Gate-voltage control of chemical potential and weak antilocalization in Bi₂Se₃

Magnetic field-induced helical mode and topological transitions in a topological insulator nanoribbon

The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.

Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators

The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity σ(yx) = e2/h without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.

Large and Anisotropic Linear Magnetoresistance in Single Crystals of Black Phosphorus Arising From Mobility Fluctuations

Black Phosphorus (BP) is presently attracting immense research interest on the global level due to its high mobility and suitable band gap for potential application in optoelectronics and flexible devices. It was theoretically predicted that BP has a large direction-dependent electrical and magnetotransport anisotropy. Investigations on magnetotransport of BP may therefore provide a new platform for studying the nature of electron transport in layered materials. However, to the best of our knowledge, magnetotransport studies, especially the anisotropic magnetoresistance (MR) effect in layered BP, are rarely reported. Here, we report a large linear MR up to 510% at a magnetic field of 7 Tesla in single crystals of BP. Analysis of the temperature and angle dependence of MR revealed that the large linear MR in our sample originates from mobility fluctuations. Furthermore, we reveal that the large linear MR of layered BP in fact follows a three-dimensional behavior rather than a two-dimensional one. Our results have implications to both the fundamental understanding and magnetoresistive device applications of BP.

Stable topological insulators achieved using high energy electron beams

Topological insulators are potentially transformative quantum solids with metallic surface states which have Dirac band structure and are immune to disorder. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to surface charge transport. Here we demonstrate that irradiation with swift (∼2.5 MeV energy) electron beams allows to compensate these defects, bring the Fermi level back into the bulk gap and reach the charge neutrality point (CNP). Controlling the beam fluence, we tune bulk conductivity from p- (hole-like) to n-type (electron-like), crossing the Dirac point and back, while preserving the Dirac energy dispersion. The CNP conductance has a two-dimensional character on the order of ten conductance quanta and reveals, both in Bi₂Te₃ and Bi₂Se₃, the presence of only two quantum channels corresponding to two topological surfaces. The intrinsic quantum transport of the topological states is accessible disregarding the bulk size.

Defects in solids may introduce additional charges that influence the overall charge transport behaviour. Here, Zhao et al. use swift electron beams to compensate charge defects, which effectively tune Bi₂Te₃ and Bi₂Se₃ from p-type to n-type while preserving their topological properties.

Nanoclusters of CaSe in calcium-doped Bi2Se3 grown by molecular-beam epitaxy

In calcium (Ca) doped Bi2Se3 films grown by molecular beam epitaxy, nanoclusters of CaSe are revealed by high-angle annular dark field imaging and energy dispersive x-ray spectroscopy analysis using a scanning transmission electron microscope. As the interface between the ordinary insulator CaSe and topological insulator, Bi2Se3, can host topological nontrivial interface state, this represents an interesting material system for further studies. We show by first principles total energy calculations that aggregation of Ca atoms in Bi2Se3 is driven by energy minimization and a preferential intercalation of Ca in the van der Waals gap between quintuple layers of Bi2Se3 induces reordering of atomic stacking and causes an increasing amount of stacking faults in film. The above findings also provide an explanation of less-than-expected electrical carrier (hole) concentrations in Ca-doped samples.

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.

Weak localization effect in topological insulator micro flakes grown on insulating ferrimagnet BaFe₁₂O₁₉

Many exotic physics anticipated in topological insulators require a gap to be opened for their topological surface states by breaking time reversal symmetry. The gap opening has been achieved by doping magnetic impurities, which however inevitably create extra carriers and disorder that undermine the electronic transport. In contrast, the proximity to a ferromagnetic/ferrimagnetic insulator may improve the device quality, thus promises a better way to open the gap while minimizing the side-effects. Here, we grow thin single-crystal Sb_1.9Bi_0.1Te₃ micro flakes on insulating ferrimagnet BaFe₁₂O₁₉ by using the van der Waals epitaxy technique. The micro flakes show a negative magnetoresistance in weak perpendicular fields below 50 K, which can be quenched by increasing temperature. The signature implies the weak localization effect as its origin, which is absent in intrinsic topological insulators, unless a surface state gap is opened. The surface state gap is estimated to be 10 meV by using the theory of the gap-induced weak localization effect. These results indicate that the magnetic proximity effect may open the gap for the topological surface attached to BaM insulating ferrimagnet. This heterostructure may pave the way for the realization of new physical effects as well as the potential applications of spintronics devices.

Tuning the Fermi level with topological phase transition by internal strain in a topological insulator Bi2Se3 thin film

In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our results, including the synthesis of a strained ultrathin topological insulator, suggest a new direction for electronic and spintronic applications for the future.

Plasma-Wave Terahertz Detection Mediated by Topological Insulators Surface States

Topological insulators (TIs) represent a novel quantum state of matter, characterized by edge or surface-states, showing up on the topological character of the bulk wave functions. Allowing electrons to move along their surface, but not through their inside, they emerged as an intriguing material platform for the exploration of exotic physical phenomena, somehow resembling the graphene Dirac-cone physics, as well as for exciting applications in optoelectronics, spintronics, nanoscience, low-power electronics, and quantum computing. Investigation of topological surface states (TSS) is conventionally hindered by the fact that in most of experimental conditions the TSS properties are mixed up with those of bulk-states. Here, we activate, probe, and exploit the collective electronic excitation of TSS in the Dirac cone. By engineering Bi2Te(3-x)Sex stoichiometry, and by gating the surface of nanoscale field-effect-transistors, exploiting thin flakes of Bi2Te2.2Se0.8 or Bi2Se3, we provide the first demonstration of room-temperature terahertz (THz) detection mediated by overdamped plasma-wave oscillations on the "activated" TSS of a Bi2Te2.2Se0.8 flake. The reported detection performances allow a realistic exploitation of TSS for large-area, fast imaging, promising superb impacts on THz photonics.

Persistent optical gating of a topological insulator

The spin-polarized surface states of topological insulators (TIs) are attractive for applications in spintronics and quantum computing. A central challenge with these materials is to reliably tune the chemical potential of their electrons with respect to the Dirac point and the bulk bands. We demonstrate persistent, bidirectional optical control of the chemical potential of (Bi,Sb)2Te3 thin films grown on SrTiO3. By optically modulating a space-charge layer in the SrTiO3 substrates, we induce a persistent field effect in the TI films comparable to electrostatic gating techniques but without additional materials or processing. This enables us to optically pattern arbitrarily shaped p- and n-type regions in a TI, which we subsequently image with scanning photocurrent microscopy. The ability to optically write and erase mesoscopic electronic structures in a TI may aid in the investigation of the unique properties of the topological insulating phase. The gating effect also generalizes to other thin-film materials, suggesting that these phenomena could provide optical control of chemical potential in a wide range of ultrathin electronic systems.

Solvothermal Synthesis of Lateral Heterojunction Sb2Te3/Bi2Te3 Nanoplates

A lateral heterojunction of topological insulator Sb2Te3/Bi2Te3 was successfully synthesized using a two-step solvothermal method. The two crystalline components were separated well by a sharp lattice-matched interface when the optimized procedure was used. Inspecting the heterojunction using high-resolution transmission electron microscopy showed that epitaxial growth occurred along the horizontal plane. The semiconducting temperature-resistance curve and crossjunction rectification were observed, which reveal a staggered-gap lateral heterojunction with a small junction voltage. Quantum correction from the weak antilocalization reveals the well-maintained transport of the topological surface state. This is appealing for a platform for spin filters and one-dimensional topological interface states.

Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator

When a three-dimensional ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall conductance. The recent realization of this phenomenon, the quantum anomalous Hall effect, provides a conceptually new platform for studies of 1D transport, distinct from the traditionally studied quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt-driven crossover from predominantly edge-state transport to diffusive transport in Cr_x(Bi,Sb)_2−xTe₃ thin films. This crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain by employing a Landauer–Büttiker formalism. Our methodology provides a powerful means of quantifying dissipative effects in temperature and chemical potential regimes far from perfect quantization.

When magnetized out-of-plane, three-dimensional ferromagnetic topological insulator thin films exhibit the quantum anomalous Hall effect. Here, the authors follow the evolution of this dissipationless chiral edge transport effect as the magnetization is brought in-plane under an applied magnetic field.

Dimensional crossover in the quantum transport behaviour of the natural topological insulator Aleksite

Three-dimensional topological insulators comprise topologically protected surface states displaying massless, Dirac-like linear dispersion with spin-momentum locking. Electrical conduction through such surface states has been documented to manifest itself in a two-dimensional character of the angle-dependent magnetotransport behavior. Here, we explore the size-dependent electronic properties of nanostructures made of the lead-containing mineral Aleksite, a naturally occurring topological insulator. Compared to its sister compound Kawazulite, a member of the well-studied Tetradymite crystal class, the crystal structure of Aleksite is distinguished by its lack of any counterpart within the group of synthetic topological insulators. Low temperature Hall measurements on thin Aleksite nanosheets reveal a significant carrier mobility on the order of 1000 cm(2)/(Vs), and a high carrier density of n = 3.9 × 10(25) m(-3). Importantly, for Aleksite nanoribbons with a width below 150 nm, a 1D weak antilocalization effect along with 1D universal conductance fluctuations emerges, which transforms into 2D behavior for larger ribbon widths.

Homoepitaxial SrTiO3(111) Film with High Dielectric Performance and Atomically Well-Defined Surface

The six-fold symmetry possessed by the (111) surfaces of perovskite oxides allows the epitaxial growth of novel quantum materials such as topological insulators. The dielectric SrTiO₃(111) thin film is an ideal buffer layer, providing the readily tunability of charge density in gate-controlled structures. But the high-quality film growth is challenging due to its strong surface polarity as well as the difficulty of obtaining the chemical stoichiometry. Here we show that the layer-by-layer growth of homoepitaxial SrTiO₃(111) thin films can be achieved in molecular beam epitaxy method by keeping the growing surface reconstructed. And the cation stoichiometry is optimized precisely with the reflective high energy electron diffraction as the feedback signal that changes sensitively to the variation of metal concentration during growth. With atomically well-defined surfaces, the SrTiO₃(111) films show high dielectric performance with the charge density modulated in the range of 2 × 10¹³/cm² with the back gate voltage lower than 0.2 V. Methods of further broadening the range are also discussed.

Revealing Surface States in In-Doped SnTe Nanoplates with Low Bulk Mobility

Indium (In) doping in topological crystalline insulator SnTe induces superconductivity, making In-doped SnTe a candidate for a topological superconductor. SnTe nanostructures offer well-defined nanoscale morphology and high surface-to-volume ratios to enhance surface effects. Here, we study In-doped SnTe nanoplates, In(x)Sn(1-x)Te, with x ranging from 0 to 0.1 and show they superconduct. More importantly, we show that In doping reduces the bulk mobility of In(x)Sn(1-x)Te such that the surface states are revealed in magnetotransport despite the high bulk carrier density. This is manifested by two-dimensional linear magnetoresistance in high magnetic fields, which is independent of temperature up to 10 K. Aging experiments show that the linear magnetoresistance is sensitive to ambient conditions, further confirming its surface origin. We also show that the weak antilocalization observed in In(x)Sn(1-x)Te nanoplates is a bulk effect. Thus, we show that nanostructures and reducing the bulk mobility are effective strategies to reveal the surface states and test for topological superconductors.

Observation of Anderson localization in ultrathin films of three-dimensional topological insulators

Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly observed. Here, we report experimental demonstration of a crossover from diffusive transport in the weak antilocalization regime to variable range hopping transport in the Anderson localization regime with ultrathin (Bi_{1-x}Sb_{x})_{2}Te_{3} films. As disorder becomes stronger, negative magnetoconductivity due to the weak antilocalization is gradually suppressed, and eventually, positive magnetoconductivity emerges when the electron system becomes strongly localized. This work reveals the critical role of disorder in the quantum transport properties of ultrathin topological insulator films, in which theories have predicted rich physics related to topological phase transitions.

Chiral tunneling of topological states: towards the efficient generation of spin current using spin-momentum locking

We show that the interplay between chiral tunneling and spin-momentum locking of helical surface states leads to spin amplification and filtering in a 3D topological insulator (TI). Our calculations show that the chiral tunneling across a TI pn junction allows normally incident electrons to transmit, while the rest are reflected with their spins flipped due to spin-momentum locking. The net result is that the spin current is enhanced while the dissipative charge current is simultaneously suppressed, leading to an extremely large, gate-tunable spin-to-charge current ratio (∼20) at the reflected end. At the transmitted end, the ratio stays close to 1 and the electrons are completely spin polarized.

Dual-gated topological insulator thin-film device for efficient Fermi-level tuning

Observations of novel quantum phenomena expected for three-dimensional topological insulators (TIs) often require fabrications of thin-film devices and tuning of the Fermi level across the Dirac point. Since thin films have both top and bottom surfaces, an effective control of the surface chemical potential requires dual gating. However, a reliable dual-gating technique for TI thin films has not yet been developed. Here we report a comprehensive method to fabricate a dual-gated TI device and demonstrate tuning of the chemical potential of both surfaces across the Dirac points. The most important part of our method is the recipe for safely detaching high-quality, bulk-insulating (Bi(1-x)Sb(x))2Te3 thin films from sapphire substrates and transferring them to Si/SiO2 wafers that allow back gating. Fabrication of an efficient top gate by low-temperature deposition of a SiN(x) dielectric complements the procedure. Our dual-gated devices are shown to be effective in tuning the chemical potential in a wide range encompassing the Dirac points on both surfaces.

Ultrafast helicity control of surface currents in topological insulators with near-unity fidelity

In recent years, a class of solid-state materials, called three-dimensional topological insulators, has emerged. In the bulk, a topological insulator behaves like an ordinary insulator with a band gap. At the surface, conducting gapless states exist showing remarkable properties such as helical Dirac dispersion and suppression of backscattering of spin-polarized charge carriers. The characterization and control of the surface states via transport experiments is often hindered by residual bulk contributions. Here we show that surface currents in Bi₂Se₃ can be controlled by circularly polarized light on a picosecond timescale with a fidelity near unity even at room temperature. We reveal the temporal separation of such ultrafast helicity-dependent surface currents from photo-induced thermoelectric and drift currents in the bulk. Our results uncover the functionality of ultrafast optoelectronic devices based on surface currents in topological insulators.

Bulk contributions to transport measurements often inhibit the study of the surface states of topological insulators. Here, Kastl et al. demonstrate high-fidelity helicity-dependent photocurrents in the surface states of Bi₂Se₃, controlled via circularly polarized light with a picosecond time-resolution.

Electrically tunable in-plane anisotropic magnetoresistance in topological insulator BiSbTeSe2 nanodevices

We report tunable in-plane anisotropic magnetoresistance (AMR) in nanodevices based on topological insulator BiSbTeSe2 (BSTS) nanoflakes by electric gating. The AMR can be changed continuously from negative to positive when the Fermi level is manipulated to cross the Dirac point by an applied gate electric field. We also discuss effects of the gate electric field, current density, and magnetic field on the in-plane AMR with a simple physical model, which is based on the in-plane magnetic field induced shift of the spin-momentum locked topological two surface states that are coupled through side surfaces and bulk weak antilocalization (WAL). The large, tunable and bipolar in-plane AMR in BSTS devices provides the possibility of fabricating more sensitive logic and magnetic random access memory AMR devices.

Highly tunable Berry phase and ambipolar field effect in topological crystalline insulator Pb(1-x)Sn(x)Se

Recently, rock-salt IV-VI semiconductors, such as Pb(1-x)Sn(x)Se(Te) and SnTe, have been observed to host topological crystalline insulator (TCI) states. The nontrivial states have long been believed to exhibit ambipolar field effects and possess massive Dirac Fermions in two-dimension (2D) limit due to the surface hybridization. However, these exciting attributes of TCI remain previously inaccessible owing to the complicated control over composition and thickness. Here, we systematically investigate doping and thickness-induced topological phase transitions by electrical transport. We demonstrate the first evidence of the ambipolar properties in Pb(1-x)Sn(x)Se thin films. Surface gap opening is observed in 10 nm TCI originated from the strong finite-size effect. Importantly, magnetoconductance hosts a competition between weak antilocalization and weak localization, suggesting a strikingly tunable Berry phase evolution and strong electron-electron interaction. Our findings serve as a new probe to study electron behavior and pave the way for further exploring and manipulating this novel 2D TCI phase.

Gate tunable relativistic mass and Berry's phase in topological insulator nanoribbon field effect devices

Transport due to spin-helical massless Dirac fermion surface state is of paramount importance to realize various new physical phenomena in topological insulators, ranging from quantum anomalous Hall effect to Majorana fermions. However, one of the most important hallmarks of topological surface states, the Dirac linear band dispersion, has been difficult to reveal directly in transport measurements. Here we report experiments on Bi₂Te₃ nanoribbon ambipolar field effect devices on high-κ SrTiO₃ substrates, where we achieve a gate-tuned bulk metal-insulator transition and the topological transport regime with substantial surface state conduction. In this regime, we report two unambiguous transport evidences for gate-tunable Dirac fermions through π Berry's phase in Shubnikov-de Haas oscillations and effective mass proportional to the Fermi momentum, indicating linear energy-momentum dispersion. We also measure a gate-tunable weak anti-localization (WAL) with 2 coherent conduction channels (indicating 2 decoupled surfaces) near the charge neutrality point, and a transition to weak localization (indicating a collapse of the Berry's phase) when the Fermi energy approaches the bulk conduction band. The gate-tunable Dirac fermion topological surface states pave the way towards a variety of topological electronic devices.

Simultaneous electrical-field-effect modulation of both top and bottom Dirac surface states of epitaxial thin films of three-dimensional topological insulators

It is crucial for the studies of the transport properties and quantum effects related to Dirac surface states of three-dimensional topological insulators (3D TIs) to be able to simultaneously tune the chemical potentials of both top and bottom surfaces of a 3D TI thin film. We have realized this in molecular beam epitaxy-grown thin films of 3D TIs, as well as magnetic 3D TIs, by fabricating dual-gate structures on them. The films could be tuned between n-type and p-type by each gate alone. Combined application of two gates can reduce the carrier density of a TI film to a much lower level than with only one of them and enhance the film resistance by 10,000%, implying that Fermi level is tuned very close to the Dirac points of both top and bottom surface states without crossing any bulk band. The result promises applications of 3D TIs in field effect devices.

Gate-tuned quantum oscillations of topological surface states in β-Ag2Te

We report the strong experimental evidence of the existence of topological surface states with large electric field tunability and mobility in β-Ag2Te. Pronounced 2D Shubnikov-de Haas oscillations have been observed in β-Ag2Te nanoplates. A Berry phase is determined to be near π using the Landau level fan diagram for a relatively wide nanoplate while the largest electric field ambipolar effect in topological insulator so far (~2500%) is observed in a narrow nanoplate. The π Berry phase and the evolution of quantum oscillations with gate voltage (Vg) in the nanoplates strongly indicate the presence of topological surface states in β-Ag2Te. Moreover, the mobility of the narrow Ag2Te nanoplate is about several thousand cm(2)s(-1)V(-1). Our results suggest that β-Ag2Te has the potential to become an important material in the investigation of topological insulators.

Temperature evolution of magnetic and transport behavior in 5d Mott insulator Sr₂IrO₄: significance of magneto-structural coupling

We have investigated the temperature evolution of magnetism and its interrelation with structural parameters in the perovskite-based layered compound Sr2IrO4, which is believed to be a J(eff) = 1/2 Mott insulator. The structural distortion plays an important role in this material and induces a weak ferromagnetism in an otherwise antiferromagnetically ordered magnetic state with a transition temperature around 240 K. Interestingly, at low temperatures, below around 100 K, a change in the magnetic moment has been observed. Temperature dependent x-ray diffraction measurements show that sudden changes in structural parameters around 100 K are responsible for this. Resistivity measurements show insulating behavior throughout the temperature range across the magnetic phase transition. The electronic transport can be described with Mott's two-dimensional variable range hopping (VRH) mechanism, however, three different temperature ranges are found for VRH, which is a result of varying the localization length with temperature. A negative magnetoresistance (MR) has been observed at all temperatures in contrast to positive behavior generally observed in strongly spin-orbit coupled materials. The quadratic field dependence of MR implies the relevance of a quantum interference effect.

Modelling near-surface bound electron states in a 3D topological insulator: analytical and numerical approaches

We apply both analytical and ab-initio methods to explore heterostructures composed of a 3D topological insulator (3D TI) and an ultrathin normal insulator (NI) overlayer as a proving ground for the principles of topological phase engineering. Using the continual model of a semi-infinite 3D TI we study the surface potential (SP) effect caused by an attached ultrathin layer of 3D NI on the formation of topological bound states at the interface. The results reveal that the spatial profile and spectrum of these near-surface states strongly depend on both the sign and the strength of the SP. Using ab-initio band structure calculations to take the specificity of the materials into account, we investigate the NI/TI heterostructures formed by a single tetradymite-type quintuple or septuple layer block and the 3D TI substrate. The analytical continuum theory results relate the near-surface state evolution with the SP variation and are in good qualitative agreement with those obtained from density-functional theory (DFT) calculations. We also predict the appearance of the quasi-topological bound state on the 3D NI surface caused by a local band gap inversion induced by an overlayer.

Robust surface state transport in thin bismuth nanoribbons

While a two-dimensional (2D) metallic surface state in bismuth has been proposed, experimental 2D evidence of quantum transport, e.g., angular dependent Shubnikov-de Haas (SdH) oscillations is still lacking. Here, we report the angular-dependent magnetoresistance measurements in single-crystal Bi nanoribbons, and found that both the low-field weak antilocalization behavior and the high-field angle-dependent SdH oscillations follow exactly the 2D character, indicative of the 2D metallic surface states which dominate the transport properties of thin Bi nanoribbons. Moreover, by controllable exposing the ribbons to ambient environment (1 atm and room temperature), the metallic surface states were found to be robust to the oxidation although the carrier density in the surface states are modified after the exposures. These results suggest that the metallic surface states in Bi nanoribbons should be topologically protected which can provide key information in understanding the surface properties of Bi in nanometer scale.

Topological crystalline insulator nanostructures

Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators such as Bi₂Se₃ and Bi₂Te₃, topological crystalline insulators also possess surface states with exotic electronic properties such as spin-momentum locking and Dirac dispersion. Experimentally verified topological crystalline insulators to date are SnTe, Pb₁-xSnxSe, and Pb₁-xSnxTe. Because topological protection comes from the crystal symmetry, magnetic impurities or in-plane magnetic fields are not expected to open a gap in the surface states in topological crystalline insulators. Additionally, because they have a cubic structure instead of a layered structure, branched structures or strong coupling with other materials for large proximity effects are possible, which are difficult with layered Bi₂Se₃ and Bi₂Te₃. Thus, additional fundamental phenomena inaccessible in three-dimensional topological insulators can be pursued. In this review, topological crystalline insulator SnTe nanostructures will be discussed. For comparison, experimental results based on SnTe thin films will be covered. Surface state properties of topological crystalline insulators will be discussed briefly.

Observations of a metal-insulator transition and strong surface states in Bi2-x SbxSe3 thin films

High-quality thin films of the topological insulator Bi2-xSbxSe3 are grown by molecular beam epitaxy. A metal-insulator transition along with strong surface states - revealed by Shubnikov-de Haas oscillations - is observed as the Sb concentration is increased. This system represents a widely tunable platform for achieving high surface conduction, suppressing the bulk influence, and manipulating the band structure of topological insulators.

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.

Electric tuning of the surface and quantum well states in Bi2Se3 films: a first-principles study

Based on first-principles calculations in the framework of van der Waals density functional theory, we find that giant, Rashba-like spin splittings can be induced in both the surface states and quantum well states of thin Bi2Se3 films by application of an external electric field. The charge is redistributed so that the Dirac cones of the upper and lower surfaces become nondegenerate and completely gapless. Interestingly, a momentum-dependent spin texture is developed on the two surfaces of the films. Some of the quantum well states, which reside in the middle of the Bi2Se3 film under zero field, are driven to the surface by the electric field. The Rashba splitting energy has a highly non-linear dependence on the momentum and the electric field due to the large contribution of the high-order Rashba terms, which suggests complex spin dynamics in the thin films of Bi2Se3 under an electric field.

Tunable interaction-induced localization of surface electrons in antidot nanostructured Bi2Te3 thin films

Recently, a logarithmic decrease of conductivity has been observed in topological insulators at low temperatures, implying a tendency of localization of surface electrons. Here, we report quantum transport experiments on the topological insulator Bi2Te3 thin films with arrayed antidot nanostructures. With increasing density of the antidots, a systematic decrease is observed in the slope of the logarithmic temperature-dependent conductivity curves, indicating the electron-electron interaction can be tuned by the antidots. Meanwhile, the weak antilocalization effect revealed in magnetoconductivity exhibits an enhanced dominance of electron-electron interaction among decoherence mechanisms. The observation can be understood from an antidot-induced reduction of the effective dielectric constant, which controls the interactions between the surface electrons. Our results clarify the indispensable role of the electron-electron interaction in the localization of surface electrons and indicate the localization of surface electrons in an interacting topological insulator.

Topological transport and atomic tunnelling-clustering dynamics for aged Cu-doped Bi2Te3 crystals

Enhancing the transport contribution of surface states in topological insulators is vital if they are to be incorporated into practical devices. Such efforts have been limited by the defect behaviour of Bi₂Te₃ (Se₃) topological materials, where the subtle bulk carrier from intrinsic defects is dominant over the surface electrons. Compensating such defect carriers is unexpectedly achieved in (Cu_0.1Bi_0.9)₂Te_3.06 crystals. Here we report the suppression of the bulk conductance of the material by four orders of magnitude by intense ageing. The weak antilocalization analysis, Shubnikov–de Haas oscillations and scanning tunnelling spectroscopy corroborate the transport of the topological surface states. Scanning tunnelling microscopy reveals that Cu atoms are initially inside the quintuple layers and migrate to the layer gaps to form Cu clusters during the ageing. In combination with first-principles calculations, an atomic tunnelling–clustering picture across a diffusion barrier of 0.57 eV is proposed.

Enhancing the transport properties of surface states in topological insulators is vital if they are to be incorporated into practical devices. Towards this end, Chen et al. study the transport in aged (Cu_0.1Bi_0.9)₂Te_3.06, where the ageing process suppresses bulk conductance by up to four orders of magnitude.

Crossover from 3D to 2D quantum transport in Bi2Se3/In2Se3 superlattices

The topological insulator/normal insulator (TI/NI) superlattices (SLs) with multiple Dirac channels are predicted to offer great opportunity to design novel materials and investigate new quantum phenomena. Here, we report first transport studies on the SLs composed of TI Bi2Se3 layers sandwiched by NI In2Se3 layers artificially grown by molecular beam epitaxy (MBE). The transport properties of two kinds of SL samples show convincing evidence that the transport dimensionality changes from three-dimensional (3D) to two-dimensional (2D) when decreasing the thickness of building block Bi2Se3 layers, corresponding to the crossover from coherent TI transport to separated TI channels. Our findings provide the possibility to realizing "3D surface states" in TI/NI SLs.

Room-temperature high-frequency transport of dirac fermions in epitaxially grown Sb2Te3- and Bi2Te3-based topological insulators

We report on the observation of photogalvanic effects in epitaxially grown Sb2Te3 and Bi2Te3 three-dimensional (3D) topological insulators (TI). We show that asymmetric scattering of Dirac fermions driven back and forth by the terahertz electric field results in a dc electric current. Because of the "symmetry filtration" the dc current is generated by the surface electrons only and provides an optoelectronic access to probe the electron transport in TI, surface domains orientation, and details of electron scattering in 3D TI even at room temperature.

Crossover between weak antilocalization and weak localization of bulk states in ultrathin Bi₂Se₃ films

We report transport studies on the 5 nm thick Bi₂Se₃ topological insulator films which are grown via molecular beam epitaxy technique. The angle-resolved photoemission spectroscopy data show that the Fermi level of the system lies in the bulk conduction band above the Dirac point, suggesting important contribution of bulk states to the transport results. In particular, the crossover from weak antilocalization to weak localization in the bulk states is observed in the parallel magnetic field measurements up to 50 Tesla. The measured magneto-resistance exhibits interesting anisotropy with respect to the orientation of parallel magnetic field B_// and the current I, signifying intrinsic spin-orbit coupling in the Bi₂Se₃ films. Our work directly shows the crossover of quantum interference effect in the bulk states from weak antilocalization to weak localization. It presents an important step toward a better understanding of the existing three-dimensional topological insulators and the potential applications of nano-scale topological insulator devices.

Weak antilocalization effect and noncentrosymmetric superconductivity in a topologically nontrivial semimetal LuPdBi

A large number of half-Heusler compounds have been recently proposed as three-dimensional (3D) topological insulators (TIs) with tunable physical properties. However, no transport measurements associated with the topological surface states have been observed in these half-Heusler candidates due to the dominating contribution from bulk electrical conductance. Here we show that, by reducing the mobility of bulk carriers, a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hallmarks of topological surface states, was experimentally revealed from the tilted magnetic field dependence of magnetoconductance in a topologically nontrivial semimetal LuPdBi. Besides the observation of a 2D WAL effect, a superconducting transition was revealed at T_c ~ 1.7 K in the same bulk LuPdBi. Quantitative analysis within the framework of a generalized BCS theory leads to the conclusion that the noncentrosymmetric superconductivity of LuPdBi is fully gapped with a possibly unconventional pairing character. The co-existence of superconductivity and the transport signature of topological surface states in the same bulk alloy suggests that LuPdBi represents a very promising candidate as a topological superconductor.

Emergence of decoupled surface transport channels in bulk insulating Bi(2)Se(3) thin films

In ideal topological insulator (TI) films the bulk state, which is supposed to be insulating, should not provide any electric coupling between the two metallic surfaces. However, transport studies on existing TI films show that the topological states on opposite surfaces are electrically tied to each other at thicknesses far greater than the direct coupling limit where the surface wave functions overlap. Here, we show that as the conducting bulk channels are suppressed, the parasitic coupling effect diminishes, and the decoupled surface channels emerge as expected for ideal TIs. In Bi(2)Se(3) thin films with fully suppressed bulk states, the two surfaces, which are directly coupled below ∼10  QL, become gradually isolated with increasing thickness and are completely decoupled beyond ∼20  QL. On such a platform, it is now feasible to implement transport devices whose functionality relies on accessing the individual surface layers without any deleterious coupling effects.

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.

Air-stable electron depletion of Bi(2)Se(3) using molybdenum trioxide into the topological regime

We perform high-resolution photoelectron spectroscopy on in situ cleaved topological insulator Bi2Se3 single crystals and in situ transport measurements on Bi2Se3 films grown by molecular beam epitaxy. We demonstrate efficient electron depletion of Bi2Se3 via vacuum deposition of molecular MoO3, lowering the surface Fermi energy to within ∼100 meV of the Dirac point, well into the topological regime. A 100 nm MoO3 film provides an air-stable doping and passivation layer.

Proximity induced high-temperature magnetic order in topological insulator--ferrimagnetic insulator heterostructure

Introducing magnetic order in a topological insulator (TI) breaks time-reversal symmetry of the surface states and can thus yield a variety of interesting physics and promises for novel spintronic devices. To date, however, magnetic effects in TIs have been demonstrated only at temperatures far below those needed for practical applications. In this work, we study the magnetic properties of Bi2Se3 surface states (SS) in the proximity of a high Tc ferrimagnetic insulator (FMI), yttrium iron garnet (YIG or Y3Fe5O12). Proximity-induced butterfly and square-shaped magnetoresistance loops are observed by magneto-transport measurements with out-of-plane and in-plane fields, respectively, and can be correlated with the magnetization of the YIG substrate. More importantly, a magnetic signal from the Bi2Se3 up to 130 K is clearly observed by magneto-optical Kerr effect measurements. Our results demonstrate the proximity-induced TI magnetism at higher temperatures, an important step toward room-temperature application of TI-based spintronic devices.

Identification of helicity-dependent photocurrents from topological surface states in Bi2Se3 gated by ionic liquid

Dirac-like surface states on surfaces of topological insulators have a chiral spin structure with spin locked to momentum, which is interesting in physics and may also have important applications in spintronics. In this work, by measuring the tunable helicity-dependent photocurrent (HDP), we present an identification of the HDP from the Dirac-like surface states at room temperature. It turns out that the total HDP has two components, one from the Dirac-like surface states, and the other from the surface accumulation layer. These two components have opposite directions. The clear gate tuning of the electron density as well as the HDP signal indicates that the surface band bending and resulted surface accumulation are successfully modulated by the applied ionic liquid gate, which provides a promising way to the study of the Dirac-like surface states and also potential applications in spintronic devices.

Quantum and classical magnetoresistance in ambipolar topological insulator transistors with gate-tunable bulk and surface conduction

Weak antilocalization (WAL) and linear magnetoresistance (LMR) are two most commonly observed magnetoresistance (MR) phenomena in topological insulators (TIs) and often attributed to the Dirac topological surface states (TSS). However, ambiguities exist because these phenomena could also come from bulk states (often carrying significant conduction in many TIs) and are observable even in non-TI materials. Here, we demonstrate back-gated ambipolar TI field-effect transistors in (Bi_0.04Sb_0.96)₂Te₃ thin films grown by molecular beam epitaxy on SrTiO₃(111), exhibiting a large carrier density tunability (by nearly 2 orders of magnitude) and a metal-insulator transition in the bulk (allowing switching off the bulk conduction). Tuning the Fermi level from bulk band to TSS strongly enhances both the WAL (increasing the number of quantum coherent channels from one to peak around two) and LMR (increasing its slope by up to 10 times). The SS-enhanced LMR is accompanied by a strongly nonlinear Hall effect, suggesting important roles of charge inhomogeneity (and a related classical LMR), although existing models of LMR cannot capture all aspects of our data. Our systematic gate and temperature dependent magnetotransport studies provide deeper insights into the nature of both MR phenomena and reveal differences between bulk and TSS transport in TI related materials.

Transport discovery of emerging robust helical surface States in Z2 = 0 systems

We study the possibility of realizing robust helical surface states in Z(2) = 0 systems. We find that the combination of anisotropy and finite-size confinement leads to the emergence of robust helical edge states in both two-dimensional and three-dimensional Z(2) = 0 systems. By investigating an anisotropic Bernevig-Hughes-Zhang model in a finite sample, we demonstrate that the transport manifestation of the surface states is robust against nonmagnetic disorder, resembling that of a Z(2) = 1 phase. Notably, the effective energy gap of the robust helical states can be efficiently engineered, allowing for potential applications as valley filters and valley valves. The realization of emerging robust helical surface states in realistic materials is also discussed.

Finite-temperature conductivity and magnetoconductivity of topological insulators

The electronic transport experiments on topological insulators exhibit a dilemma. A negative cusp in magnetoconductivity is widely believed as a quantum transport signature of the topological surface states, which are immune from localization and exhibit the weak antilocalization. However, the measured conductivity drops logarithmically when lowering temperature, showing a typical feature of the weak localization as in ordinary disordered metals. Here, we present a conductivity formula for massless and massive Dirac fermions as a function of magnetic field and temperature, by taking into account the electron-electron interaction and quantum interference simultaneously. The formula reconciles the dilemma by explicitly clarifying that the temperature dependence of the conductivity is dominated by the interaction, while the magnetoconductivity is mainly contributed by the quantum interference. The theory paves the road to quantitatively study the transport in topological insulators, and can be extended to other two-dimensional Dirac-like systems, such as graphene, transition metal dichalcogenides, and silicene.

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.

Transferring MBE-grown topological insulator films to arbitrary substrates and metal-insulator transition via Dirac gap

Mechanical exfoliation of bulk crystals has been widely used to obtain thin topological insulator (TI) flakes for device fabrication. However, such a process produces only microsized flakes that are highly irregular in shape and thickness. In this work, we developed a process to transfer the entire area of TI Bi2Se3 thin films grown epitaxially on Al2O3 and SiO2 to arbitrary substrates, maintaining their pristine morphology and crystallinity. Transport measurements show that these transferred films have lower carrier concentrations and comparable or higher mobilities than before the transfer. Furthermore, using this process we demonstrated a clear metal-insulator transition in an ultrathin Bi2Se3 film by gate-tuning its Fermi level into the hybridization gap formed at the Dirac point. The ability to transfer large area TI films to any substrate will facilitate fabrication of TI heterostructure devices, which will help explore exotic phenomena such as Majorana fermions and topological magnetoelectricity.

Dirac electron states formed at the heterointerface between a topological insulator and a conventional semiconductor

Topological insulators are a class of semiconductor exhibiting charge-gapped insulating behaviour in the bulk, but hosting a spin-polarized massless Dirac electron state at the surface. The presence of a topologically protected helical edge channel has been verified for the vacuum-facing surface of several topological insulators by means of angle-resolved photoemission spectroscopy and scanning tunnelling microscopy. By performing tunnelling spectroscopy on heterojunction devices composed of p-type topological insulator (Bi1−xSbx)2Te3 and n-type conventional semiconductor InP, we report the observation of such states at the solid-state interface. Under an applied magnetic field, we observe a resonance in the tunnelling conductance through the heterojunction due to the formation of Landau levels of two-dimensional Dirac electrons at the interface. Moreover, resonant tunnelling spectroscopy reveals a systematic dependence of the Fermi velocity and Dirac point energy on the composition x. The successful formation of robust non-trivial edge channels at a solid-state interface is an essential step towards functional junctions based on topological insulators.

Chemical-potential-dependent gap opening at the Dirac surface states of Bi2Se3 induced by aggregated substitutional Cr atoms

With angle-resolved photoemission spectroscopy, gap opening is resolved at up to room temperature in the Dirac surface states of molecular beam epitaxy grown Cr-doped Bi2Se3 topological insulator films, which, however, show no long-range ferromagnetic order down to 1.5 K. The gap size is found decreasing with increasing electron-doping level. Scanning tunneling microscopy and first-principles calculations demonstrate that substitutional Cr atoms aggregate into superparamagnetic multimers in the Bi2Se3 matrix, which contribute to the observed chemical-potential-dependent gap opening in the Dirac surface states without long-range ferromagnetic order.