investigations that can provide direct experimental evidence for potentially practical applications of topological insulators are limited, and realization of functional devices based on topological insulators is still under exploration. Here, using the Sn-doping Bi2Te3 polycrystalline topological insulator films, we fabricated high-performance current-controlled magnetic field detectors. When a parallel magnetic field is applied, the as-fabricated device exhibits a stable and reproducible magneto-resistance (MR) switching behavior, and the corresponding MR ratio can be modulated by the applied current. Even under such a low magnetic field (0.5 kG), the device still shows a distinguishable MR switching performance, suggesting that topological insulator devices are very sensitive to external stimulation and potentially applicable to weak magnetic field detection.

Snapshots of Dirac fermions near the Dirac point in topological insulators

The recent focus on topological insulators is due to the scientific interest in the new state of quantum matter as well as the technology potential for a new generation of THz optoelectronics, spintronics and quantum computations. It is important to elucidate the dynamics of the Dirac fermions in the topologically protected surface state. Hence we utilized a novel ultrafast optical pump mid-infrared probe to explore the dynamics of Dirac fermions near the Dirac point. The femtosecond snapshots of the relaxation process were revealed by the ultrafast optics. Specifically, the Dirac fermion-phonon coupling strength in the Dirac cone was found to increase from 0.08 to 0.19 while Dirac fermions were away from the Dirac point into higher energy states. Further, the energy-resolved transient reflectivity spectra disclosed the energy loss rate of Dirac fermions at room temperature was about 1 meV/ps. These results are crucial to the design of Dirac fermion devices.

Surface hall effect and nonlocal transport in SmB₆: evidence for surface conduction

A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations. The surface transport, however, remains difficult to isolate from the bulk conduction in most existing TI crystals (particularly Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃) due to impurity caused bulk conduction. We report in large crystals of topological Kondo insulator (TKI) candidate material SmB₆ the thickness-independent surface Hall effects and non-local transport, which persist after various surface perturbations. These results serve as proof that at low temperatures SmB₆ has a metallic surface that surrounds an insulating bulk, paving the way for transport studies of the surface state in this proposed TKI material.

Observation of Dirac cone warping and chirality effects in silicene

We performed low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) studies on the electronic properties of (√3 × √3)R30° phase of silicene on Ag(111) surface. We found the existence of Dirac Fermion chirality through the observation of -1.5 and -1.0 power law decay of quasiparticle interference (QPI) patterns. Moreover, in contrast to the trigonal warping of Dirac cone in graphene, we found that the Dirac cone of silicene is hexagonally warped, which is further confirmed by density functional calculations and explained by the unique superstructure of silicene. Our results demonstrate that the (√3 × √3)R30° phase is an ideal system to investigate the unique Dirac Fermion properties of silicene.

Signatures of a pressure-induced topological quantum phase transition in BiTeI

We report the observation of two signatures of a pressure-induced topological quantum phase transition in the polar semiconductor BiTeI using x-ray powder diffraction and infrared spectroscopy. The x-ray data confirm that BiTeI remains in its ambient-pressure structure up to 8 GPa. The lattice parameter ratio c/a shows a minimum between 2.0-2.9 GPa, indicating an enhanced c-axis bonding through p(z) band crossing as expected during the transition. Over the same pressure range, the infrared spectra reveal a maximum in the optical spectral weight of the charge carriers, reflecting the closing and reopening of the semiconducting band gap. Both of these features are characteristics of a topological quantum phase transition and are consistent with a recent theoretical proposal.

Temperature-induced coexistence of a conducting bilayer and the bulk-terminated surface of the topological insulator Bi2Te3

Topological insulators such as Bi2Se3 and Bi2Te3 have extremely promising transport properties, due to their unique electronic behavior: they are insulators in the bulk and conducting at the surface. Recently, the coexistence of two types of surface conducting channels has been observed for Bi2Se3, one being Dirac electrons from the topological state and the other electrons from a conventional two-dimensional gas. As an explanation for this effect, a possible structural modification of the surface of these materials has been hypothesized. Using scanning tunneling microscopy we have directly observed the coexistence of a conducting bilayer and the bare surface of bulk-terminated Bi2Te3. X-ray crystal truncation rod scattering was used to directly show the stabilization of this epitaxial bilayer which is primarily composed of bismuth. Using this information, we have performed density functional theory calculations to determine the electronic properties of the possible surface terminations. They can be used to understand recent angular resolved photoemission data which have revealed this dual surface electronic behavior.

Surface reactivity enhancement on a Pd/Bi2Te3 heterostructure through robust topological surface states

We present a study of the surface reactivity of a Pd/Bi2Te3 thin film heterostructure. The topological surface states from Bi2Te3, being delocalized and robust owing to their topological natures, were found to act as an effective electron bath that significantly enhances the surface reactivity of palladium in the presence of two oxidizing agents, oxygen and tellurium respectively, which is consistent with a theoretical calculation. The surface reactivity of the adsorbed tellurium on this heterostructure is also intensified possibly benefitted from the effective transfer of the bath electrons. A partially inserted iron ferromagnetic layer at the interface of this heterostructure was found to play two competing roles arising from the higher-lying d-band center of the Pd/Fe bilayer and the interaction between the ferromagnetism and the surface spin texture of Bi2Te3 on the surface reactivity and their characteristics also demonstrate that the electron bath effect is long-lasting against accumulated thickness of adsorbates.