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1When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect [1, 2] dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin-orbit interactions may also naturally support conducting topological boundary states in the extreme quantum limit [3, 4, 5], which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields [6]. Bulk Bi 1−x Sb x single crystals are predicted to be prime candidates [7, 8] for one such unusual Hall phase of matter known as the topological insulator [9,10,11]. The hallmark of a topological insulator is the existence of metallic surface states that are higher dimensional analogues of the edge states that characterize a quantum spin Hall insulator [3, 4, 5, 6, 7, 8, 9,10,11,12,13]. In addition to its interesting boundary states, the bulk of Bi 1−x Sb x is predicted to exhibit three-dimensional Dirac particles [14,15,16,17], another topic of heightened current interest following the new findings of two-dimensional graphene [18,19,20] and charge quantum Hall fractionalization observed in pure bismuth [21]. However, despite numerous transport and magnetic measurements on the Bi 1−x Sb x family since the 1960s [17], no direct evidence of either topological quantum Hall-like states or bulk Dirac particles has ever been found. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES), we report the direct observation of massive Dirac particles in the bulk of Bi 0.9 Sb 0.1 , locate the Kramers' points at the sample's boundary and provide a comprehensive mapping of the topological Dirac insulator's gapless surface modes. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the much sought exotic "topological metal" [9,10,11]. They also suggest that this material has potential application in developing next-generation quantum computing devices that may incorporate "light-like" bulk carriers and topologically protected spin-textured edge-surface currents. 2Bismuth is a semimetal with strong spin-orbit interactions. Its band structure is believed to feature an indirect negative gap between the valence band maximum at the T point of the bulk Brillouin zone (BZ) and the conduction band minima at three equivalent L points [17,22] (here we generally refer to these as a single point, L). The valence and conduction bands at L are derived from antisymmetric (L a ) and symmetric (L s ) p-type orbitals, respectively, and the effective low-energy Hamiltonian at this point is described by the (3+1)-dimensional relativistic Dirac equation [14,15,16]. The resulting dispersionis highly linear owing to the combination of an unusually large band velocity v and a small gap ∆ (such that |∆/| v|| ≈ 5 × 10 −3Å−1 ) and has been used to explain various peculiar proper...

Helical Dirac fermions-charge carriers that behave as massless relativistic particles with an intrinsic angular momentum (spin) locked to its translational momentum-are proposed to be the key to realizing fundamentally new phenomena in condensed matter physics. Prominent examples include the anomalous quantization of magneto-electric coupling, half-fermion states that are their own antiparticle, and charge fractionalization in a Bose-Einstein condensate, all of which are not possible with conventional Dirac fermions of the graphene variety. Helical Dirac fermions have so far remained elusive owing to the lack of necessary spin-sensitive measurements and because such fermions are forbidden to exist in conventional materials harbouring relativistic electrons, such as graphene or bismuth. It has recently been proposed that helical Dirac fermions may exist at the edges of certain types of topologically ordered insulators-materials with a bulk insulating gap of spin-orbit origin and surface states protected against scattering by time-reversal symmetry-and that their peculiar properties may be accessed provided the insulator is tuned into the so-called topological transport regime. However, helical Dirac fermions have not been observed in existing topological insulators. Here we report the realization and characterization of a tunable topological insulator in a bismuth-based class of material by combining spin-imaging and momentum-resolved spectroscopies, bulk charge compensation, Hall transport measurements and surface quantum control. Our results reveal a spin-momentum locked Dirac cone carrying a non-trivial Berry's phase that is nearly 100 per cent spin-polarized, which exhibits a tunable topological fermion density in the vicinity of the Kramers point and can be driven to the long-sought topological spin transport regime. The observed topological nodal state is shown to be protected even up to 300 K. Our demonstration of room-temperature topological order and non-trivial spin-texture in stoichiometric Bi(2)Se(3).M(x) (M(x) indicates surface doping or gating control) paves the way for future graphene-like studies of topological insulators, and applications of the observed spin-polarized edge channels in spintronic and computing technologies possibly at room temperature.

A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetry-based classification of condensed matter. Exotic spin-transport phenomena, such as the dissipationless quantum spin Hall effect, have been speculated to originate from a topological order whose identification requires a spin-sensitive measurement, which does not exist to this date in any system. Using Mott polarimetry, we probed the spin degrees of freedom and demonstrated that topological quantum numbers are completely determined from spin texture-imaging measurements. Applying this method to Sb and Bi(1-x)Sb(x), we identified the origin of its topological order and unusual chiral properties. These results taken together constitute the first observation of surface electrons collectively carrying a topological quantum Berry's phase and definite spin chirality, which are the key electronic properties component for realizing topological quantum computing bits with intrinsic spin Hall-like topological phenomena.

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We show that the strongly spin-orbit coupled materials Bi2Te3 and Sb2Te3 and their derivatives belong to the Z2 topological-insulator class. Using a combination of first-principles theoretical calculations and photoemission spectroscopy, we directly show that Bi2Te3 is a large spin-orbit-induced indirect bulk band gap (delta approximately 150 meV) semiconductor whose surface is characterized by a single topological spin-Dirac cone. The electronic structure of self-doped Sb2Te3 exhibits similar Z2 topological properties. We demonstrate that the dynamics of spin-Dirac fermions can be controlled through systematic Mn doping, making these materials classes potentially suitable for topological device applications.

Topological insulators embody a state of bulk matter characterized by spin-momentum-locked surface states that span the bulk bandgap 1-7 . This highly unusual surface spin environment provides a rich ground for uncovering new phenomena 4-24 . Understanding the response of a topological surface to strong Coulomb perturbations represents a frontier in discovering the interacting and emergent many-body physics of topological surfaces. Here we present the first controlled study of topological insulator surfaces under Coulomb and magnetic perturbations. We have used time-resolved deposition of iron, with a large Coulomb charge and significant magnetic moment, to systematically modify the topological spin structure of the Bi 2 Se 3 surface. We observe that such perturbation leads to the creation of odd multiples of Dirac fermions and that magnetic interactions break time-reversal symmetry in the presence of band hybridizations. We present a theoretical model to account for the observed electron dynamics of the topological surface. Taken collectively, these results are a critical guide in controlling electron mobility and quantum behaviour of topological surfaces, not only for device applications but also in setting the stage for creating exotic particles such as axions or imaging monopoles on the surface.