## Abstract

In addition to a bulk energy gap, topological insulators accommodate a conducting, linearly dispersed Dirac surface state. This state is predicted to become massive if time reversal symmetry is broken, and to become insulating if the Fermi energy is positioned inside both the surface and bulk gaps. We introduced magnetic dopants into the three-dimensional topological insulator dibismuth triselenide (Bi_{2}Se_{3}) to break the time reversal symmetry and further position the Fermi energy inside the gaps by simultaneous magnetic and charge doping. The resulting insulating massive Dirac fermion state, which we observed by angle-resolved photoemission, paves the way for studying a range of topological phenomena relevant to both condensed matter and particle physics.

Topological insulators are a state of matter that may serve as a platform for both fundamental physics phenomena and technological applications, such as spintronics and quantum information processing. Since their discovery in two-dimensional (2D) HgTe quantum wells (*1*, *2*), topological insulators have been at the core of a very active research area (*3*–*11*). Recently, a class of 3D compounds—Bi_{2}Te_{3}, Bi_{2}Se_{3}, and Sb_{2}Te_{3}—were identified (*12*–*14*) with the surface state consisting of a single Dirac cone. The conducting surface states of topological insulators are immune to localization as long as the disorder potential does not violate time reversal symmetry (TRS) (*4*, *5*, *9*), and one way to destroy this robust surface metallicity is to break the TRS by introducing magnetic order (*5*). In the bulk, a topological insulator doped with magnetic impurities can have a long-range magnetic order both in the metallic (*15*, *16*) and insulating (*17*) phases; on the surface, such a long-range magnetic order can also be formed independent of the bulk magnetic ordering, as the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induced by the Dirac fermions is generally ferromagnetic when the Fermi energy (*E*_{F}) is close to the Dirac point (*18*). Both effects can lead to the breaking of TRS, resulting in a gap opening at the Dirac point that makes the surface Dirac fermion massive; indeed, we find that the Dirac gap can be observed in magnetically doped samples with or without bulk ferromagnetism (*19*). Furthermore, if *E*_{F} can be tuned into this surface-state gap, an insulating massive Dirac fermion state is formed; this state may support many striking topological phenomena, such as the image magnetic monopole induced by a point charge (*20*, *21*), the half quantum Hall effect on the surface with a Hall conductance of *e*^{2}/2*h*, and a topological contribution to the Faraday and Kerr effects (*5*). In addition, this state is a concrete realization of the “θ vacuum” state of axion physics in a condensed matter system (*5*), and thus has implications for particle physics and cosmology (*22*). Finally, a tunable energy gap at the surface Dirac point provides a means to control the surface electric transport, which is of great importance for applications.

The insulating massive Dirac fermion state is challenging to realize, because there are two critical requirements that must be simultaneously satisfied: (i) A gap should open at the Dirac point of the topological surface state (as a result of the breaking of TRS); (ii) the *E*_{F} of the system must reside inside both the surface and bulk gaps. We report the realization of this state with simultaneous fulfillment of both requirements in the topological insulator Bi_{2}Se_{3} by introducing an exact amount of magnetic dopants to break the TRS and precisely controlling the *E*_{F} position.

We performed angle-resolved photoemission spectroscopy (ARPES) to investigate the electronic structures of intrinsic, nonmagnetically doped, and magnetically doped Bi_{2}Se_{3} (*19*). Figure 1 illustrates the measured band structure of undoped Bi_{2}Se_{3}. Similar to Bi_{2}Te_{3} (*14*), besides the Fermi surface (FS) pocket from the surface-state band (SSB), there is also a FS pocket from the bulk conduction band (BCB) (Fig. 1, A to D) due to the Se deficiencies and the Bi-Se intersite defects. The bottom of the BCB is located at 190 meV above the Dirac point (Fig. 1, A and C), indicating a direct bulk gap (*19*). The in-gap Dirac point makes Bi_{2}Se_{3} a better candidate for realizing the insulating massive Dirac fermion state than Bi_{2}Te_{3}, in which the Dirac point is below the top of the bulk valence band (BVB) (*14*), thus demanding a much larger surface energy gap for *E*_{F} to reside inside both the surface and bulk gaps. The cross-sectional plot of the band structure (Fig. 1B) shows how the SSB evolves from the Dirac point to a hexagonal shape at *E*_{F}. Unlike the Bi_{2}Te_{3} band structure, where the SSB FS starts being warped at energies close to the BCB minimum (*14*) and becomes a concave hexagram, the SSB FS of Bi_{2}Se_{3} remains convex hexagonal even in the presence of the BCB. This difference will be reflected in other experiments, such as scanning tunneling microscopy/spectroscopy (STM/STS), where the surface quasi-particle interference around defects can be suppressed in Bi_{2}Se_{3} but not in Bi_{2}Te_{3}, where the concave SSB FS shape favors such scattering along specific directions (*23*–*27*).

The surface nature of the hexagonal SSB FS was confirmed by the photon energy–dependent ARPES (Fig. 1D), where its nonvarying shape with different excitation photon energies indicates its 2D nature. By contrast, the shape and the existence of the inner BCB FS pocket changes markedly because of its 3D nature with strong *k*_{z} dispersion.

In the presence of TRS, the SSB of Bi_{2}Se_{3} is degenerate at the Dirac point, which connects the upper- and lower-surface Dirac cone (Fig. 2B) even if the system is perturbed by nonmagnetic dopants (Fig. 2A). This is confirmed by the ARPES measurements (Fig. 2, C and D), where the band structures of an intrinsic sample and a nominally 10% Tl-doped sample are shown, respectively. In both cases, the continuity at the Dirac point is indicated by the strong spectral intensity (left subpanels) and the single-peak structure of the energy distribution curve (EDC) at the Dirac point (right subpanels). In Fig. 2D, the charge doping effect of Tl is clearly shown by the marked shift of *E*_{F} into the bulk gap (*E*_{F} – *E*_{D} = 160 meV). Nonetheless, the topology of the SSB remains the same with a continuous Dirac point (*19*).

The TRS protection of the Dirac point can be lifted by magnetic dopants (Fig. 2E), resulting in a gap that separates the upper and lower branches of the Dirac cone (Fig. 2F). This is illustrated in the band structure (Fig. 2, G and H) of two Fe-doped samples. Unlike nonmagnetically doped samples, for both Fe-doped samples, the SSB dispersion at the Dirac point is broken, as indicated by the suppressed intensity regions in the spectral density plots (left subpanels) and the twin-peak structure around the Dirac point in the EDC plots (right subpanels). The data have sufficient *k*-space sampling density to reveal the qualitative difference between the nonmagnetic and magnetic dopants: One always finds a single-peak structure in as-grown and nonmagnetically doped samples, whereas the twin-peak structure is present only in magnetically doped samples (*19*). By fitting the twin-peak structure with two Lorentzian peaks (insets in EDC plots of Fig. 2, G and H), the gap size can be acquired, showing a larger value (~50 meV) in Fig. 2H than that (~44 meV) in Fig. 2G. This trend (*19*) is consistent with the increase of the magnetic moment upon increasing the magnetic dopant concentration.

The SSB gap formation at the Dirac point with broken TRS is the first step in realizing the insulating massive Dirac fermion state; the second step is to tune the *E*_{F} into this gap. In the Fe-doped Bi_{2}Se_{3}, however, *E*_{F} was found to always reside above the Dirac point (similar to undoped Bi_{2}Se_{3}), making the material n-type (Fig. 2, G and H). To remove these excess n-type carriers while maintaining the magnetic doping effect, we changed the dopant from Fe to Mn, another magnetic material with one less valence electron than Fe. Indeed, Mn dopants not only introduce magnetic moments into the system, but also naturally p-dope the samples. The measurements on an optimally doped sample (*19*) show *E*_{F} residing just inside the SSB gap (Fig. 3B). By comparing the leading edge of the EDC at the Γ point to *E*_{F} (Fig. 3C; also shown is an Au reference spectrum), we found a 7-meV difference, indicating a SSB Dirac gap of at least 7 meV (Fig. 3A). Such a gap suggests a ferromagnetic order of the Mn dopants on the surface, which can be induced by the ferromagnetic spin-spin interaction mediated by the surface states (*18*). This optimally doped sample thus fully realizes the insulating massive Dirac fermion state and provides a model system for studying striking topological phenomena (*5*, *20*–*22*).

To maintain this insulating massive Dirac fermion state at higher temperatures requires a further increase of the Dirac gap (while keeping *E*_{F} inside it). However, because of the hole-doping effect of Mn dopants, one cannot simply increase the Mn concentration in (Bi_{1–δ}Mn_{δ})_{2}Se_{3} to acquire a larger Dirac gap, as the system will become p-type before the gap magnitude increases appreciably (*19*). However, we found that it was possible to introduce many Fe dopants into Bi_{2}Se_{3} to increase the gap size without substantially altering the *E*_{F} position relative to the undoped Bi_{2}Se_{3}; if we can then move *E*_{F} into the gap by introducing additional p-type dopants, we can achieve a larger gap while preserving the insulating nature of the state.

Figure 4 demonstrates the full range of *E*_{F} tuning by introducing such p-type doping, with three doping regions and the topological transport point (where *E*_{F} coincides with the Dirac point) shown in Fig. 4A. By either surface doping [Fig. 4B and (*19*)] or bulk doping (Fig. 4, C to F), we were able to tune the *E*_{F} to any of the regions defined in Fig. 4A. The ability to convert the original n-type sample to p-type by surface doping (Fig. 4B, region III) is critical for applications requiring both types of carriers or p-n junctions. On the other hand, full-range bulk doping (Fig. 4, C to F) has advantages over surface doping in bulk applications.

## Supporting Online Material

www.sciencemag.org/cgi/content/full/329/5992/659/DC1

Materials and Methods

SOM Text

Figs. S1 to S6

Movies S1 to S3

References