Topological surface states and Dirac point tuning in ternary topological insulators

M. Neupane, S.-Y. Xu, L. A. Wray, A. Petersen, R. Shankar, N. Alidoust, Chang Liu, A. Fedorov, H. Ji, J. M. Allred, Y. S. Hor, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, R. J. Cava, and M. Z. Hasan

Phys. Rev. B 85, 235406 – Published 4 June 2012

Abstract

Using angle-resolved photoemission spectroscopy, we report electronic structure for representative members of ternary topological insulators. We show that several members of this family, such as Bi $_{2}$ Se $_{2}$ Te, Bi $_{2}$ Te $_{2}$ Se, and GeBi $_{2}$ Te $_{4}$ , exhibit a singly degenerate Dirac-like surface state, while Bi $_{2}$ Se $_{2}$ S is a fully gapped insulator with no measurable surface state. One of these compounds, Bi $_{2}$ Se $_{2}$ Te, shows tunable surface state dispersion upon its electronic alloying with Sb (Sb $_{x}$ Bi $_{2 - x}$ Se $_{2}$ Te series). Other members of the ternary family such as GeBi $_{2}$ Te $_{4}$ and BiTe $_{1.5}$ S $_{1.5}$ show an in-gap surface Dirac point, the former of which has been predicted to show nonzero weak topological invariants such as (1;111); thus belonging to a different topological class than BiTe $_{1.5}$ S $_{1.5}$ . The measured band structure presented here will be a valuable guide for interpreting transport, thermoelectric, and thermopower measurements on these compounds. The unique surface band topology observed in these compounds contributes towards identifying designer materials with desired flexibility needed for thermoelectric and spintronic device fabrication.

Received 16 March 2012

DOI:https://doi.org/10.1103/PhysRevB.85.235406

Authors & Affiliations

M. Neupane¹, S.-Y. Xu¹, L. A. Wray^1,2, A. Petersen¹, R. Shankar¹, N. Alidoust¹, Chang Liu¹, A. Fedorov², H. Ji³, J. M. Allred³, Y. S. Hor³, T.-R. Chang⁴, H.-T. Jeng^4,5, H. Lin⁶, A. Bansil⁶, R. J. Cava³, and M. Z. Hasan¹

¹Joseph Henry Laboratory, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94305, USA
³Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
⁴Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
⁵Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
⁶Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

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Vol. 85, Iss. 23 — 15 June 2012

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Figure 1
Crystal structure and topological surface states in ternary spin-orbit compounds: $B_{2} X_{2} X^{'}$ , $A B_{2} X_{4}$ , $A_{2} B_{2} X_{5}$ , and $A B_{4} X_{7}$ ( $A$ $=$ Pb, Ge; $B$ $=$ Bi, Sb; $X, X^{'}$ $=$ Se, Te). (a)–(d) crystal structure and calculated bulk and surface band structures for the (111) surface of $B_{2} X_{2} X^{'}$ , $A B_{2} X_{4}$ , $A_{2} B_{2} X_{5}$ , and $A B_{4} X_{7}$ , respectively. The bulk band projections are represented by shaded areas.Reuse & Permissions
Figure 2
Observation of an isolated Dirac node in Sb $_{x}$ Bi $_{2 - x}$ Se $_{2}$ Te via Dirac point tuning. (a) ARPES $k$ - $E$ maps along the $\bar{Γ}$ - $\bar{M}$ momentum direction for Sb $_{x}$ Bi $_{2 - x}$ Se $_{2}$ Te with $x = 0$ , 0.8, 1, 1.2, and 1.6. The blue dash line marks the binding energy of the Dirac point for $x = 0$ . (b) Binding energy of the Dirac point as a function of $x$ . Inset shows the definition of the Dirac point binding energy. (c) Photon energy dependence of ARPES spectra for Sb $_{x}$ Bi $_{2 - x}$ Se $_{2}$ Te ( $x = 1$ ). The isolated Dirac point is observed to be in close vicinity to the Fermi level.Reuse & Permissions
Figure 3
First-principles band structures of Sb $_{x}$ Bi $_{2 - x}$ Se $_{2}$ Te based on slab calculations with six quintuple layers for (a) $x = 0$ , (b) 1, and (c) 1.67. The size of the blue dots represents the fraction of electronic charge residing in the surface layers. All three doping levels show gapless Dirac-cone-like surface bands.Reuse & Permissions
Figure 4
(a) ARPES $k$ - $E$ maps along the high symmetry directions $\bar{Γ} - \bar{M}$ and $\bar{Γ} - \bar{K}$ of Bi $_{2}$ Te $_{2}$ Se for three different samples: Bi $_{2}$ Te $_{2}$ Se “native 1,” Bi $_{2}$ Te $_{2}$ Se “native 2,” and Bi $_{2}$ Te $_{2}$ Se “ $n$ type,” respectively (see text). Single Dirac cone on the cleaved (111) surface is observed. (b) Resistivity profiles of native Bi $_{2}$ Te $_{2}$ Se, compared to native and improved Bi $_{2}$ Te $_{3}$ are presented in linear (left) and logarithmic scale (right). (c) ARPES maps of constant energy contours presented at several binding energies for the “native 2” sample. (d) Three-dimensional illustration of the electronic structure in (c).Reuse & Permissions
Figure 5
Sulfur substitution in Bi $_{2}$ $X$ $_{3}$ ( $X$ $=$ Se, Te). ARPES $k$ - $E$ maps for (a) Bi $_{2}$ Se $_{3}$ and Bi $_{2}$ Se $_{2}$ S and (b) Bi $_{2}$ Te $_{3}$ and Bi $_{2}$ Te $_{1.5}$ S $_{1.5}$ . Inset in (a) shows the zoom of the Bi $_{2}$ Se $_{3}$ spectrum near the Dirac point. Bi $_{2}$ Se $_{2}$ S is a trivial insulator with a bulk insulating gap of $\sim$ 1.2 eV, while Bi $_{2}$ Te $_{1.5}$ S $_{1.5}$ is a topological insulator with single Dirac cone. (c) Photon energy dependence measurements for Bi $_{2}$ Te $_{1.5}$ S $_{1.5}$ , showing isolated nature of the Dirac point. The measured photon energies are marked on each panel. All data are presented along $\bar{Γ}$ - $\bar{M}$ momentum direction. (d) First-principles band structures of Bi $_{2}$ Te $_{1.5}$ S $_{1.5}$ based on slab calculations with six quintuple layers. The size of the blue dots represents the fraction of electronic charge residing in the surface layers.Reuse & Permissions
Figure 6
(a) ARPES $k$ - $E$ maps of GeBi $_{2}$ Te $_{4}$ along $\bar{M}$ - $\bar{Γ}$ - $\bar{M}$ and $\bar{K}$ - $\bar{Γ}$ - $\bar{K}$ high-symmetry directions. (b) ARPES intensity maps for various binding energies between $E_{F}$ and 0.4 eV. (c) ARPES spectra of GeBi $_{2}$ Te $_{4}$ along the $\bar{Γ}$ - $\bar{K}$ direction as potassium is deposited. Average thickness of the deposition layer is indicated on the top of each panel. (d) Energy distribution curves (EDCs) for the ARPES spectra shown in (c).Reuse & Permissions

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