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Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator

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Science  06 Aug 2010:
Vol. 329, Issue 5992, pp. 659-662
DOI: 10.1126/science.1189924

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 (Bi2Se3) 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 (311). Recently, a class of 3D compounds—Bi2Te3, Bi2Se3, and Sb2Te3—were identified (1214) 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 (EF) 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 EF 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 e2/2h, 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 EF 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 Bi2Se3 by introducing an exact amount of magnetic dopants to break the TRS and precisely controlling the EF position.

We performed angle-resolved photoemission spectroscopy (ARPES) to investigate the electronic structures of intrinsic, nonmagnetically doped, and magnetically doped Bi2Se3 (19). Figure 1 illustrates the measured band structure of undoped Bi2Se3. Similar to Bi2Te3 (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 Bi2Se3 a better candidate for realizing the insulating massive Dirac fermion state than Bi2Te3, 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 EF 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 EF. Unlike the Bi2Te3 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 Bi2Se3 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 Bi2Se3 but not in Bi2Te3, where the concave SSB FS shape favors such scattering along specific directions (2327).

Fig. 1

Electronic band structure of undoped Bi2Se3 measured by ARPES. (A) The bulk conduction band (BCB), bulk valence band (BVB), and surface-state band (SSB) are indicated, along with the Fermi energy (EF), the bottom of the BCB (EB), and the Dirac point (ED). (B) Constant-energy contours of the band structure show the SSB evolution from the Dirac point to a hexagonal shape (green dashed lines). (C) Band structure along the K-Γ-K direction, where Γ is the center of the hexagonal surface Brillouin zone (BZ), and the K and M points [see (D)] are the vertex and the midpoint of the side of the BZ, respectively (14). The BCB bottom is ~190 meV above ED and 150 meV below EF. (D) Photon energy–dependent FS maps (symmetrized according to the crystal symmetry). Blue dashed lines around the BCB FS pocket indicate their different shapes.

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 kz dispersion.

In the presence of TRS, the SSB of Bi2Se3 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 EF into the bulk gap (EFED = 160 meV). Nonetheless, the topology of the SSB remains the same with a continuous Dirac point (19).

Fig. 2

(A and B) A nonmagnetically doped topological insulator with a Dirac point connecting the upper and lower Dirac cones as in the undoped case. (C) Band structure along the K-Γ-K direction of undoped Bi2Se3. Left and right subpanels show the ARPES spectral intensity plot and a stacking plot of the energy distribution curves (EDCs), respectively. The red curve in the right subpanel indicates the EDC at the Γ point. Inset: EDC at the Γ point (red), fitted with a Lorentzian peak (green) on the Shirley background (black); the total fitting function is shown in blue. The same convention is used in (D), (G), and (H). (D) Band structure for a Tl-doped sample, (Bi0.9Tl0.1)2Se3. The Dirac point remains continuous. (E and F) A magnetically doped topological insulator with a broken Dirac point and a gap separating the upper and lower Dirac cones. (G and H) Band structure of two Fe-doped samples from two growth batches with melt composition (Bi0.88Fe0.12)2Se3.7 and (Bi0.84Fe0.16)2Se3.7, respectively. At the Dirac point, the reduced spectral intensity (left subpanels) and the twin-peak structure in the EDCs (right subpanels) indicate a gap formation.

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 EF into this gap. In the Fe-doped Bi2Se3, however, EF was found to always reside above the Dirac point (similar to undoped Bi2Se3), 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 EF residing just inside the SSB gap (Fig. 3B). By comparing the leading edge of the EDC at the Γ point to EF (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, 2022).

Fig. 3

Realization of the insulating massive Dirac fermion state by simultaneous magnetic and charge doping. (A) Gap formation at the Dirac point (caused by magnetic impurities on the surface) and the in-gap EF position. The occupied and unoccupied Dirac cones are shown in blue and gray, respectively; Δ is the energy difference between the top of the occupied Dirac cone and EF. (B) ARPES spectra intensity plot of the band structure along the K-Γ-K direction of Mn-doped sample (Bi0.99Mn0.01)2Se3 showing the EF inside the surface Dirac gap. Inset: close-up of the dispersion in the vicinity of EF, indicating a gap between the leading edge of the SSB and EF. Vertical white dashed line shows the location of the EDC plotted in (C). (C) Comparison between the Γ point EDC (blue) and EF shows a leading-edge gap of 7 meV (EDC on the full energy scale is plotted in the inset). A reference EDC from a polycrystalline Au sample whose leading edge, as expected, coincides with EF is shown in red.

To maintain this insulating massive Dirac fermion state at higher temperatures requires a further increase of the Dirac gap (while keeping EF inside it). However, because of the hole-doping effect of Mn dopants, one cannot simply increase the Mn concentration in (Bi1–δMnδ)2Se3 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 Bi2Se3 to increase the gap size without substantially altering the EF position relative to the undoped Bi2Se3; if we can then move EF 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 EF tuning by introducing such p-type doping, with three doping regions and the topological transport point (where EF 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 EF 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.

Fig. 4

Full-range control of EF position by surface or bulk doping. (A) Different carrier type regions: n-type (region I), bulk insulating (region II), Dirac transport and p-type (region III) determined by the EF position. (B) Evolution of the band structure (along the M-Γ-M direction) by photon-assisted surface doping with O2 , where the unit Langmuir (L) corresponds to an exposure of 10–6 torr·s (19). The blue dashed line traces the upshift of the Dirac point with the O2 doping. Green dashed lines indicate the dosages that separate the three doping regions shown in (A): At 0.95L O2 dosage, the BCB bottom reaches EF; at 3.6L, the Dirac point reaches EF; and beyond 3.6L, the Dirac point is above EF. (C to F) Bulk doping: the FS and the band structure of (C) nominally undoped Bi2Se3, showing the coexistence of BCB and SSB FS pockets; (D) Se-rich sample (melt composition Bi1.7Se3.3) with only an SSB FS, and EF residing inside the bulk gap (EFED = 145 meV); (E) Mg-doped (Bi0.999Mg0.001)2Se3 sample with a point-like FS and EF precisely at the Dirac point; and (F) more richly Mg-doped (Bi0.998Mg0.002)2Se3 sample driven into p-type, with a p-type FS and the Dirac point above EF.

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

References and Notes

  1. See supporting material on Science Online.
  2. Supported by the Department of Energy, Office of Basic Energy Science, under contract DE-AC02-76SF00515.
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