Three-dimensional topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. By investigating the surface state of Bi2Te3 with angle-resolved photoemission spectroscopy, we demonstrate that the surface state consists of a single nondegenerate Dirac cone. Furthermore, with appropriate hole doping, the Fermi level can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states. Our results establish that Bi2Te3 is a simple model system for the three-dimensional topological insulator with a single Dirac cone on the surface. The large bulk gap of Bi2Te3 also points to promising potential for high-temperature spintronics applications.

High-temperature superconductivity often emerges in the proximity of a symmetry-breaking ground state. For superconducting iron arsenides, in addition to the antiferromagnetic ground state, a small structural distortion breaks the crystal's C(4 )rotational symmetry in the underdoped part of the phase diagram. We reveal that the representative iron arsenide Ba(Fe(1)(-x)Co(x))(2)As(2) develops a large electronic anisotropy at this transition via measurements of the in-plane resistivity of detwinned single crystals, with the resistivity along the shorter b axis rho(b) being greater than rho(a). The anisotropy reaches a maximum value of ~2 for compositions in the neighborhood of the beginning of the superconducting dome. For temperatures well above the structural transition, uniaxial stress induces a resistivity anisotropy, indicating a substantial nematic susceptibility.

for studying a range of topological phenomena relevant to both condensed matter and particle physics.

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quantum phase transition at the composition with optimal superconducting transition temperature. [6][7][8][9] and iron pnictides [10][11][12] have been proposed as candidate platforms that might harbour an electronic nematic phase, which opens up exciting new possibilities related to the interplay of nematic order with high temperature superconductivity. However, one of the key doubts accompanied by the experimental discoveries is that the crystal lattice of these two systems does not retain a fourfold symmetry. In particular, in iron pnictides there is an orthorhombic structural distortion accompanying the rapid increase of resistivity anisotropy, which puts the legitimacy of the term "electronic nematic" into question. Here we report measurements of the resistivity anisotropy of Ba(Fe 1−x Co x ) 2 As 2 induced by a tunable uni-axial strain, which exhibits a divergent behaviour as the system approaches the phase transition from the high temperature side. Our result explicitly shows that the structural phase transition in Ba(Fe 1−x Co x ) 2 As 2 is purely driven by the instability in the electronic part of the free energy, and furthermore reveals an electronic nematic quantum phase transition at the composition with optimal superconducting transition temperature.We apply a tuneable in-plane uniaxial strain to single crystal samples of Ba(Fe 1−x Co x ) 2 As 2 to probe the nematic response. As shown in Fig. 1(A), by gluing the sample on the side wall of a piezostack, strains can be applied by the deformation of the piezo, which is controlled by an applied voltage(V P ) [13]. The strain (i.e. the fractional change of length along the current direction, ǫ P = ∆L/L) was monitored via a strain gauge glued on the back side of the piezo stack. Both ǫ P and the fractional change of resistivity (η = ∆ρ/ρ 0 , where ρ 0 is the resistivity of the free standing sample before gluing on the piezo stack) were measured at constant temperature while the applied voltage was swept, as shown in Fig.

Pulsed magnetic fields of up to 55T are used to investigate the transport properties of the topological insulator Bi2Se3 in the extreme quantum limit. For samples with a bulk carrier density of n = 2.9 × 10 16 cm −3 , the lowest Landau level of the bulk 3D Fermi surface is reached by a field of 4T. For fields well beyond this limit, Shubnikov-de Haas oscillations arising from quantization of the 2D surface state are observed, with the ν =1 Landau level attained by a field of ∼ 35T. These measurements reveal the presence of additional oscillations which occur at fields corresponding to simple rational fractions of the integer Landau indices.The recent prediction and discovery that Bi 2 Se 3 and Bi 2 Te 3 are three-dimensional topological insulators (TI) [1][2][3][4][5] has sparked a flurry of investigations. In a magnetic field, their relativistic dispersion causes the energy spectrum to be quantized so that E ν ∝ √ Bν, where B is the magnetic field and ν = 1, 2, 3, .., is the energy level, known as the Landau level (LL). The progression of energy levels E ν has been recently observed in scanningtunneling microscopy (STM) on Bi 2 Se 3 [6,7]. Other experiments on bulk samples and nanoribbons have reported universal conductance fluctuations attributed to the surface state [8,9]. However, all of the unambiguous measurements for the existence of the surface state have been made by surface sensitive probes. In this letter, we study samples of (Bi 1−x Sb x ) 2 Se 3 in which the Fermi surface of the Dirac fermions is small enough that pulsed fields of up to 55 T can access their quantum limit -the limit in which only a few of the lowest LLs are occupied. This is achieved by depleting the carrier density of the bulk and thereby reducing the size of the Dirac Fermi surface [10,11]). We demonstrate for the first time, a system in which not only the transport properties of Dirac fermions can be studied, but studied in the 2D quantum limit where novel correlation effects are most likely to arise [12,13].Generally speaking, transport measurements in Bi 2 Se 3 and Bi 2 Te 3 are plagued by bulk conducting channels from either the conduction band or by impurity bands introduced by foreign dopants [14,15]. The materials challenge is therefore finding a way to cleanly eliminate the bulk conductivity so that the properties of the surface can be observed. However, the carrier densities reported to date in studies of TI remain only as low [2][3][4][5] and 33×10 16 cm −3 (red and orange curves on Figure 1 (a)) were obtained by slow cooling a binary melt with different Bi:Se ratio. The principal origin of these relatively high carrier densities is Se deficiency and antisite defects. Samples with n≤ 11 × 10 16 cm −3 were obtained by slow cooling a ternary melt containing progressively more Sb. Although Sb is isovalent with Bi, Sb substitution apparently acts to control the defect density in the bulk crystals, reducing the bulk carrier density. Before measurements were performed, samples were cleaved on both sides with a scalpel blade i...

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Electron valley, a degree of freedom that is analogous to spin, can lead to novel topological phases in bilayer graphene. A tunable bandgap can be induced in bilayer graphene by an external electric field, and such gapped bilayer graphene is predicted to be a topological insulating phase protected by no-valley mixing symmetry, featuring quantum valley Hall effects and chiral edge states. Observation of such chiral edge states, however, is challenging because inter-valley scattering is induced by atomic-scale defects at real bilayer graphene edges. Recent theoretical work has shown that domain walls between AB- and BA-stacked bilayer graphene can support protected chiral edge states of quantum valley Hall insulators. Here we report an experimental observation of ballistic (that is, with no scattering of electrons) conducting channels at bilayer graphene domain walls. We employ near-field infrared nanometre-scale microscopy (nanoscopy) to image in situ bilayer graphene layer-stacking domain walls on device substrates, and we fabricate dual-gated field effect transistors based on the domain walls. Unlike single-domain bilayer graphene, which shows gapped insulating behaviour under a vertical electrical field, bilayer graphene domain walls feature one-dimensional valley-polarized conducting channels with a ballistic length of about 400 nanometres at 4 kelvin. Such topologically protected one-dimensional chiral states at bilayer graphene domain walls open up opportunities for exploring unique topological phases and valley physics in graphene.

Scanning tunneling spectroscopy studies on high-quality Bi2Te3 crystals exhibit perfect correspondence to ARPES data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear which disperse with a particular wave-vector that may result from an unconventional hexagonal warping term.PACS numbers: 71.18.+y, 71.20.Nr, A new type of three-dimensional (3D) bulk insulating materials with surface Quantum Spin Hall Effect states protected by time reversal symmetry has been recently predicted [1], and soon afterwards observed experimentally in BiSb bulk crystals [2]. Subsequently, Bi 2 Te 3 has been argued to be a similar three-dimensional topological insulator (TI), exhibiting a bulk gap and a single, non-degenerate Dirac fermion band on the surface [3]. Indeed, recent angle resolved photoemission spectroscopy (ARPES) confirmed that prediction [4]. In particular, with appropriate hole-doping, the Fermi level could be tuned to intersect only the surface states, indicating fully gapped bulk states as is expected from a three-dimensional TI. While ARPES could confirm the nature of the band, it is still a challenge to demonstrate unambiguously the topologically "protected" nature of the surface state in Bi 2 Te 3 , or any other 3D TI system.In this paper we present scanning tunneling microscopy (STM) and spectroscopy (STS) studies on high-quality doped Bi 2 Te 3 crystals. First we show that the STS spectra exhibit remarkable correspondence to ARPES data, hence enabling us to identify each region of the local density of states (LDOS) measured. Second, by analyzing the electron-waves (Friedel-oscillations) observed near cleavage steps, we show that within the main part of the surface state band oscillations are strongly damped, a hallmark of the strong supression of backscattering, hence supporting the hypothesis of a protected band. Finally, we show that in the region in which the surface band is warped, pronounced oscillations appear, with a distinct nesting wave-vector. Possible influence of the bulk conduction band on the oscillations is also proposed.For the present study we used Sn and Cd doped single crystals of Bi 2 Te 3 (see Fig. 1a for crystal structure and Fig. 1b,c for ARPES data). Nominal doping levels between 0 and 0.27% for Sn, and up to 1% for Cd were incorporated to compensate n-type doping from vacancy and anti-site defects that are common in the Bi 2 Te 3 system. Actual doping was determined separately using chemical and Hall-effect methods and were shown by ARPES [4] to be in excellent agreement with the relative position of the Dirac point with respect to the Fermi energy. For example, undoped crystals exhibit a Dirac point at ∼ −335 meV, 0.27% Sn doping yielded a Dirac point at ∼ −300 meV, while for a typical ∼ 1% Cd...