Landau quantization of topological surface states in Bi2Se3

Introduction to Topological Insulators

In this article, we will give a brief introduction to the topological insulators. We will briefly review some of the recent progresses from both theoretical and experimental sides. In particular, we will emphasize the recent progresses achieved in China.

Quantized Hall effect and Shubnikov-de Haas oscillations in highly doped Bi2Se3: evidence for layered transport of bulk carriers

Bi2Se3 is an important semiconductor thermoelectric material and a prototype topological insulator. Here we report observation of Shubnikov-de Hass oscillations accompanied by quantized Hall resistances (R(xy)) in highly doped n-type Bi2Se3 with bulk carrier concentrations of few 10(19) cm(-3). Measurements under tilted magnetic fields show that the magnetotransport is 2D-like, where only the c-axis component of the magnetic field controls the Landau level formation. The quantized step size in 1/R(xy) is found to scale with the sample thickness, and average ~e(2)/h per quintuple layer. We show that the observed magnetotransport features do not come from the sample surface, but arise from the bulk of the sample acting as many parallel 2D electron systems to give a multilayered quantum Hall effect. In addition to revealing a new electronic property of Bi2Se3, our finding also has important implications for electronic transport studies of topological insulator materials.

Electronic properties of graphene: a perspective from scanning tunneling microscopy and magnetotransport

This review covers recent experimental progress in probing the electronic properties of graphene and how they are influenced by various substrates, by the presence of a magnetic field and by the proximity to a superconductor. The focus is on results obtained using scanning tunneling microscopy, spectroscopy, transport and magnetotransport techniques.

Quasiparticle states and quantum interference induced by magnetic impurities on a two-dimensional topological superconductor

We theoretically study the effect of localized magnetic impurities on two-dimensional topological superconductor (TSC). We show that the local density of states (LDOS) can be tuned by the effective exchange field m, the chemical potential μ of TSC, and the distance Δr as well as the relative spin angle α between two impurities. The changes in Δr between two impurities alter the interference and result in significant modifications to the bonding and antibonding states. Furthermore, the bound-state spin LDOS induced by single and double magnetic impurity scattering, the quantum corrals and the quantum mirages are also discussed. Finally, we briefly compare the impurities in TSC with those in topological insulators.

Spiral growth without dislocations: molecular beam epitaxy of the topological insulator Bi2Se3 on epitaxial graphene/SiC(0001)

We report a new mechanism that does not require the formation of interfacial dislocations to mediate spiral growth during molecular beam epitaxy of Bi2Se3. Based on in situ scanning tunneling microscopy observations, we find that Bi2Se3 growth on epitaxial graphene/SiC(0001) initiates with two-dimensional (2D) nucleation, and that the spiral growth ensues with the pinning of the 2D growth fronts at jagged steps of the substrate or at domain boundaries created during the coalescence of the 2D islands. Winding of the as-created growth fronts around these pinning centers leads to spirals. The mechanism can be broadly applied to the growth of other van der Waals materials on weakly interacting substrates. We further confirm, using scanning tunneling spectroscopy, that the one-dimensional helical mode of a line defect is not supported in strong topological insulators such as Bi2Se3.

Gate-controlled surface conduction in Na-doped Bi2Te3 topological insulator nanoplates

Exploring exciting and exotic physics, scientists are pursuing practical device applications for topological insulators. The Dirac-like surface states in topological insulators are protected by the time-reversal symmetry, which naturally forbids backscattering events during the carrier transport process, and therefore offers promising applications in dissipationless spintronic devices. Although considerable efforts have been devoted to controlling their surface conduction, limited work has been focused on tuning surface states and bulk carriers in Bi(2)Te(3) nanostructures by external field. Here we report gate-tunable surface conduction in Na-doped Bi(2)Te(3) topological insulator nanoplates. Significantly, by applying external gate voltages, such topological insulators can be tuned from p-type to n-type. Our results render a promise in finding novel topological insulators with enhanced surface states.

Robustness of topological order and formation of quantum well states in topological insulators exposed to ambient environment

The physical property investigation (like transport measurements) and ultimate application of the topological insulators usually involve surfaces that are exposed to ambient environment (1 atm and room temperature). One critical issue is how the topological surface state will behave under such ambient conditions. We report high resolution angle-resolved photoemission measurements to directly probe the surface state of the prototypical topological insulators, Bi(2)Se(3) and Bi(2)Te(3), upon exposing to various environments. We find that the topological order is robust even when the surface is exposed to air at room temperature. However, the surface state is strongly modified after such an exposure. Particularly, we have observed the formation of two-dimensional quantum well states near the exposed surface of the topological insulators. These findings provide key information in understanding the surface properties of the topological insulators under ambient environment and in engineering the topological surface state for applications.

Josephson supercurrent through a topological insulator surface state

The long-sought yet elusive Majorana fermion is predicted to arise from a combination of a superconductor and a topological insulator. An essential step in the hunt for this emergent particle is the unequivocal observation of supercurrent in a topological phase. Here, direct evidence for Josephson supercurrents in superconductor (Nb)-topological insulator (Bi(2)Te(3))-superconductor electron-beam fabricated junctions is provided by the observation of clear Shapiro steps under microwave irradiation, and a Fraunhofer-type dependence of the critical current on magnetic field. Shubnikov-de Haas oscillations in magnetic fields up to 30 T reveal a topologically non-trivial two-dimensional surface state. This surface state is attributed to mediate the ballistic Josephson current despite the fact that the normal state transport is dominated by diffusive bulk conductivity. The lateral Nb-Bi(2)Te(3)-Nb junctions hence provide prospects for the realization of devices supporting Majorana fermions.

Fermi-level tuning of epitaxial Sb2Te3 thin films on graphene by regulating intrinsic defects and substrate transfer doping

High-quality Sb2Te3 films are obtained by molecular beam epitaxy on a graphene substrate and investigated by in situ scanning tunneling microscopy and spectroscopy. Intrinsic defects responsible for the natural p-type conductivity of Sb2Te3 are identified to be the Sb vacancies and Sb(Te) antisites in agreement with first-principles calculations. By minimizing defect densities, coupled with a transfer doping by the graphene substrate, the Fermi level of Sb2Te3 thin films can be tuned over the entire range of the bulk band gap. This establishes the necessary condition to explore topological insulator behaviors near the Dirac point.

Three-dimensional topological insulator in a magnetic field: chiral side surface states and quantized Hall conductance

Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field are investigated. It is found that chiral surface states parallel to the magnetic field are responsible for the quantized Hall (QH) conductance (2n + 1)e²/h multiplied by the number of Dirac cones. Due to the two-dimensional nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed.

Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3

We report the experimental observation of Landau quantization of molecular beam epitaxy grown Sb{2}Te{3} thin films by a low-temperature scanning tunneling microscope. Different from all the reported systems, the Landau quantization in a Sb{2}Te{3} topological insulator is not sensitive to the intrinsic substitutional defects in the films. As a result, a nearly perfect linear energy dispersion of surface states as a 2D massless Dirac fermion system is achieved. We demonstrate that four quintuple layers are the thickness limit for a Sb{2}Te{3} thin film being a 3D topological insulator. The mechanism of the Landau-level broadening is discussed in terms of enhanced quasiparticle lifetime.

Gate-tuned normal and superconducting transport at the surface of a topological insulator

Three-dimensional topological insulators are characterized by the presence of a bandgap in their bulk and gapless Dirac fermions at their surfaces. New physical phenomena originating from the presence of the Dirac fermions are predicted to occur, and to be experimentally accessible via transport measurements in suitably designed electronic devices. Here we study transport through superconducting junctions fabricated on thin Bi₂Se₃ single crystals, equipped with a gate electrode. In the presence of perpendicular magnetic field B, sweeping the gate voltage enables us to observe the filling of the Dirac fermion Landau levels, whose character evolves continuously from electron- to hole-like. When B=0, a supercurrent appears, whose magnitude can be gate tuned, and is minimum at the charge neutrality point determined from the Landau level filling. Our results demonstrate how gated nano-electronic devices give control over normal and superconducting transport of Dirac fermions at an individual surface of a three-dimensional topological insulators.

Topological insulators are a unique class of materials characterized by exotic metallic states at their surface, while remaining insulated in the bulk. Sacépé et al. show how to manipulate normal and superconducting electronic transport at the surface of the topological insulator Bi₂Se₃, by tuning a gate-voltage to vary the electronic density.

Metal-supported high crystalline Bi₂Se₃ quintuple layers

Atomically flat thin films of Bi(2)Se(3) were grown on Au(111) metal substrate using molecular beam epitaxy. Hexagonal atomic structures and quintuple layer steps were observed at the surfaces of grown films using scanning tunneling microscopy. Multiple sharp peaks from (003) family layers were characterized by x-ray diffraction measurements. The atomic stoichiometry of Bi and Se was considered using x-ray photoemission spectroscopy. Moiré patterns were obtained at the surfaces of one quintuple layer films due to lattice mismatch between Bi(2)Se(3) and Au. Our experiments suggest that Au is a reasonable material for electrodes in Bi(2)Se(3) devices.

Rashba spin-splitting control at the surface of the topological insulator Bi2Se3

The electronic structure of Bi(2)Se(3) is studied by angle-resolved photoemission and density functional theory. We show that the instability of the surface electronic properties, observed even in ultrahigh-vacuum conditions, can be overcome via in situ potassium deposition. In addition to accurately setting the carrier concentration, new Rashba-like spin-polarized states are induced, with a tunable, reversible, and highly stable spin splitting. Ab initio slab calculations reveal that these Rashba states are derived from 5-quintuple-layer quantum-well states. While the K-induced potential gradient enhances the spin splitting, this may be present on pristine surfaces due to the symmetry breaking of the vacuum-solid interface.

Interacting dirac fermions on a topological insulator in a magnetic field

We study the fractional quantum Hall states on the surface of a topological insulator thin film in an external magnetic field, where the Dirac fermion nature of the charge carriers have been experimentally established only recently. Our studies indicate that the fractional quantum Hall states should indeed be observable in the surface Landau levels of a topological insulator. The strength of the effect will however be different, compared to that in graphene, due to the finite thickness of the topological insulator film and due to the admixture of Landau levels of the two surfaces of the film. At a small film thickness, that mixture results in a strongly nonmonotonic dependence of the excitation gap on the film thickness. At a large enough thickness of the film, the excitation gap in the lowest two Landau levels are comparable in strength.

Reactive chemical doping of the Bi2Se3 topological insulator

Using angular resolved photoemission spectroscopy we studied the evolution of the surface electronic structure of the topological insulator Bi(2)Se(3) as a function of water vapor exposure. We find that a surface reaction with water induces a band bending, which shifts the Dirac point deep into the occupied states and creates quantum well states with a strong Rashba-type splitting. The surface is thus not chemically inert, but the topological state remains protected. The band bending is traced back to Se abstraction, leaving positively charged vacancies at the surface. Because of the presence of water vapor, a similar effect takes place when Bi(2)Se(3) crystals are left in vacuum or cleaved in air, which likely explains the aging effect observed in the Bi(2)Se(3) band structure.

Liquid-gated ambipolar transport in ultrathin films of a topological insulator Bi2Te3

Using ionic-liquid (IL) gating in electric-double-layer transistors (EDLTs), we investigate field-effect electrical transport properties of ultrathin epitaxial films of a topological insulator (TI), Bi(2)Te(3). Because of their extreme thinness, the Bi(2)Te(3) films show a band gap opening and resulting semiconducting transport properties. Near room temperature, an obvious ambipolar transistor operation with an ON-OFF ratio close to 10(3) was observed in the transfer characteristics of liquid-gated EDLTs and further confirmed by a sign change of the Hall coefficients. Modulation of the electronic states and a phase transition from a semiconducting conduction (dR(xx)/dT < 0) to a metallic transport (dR(xx)/dT > 0) were observed in the temperature-dependent resistance of the ultrathin Bi(2)Te(3) channel, demonstrating that the liquid gating is an effective way to modulate the electronic states of TIs.

Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets

We report on Raman spectroscopy of few quintuple layer topological insulator bismuth selenide (Bi2Se3) nanoplatelets (NPs), synthesized by a polyol method. The as-grown NPs exhibit excellent crystalline quality, hexagonal or truncated trigonal morphology, and uniformly flat surfaces down to a few quintuple layers. Both Stokes and anti-Stokes Raman spectroscopy for the first time resolve all four optical phonon modes from individual NPs down to 4 nm, where the out-of-plane vibrational A(1g)(1) mode shows a few wavenumbers red shift as the thickness decreases below ~15 nm. This thickness-dependent red shift is tentatively explained by a phonon softening due to the decreasing of the effective restoring force arising from a decrease of the van der Waals forces between adjacent layers. Quantitatively, we found that the 2D phonon confinement model proposed by Faucet and Campbell cannot explain the red shift values and the line shape of the A(1g)(1) mode, which can be described better by a Breit–Wigner–Fano resonance line shape. Considerable broadening (~17 cm(–1) for six quintuple layers) especially for the in-plane vibrational mode E(g)(2) is identified, suggesting that the layer-to-layer stacking affects the intralayer bonding. Therefore, a significant reduction in the phonon lifetime of the in-plane vibrational modes is probably due to an enhanced electron–phonon coupling in the few quintuple layer regime.

Molecular beam epitaxial growth of topological insulators

With the molecular beam epitaxy technique, layer-by-layer growth of atomically flat topological insulator Bi(2) Te(3) and Bi(2) Se(3) thin films has been realized on Si(111) and graphene substrates, respectively. The growth criteria by which intrinsic topological insulators can readily be obtained is established. By using in situ angle-resolved photoemission spectroscopy and scanning tunneling microscopy measurements, the band structure and surface morphology of Bi(2) Te(3) and Bi(2) Se(3) thin films of different thickness can be studied. Molecular beam epitaxy technique was shown to not only provide an excellent method to prepare high quality topological insulators but show possibilities of engineering their electronic and spin structures as well, which is of significant importance for potential applications of topological insulators based on well-developed Si technology.

Hybridization wave as the "hidden order" in URu2Si2

A phenomenological model for the "hidden order" transition in the heavy-Fermion material URu(2)Si(2) is introduced. The hidden order is identified as an incommensurate, momentum-carrying hybridization between the light hole band and the heavy electron band. This modulated hybridization appears after a Fano hybridization at higher temperatures takes place. We focus on the hybridization wave as the order parameter in URu(2)Si(2) and possibly other materials with similar band structures. The model is qualitatively consistent with numerous experimental results obtained from, e.g., neutron scattering and scanning tunneling microscopy. Specifically, we find a gaplike feature in the density of states and the appearance of features at an incommensurate vector Q(*)∼0.6π/a(0). Finally, the model allows us to make various predictions which are amenable to current experiments.

Tunneling into clean heavy fermion compounds: origin of the Fano line shape

Recently observed tunneling spectra on clean heavy-fermion compounds show a lattice periodic Fano line shape similar to what is observed in the case of tunneling to a Kondo ion adsorbed at the surface. We show that the translation symmetry of a clean surface in the case of weakly correlated metals leads to a tunneling spectrum which shows a hybridization gap but does not have a Fano line shape. By contrast, in a strongly correlated heavy-fermion metal the heavy quasiparticle states will be broadened by interaction effects. The hybridization gap is completely filled in this way, and an ideal Fano line shape of width ∼2TK results. In addition, we discuss the possible influence of the tunneling tip on the surface, in (i) leading to additional broadening of the Fano line and (ii) enhancing the hybridization locally, hence adding to the impurity type behavior. The latter effects depend on the tip-surface distance.