## Abstract

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 Bi_{2}Te_{3} 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 Bi_{2}Te_{3} is a simple model system for the three-dimensional topological insulator with a single Dirac cone on the surface. The large bulk gap of Bi_{2}Te_{3} also points to promising potential for high-temperature spintronics applications.

Soon after the theoretical prediction (*1*), a new state of quantum matter—the two-dimensional (2D) topological insulator displaying the quantum spin Hall (QSH) effect—was experimentally observed in HgTe quantum wells (*2*). The QSH state (*3*, *4*) has an insulating gap in the bulk and gapless states at the edge where opposite spin states counterpropagate. The two opposite spin states form a single massless Dirac fermion at the edge, and the crossing of their dispersion branches at a time-reversal invariant (TRI) point is protected by the time-reversal symmetry (*5*). The dissipationless edge state transport of the QSH state may enable low-power spintronics devices.

Two-dimensional massless Dirac fermions were experimentally discovered in graphene with two inequivalent massless Dirac points for each spin orientation, giving rise to four copies of massless Dirac fermions in total. This is consistent with the experimentally observed quantized Hall conductance 2*e*^{2}*/h* (*6*), as each Dirac fermion leads to a quantized Hall conductance *e*^{2}*/*2*h* in an external magnetic field (*h* is Planck’s constant). Graphene has an even number of massless Dirac fermions, because no TRI purely 2D free fermion system can have a single or odd number of massless Dirac fermions. However, a single Dirac fermion can occur in a 2D TRI system when it is the boundary of a 3D topological insulator (*7*–*10*), which has a bulk insulating gap and odd number of gapless Dirac cones on the surface. The electrodynamics of the topological insulator is described by an additional topological term in Maxwell’s equation (*10*), and the surface state leads to striking quantum phenomena such as an image magnetic monopole induced by an electric charge (*11*) and Majorana fermions induced by the proximity effect from a superconductor (*12*–*14*).

The 3D material HgTe under strain is predicted to have a single Dirac cone on the surface (*15*). However, experiments are difficult to perform under the strain condition. The Bi_{1-δ}Sb_{δ} alloy is also predicted to be a 3D topological insulator in the narrow alloying content regime of δ = 0.07 ~ 0.22 (*16*, *17*), and a recent angle-resolved photoemission spectroscopy (ARPES) study reveals the topological nature of the surface state despite its complexity, with as many as five branches crossing the Fermi level (*E*_{F}) (*18*).

Recently, a class of stoichiometric materials, Bi_{2}Te_{3}, Bi_{2}Se_{3}, and Sb_{2}Te_{3}, were theoretically predicted to be the simplest 3D topological insulators whose surface states consist of a single Dirac cone at the Γ point (*19*). This simplicity makes them the ideal candidates to realize the magneto-electric effect (*20*). Furthermore, the predicted large bulk gap makes them possible candidates for high-temperature spintronics applications. Independent of the theoretical proposal, an ARPES study (*21*) of Bi_{2}Se_{3} reveals a single surface electron pocket with a Dirac point below *E*_{F}. However, a deep bulk electron pocket coexisting with the topologically nontrivial surface states was also observed in the same ARPES experiment. Therefore, the topological insulating behavior in this class of materials has yet to be established experimentally, which is the main goal of the present work.

We performed ARPES and transport experiments to investigate both the bulk and surface state electronic properties of (Bi_{1-δ}Sn_{δ})_{2}Te_{3} crystals (where δ represents nominal Sn concentration, incorporated to compensate for the n-type doping from vacancy and anti-site defects). Further details of the sample preparation, ARPES, and transport experiments are in the supporting online material (*22*). By scanning over the entire Brillouin zone (BZ), we confirmed that the surface states consist of a single, nondegenerate Dirac cone at the Γ point. At appropriate doping (δ = 0.67%), we found that the bulk states disappear completely at *E*_{F}, thus realizing the topological insulating behavior in this class of materials. With a much larger bulk band gap (165 meV) compared to the energy scale of room temperature (26 meV), the topological protection of the surface states in this material could lead to promising applications in low-power spintronics devices at room temperature.

Figure 1 summarizes the bulk and surface electronic structures and Fermi-surface (FS) topology of undoped Bi_{2}Te_{3}. The crystal structure of Bi_{2}Te_{3} (Fig. 1A) is of the tetradymite type, which is formed by stacking quintuple-layer groups sandwiched by three sheets of Te and two sheets of Bi within each group (*23*). Ab initio calculations predict that the undoped Bi_{2}Te_{3} is an insulator (Fig. 1B) and that the doped FS (Fig. 1C) from the bulk conduction band projected onto the surface BZ exhibits a triangular or snowflake-like electron pocket centered at the Γ point (Fig. 1C) depending on its *k _{z}* position in reciprocal space.

Actual band dispersions measured by ARPES experiments along two high-symmetry directions are shown in Fig. 1D. In addition to the broad spectra of the bulk electron pocket on top and the “M” shape valance band at bottom, as predicted in the ab initio calculation, there is an extra sharp V-shape dispersion resulting from the surface state. The linear dispersion in both plots clearly indicates a massless Dirac fermion with a velocity of 4.05 × 10^{5} m/s (2.67 eV·Å) and 3.87 × 10^{5} m/s (2.55 eV·Å) along the Γ-K and Γ-M directions, respectively (*22*), which are about 40% of the value in graphene (*6*) and agree well with our first-principle calculation [by the method described in (*19*)] that yields 2.13 and 2.02 eV·Å along the Γ-K and Γ-M directions, respectively.

This sharp surface state also forms a FS pocket in addition to the calculated FSs from bulk bands. As shown in Fig. 1, E and F(ii), in each BZ there is a hexagram-shaped FS enclosing the snowflake-like bulk FS. A broad FS map covering three adjacent BZs (Fig. 1E) confirms that there is only one such hexagram FS resulting from the V-shape Dirac-type surface state in each BZ. The spin-orbit coupling (SOC) in this material is strong. The level splitting (λ) due to SOC of Bi-6p orbital is λ = 1.25 eV (*19*), about twice that in Au (λ = 0.68 eV) (*24*). Given that our energy and momentum resolution [δ*E* < 0.016 eV and δ*k* < 0.012(1/Å) (*22*)] is better than needed to resolve even the much smaller Au surface state splitting [Δ*E* = 0.11 eV, Δ*k* = 0.023(1/Å)] (*25*), the fact that we do not observe more than one set of surface state for all dopings and under all experimental conditions—including different photon energies, polarizations, and experimental setups in different synchrotrons—rules out the possibility that the Dirac cone is spin degenerate, and we encourage future spin-resolved ARPES experiments to confirm this. This observation demonstrates that Bi_{2}Te_{3} is an ideal candidate as the parent compound for the simplest kind of 3D topological insulator (*19*)—a simplicity resembling that of the hydrogen atom in atomic physics. In contrast, graphene has two valleys with spin degeneracy, giving a total of four Dirac cones in each BZ, leading to a topological trivial state. Furthermore, because there is only one surface FS pocket in each surface BZ, the surface state will only cross *E*_{F} once between Γ and M, rather than the complex crossing of five times as observed in Bi_{0.9}Sb_{0.1} (*3*, *18*).

The surface nature of the hexagram FS resulting from the sharp V-shape dispersion is further established by a photon energy dependence study (Fig. 1F). By varying the excitation photon energy, the shape of the snowflake-like bulk FS changes from a left-pointing triangle [Fig. 1F(i)] to a right-pointing triangle [Fig. 1F(iii)] as a result of the *k _{z}* dispersion of the 3D bulk electronic structure (Fig. 1C). In contrast, the shape of the hexagram-like FS does not change with the incident photon energy, confirming its 2D nature (i.e., no

*k*dispersion). We note that the perfect Bi

_{z}_{2}Te

_{3}single crystal is predicted to be a bulk insulator, and the electron carriers observed in our experiment arise from crystal imperfections, specifically vacancies and defects (

*26*). Given the substantial bulk gap (Fig. 1D), one can tune

*E*

_{F}into the gap by doping holes to compensate for the electron carriers, thus realizing the topological insulator phase in this material. Because the surface state accommodates only a small number of carriers (orders of magnitude less than the bulk), the actual realization of the bulk insulating state by bulk doping is a challenging task. After experimenting with numerous doping levels by different dopants, we found Sn to be a suitable dopant and successfully doped Bi

_{2}Te

_{3}into its bulk insulating phase. The effect of Sn doping is demonstrated in Fig. 2, where the FSs and band dispersions from samples of four different nominal dopings are shown from panels (A) to (D), respectively.

Taking the Dirac point position as reference, one sees the doping evolution of the FSs (Fig. 2, top row) associated with the downshift of *E*_{F} (Fig. 2, middle and bottom rows). With proper doping (Fig. 2C), the topological insulator phase of Bi_{2}Te_{3} can be realized with the *E*_{F} residing inside the bulk gap. Unlike a simple circular Dirac cone, the observed surface state in Bi_{2}Te_{3} exhibits richer structure. The 3D spectra intensity plot in (*k _{x}*

_{,}

*k*,

_{y}*E*) space (Fig. 3A) and the cross sections of the Dirac-like dispersion at various binding energies (Fig. 3, B to E) are demonstrated. When approaching the Dirac point from

*E*

_{F}, the shape of the surface state FS evolves gradually from a hexagram to a hexagon, then to a circle of shrinking volume, and finally converges into a point, the Dirac point. Comparing the shape of the bulk electron FS and the surface state FS, the hexagram shape of the surface state FS is induced by the band repulsion with the snowflake-shape bulk electron pocket. Because FSs cannot have discontinuities, the “vertices” of the hexagram and hexagon are actually smoothened. From the doping evolution of the FS topology and the band dispersions shown above, we have found convincing evidence that the 0.67% Sn-doped Bi

_{2}Te

_{3}is a 3D topological insulator with a single Dirac cone and a large bulk band gap. The observations of ARPES are also supported by Hall and resistivity measurements (

*22*).

The single Dirac cone of the Bi_{2}Te_{3} family makes it the simplest model system for studying the physics of topological insulators, and the large bulk gap points to promising potential for high-temperature spintronics applications on a bulk material that is easy to produce and manipulate with current standard semiconductor technology.

## Supporting Online Material

www.sciencemag.org/cgi/content/full/1173034/DC1

Materials and Methods

Figs. S1 to S4

References

## References and Notes

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Materials and methods are available as supporting material on

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- We thank W. S. Lee, K. J. Lai, B. Moritz, and C. X. Liu for insightful discussions and C. Kucharczyk and L. Liu for assistance on crystal growth. This work was supported by the Department of Energy, Office of Basic Energy Sciences, under contract DE-AC02-76SF00515; H.J.Z., Z.F., and X.D. acknowledge the support by the NSF of China, the National Basic Research Program of China, and the International Science and Technology Cooperation Program of China.