Positron surface state as a spectroscopic probe for characterizing surfaces of topological insulator materials

Vincent Callewaert, K. Shastry, Rolando Saniz, Ilja Makkonen, Bernardo Barbiellini, Badih A. Assaf, Donald Heiman, Jagadeesh S. Moodera, Bart Partoens, Arun Bansil, and A. H. Weiss

Phys. Rev. B 94, 115411 – Published 6 September 2016

Abstract

Topological insulators are attracting considerable interest due to their potential for technological applications and as platforms for exploring wide-ranging fundamental science questions. In order to exploit, fine-tune, control, and manipulate the topological surface states, spectroscopic tools which can effectively probe their properties are of key importance. Here, we demonstrate that positrons provide a sensitive probe for topological states and that the associated annihilation spectrum provides a technique for characterizing these states. Firm experimental evidence for the existence of a positron surface state near ${Bi}_{2} {Te}_{2} Se$ with a binding energy of $E_{b} = 2.7 \pm 0.2 eV$ is presented and is confirmed by first-principles calculations. Additionally, the simulations predict a significant signal originating from annihilation with the topological surface states and show the feasibility to detect their spin texture through the use of spin-polarized positron beams.

Received 24 December 2015
Revised 16 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.115411

Physics Subject Headings (PhySH)

Topological defects

Topological insulators Topological materials

Positron annihilation spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Vincent Callewaert^1,*, K. Shastry², Rolando Saniz¹, Ilja Makkonen³, Bernardo Barbiellini⁴, Badih A. Assaf^4,5, Donald Heiman⁴, Jagadeesh S. Moodera^6,7, Bart Partoens¹, Arun Bansil⁴, and A. H. Weiss²

¹Department of Physics, Universiteit Antwerpen, Antwerpen 2020, Belgium
²Department of Physics, University of Texas at Arlington, Arlington, Texas 76019, USA
³Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Espoo, Finland
⁴Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
⁵Département de Physique, Ecole Normale Supérieure, CNRS, PSL Research University, 24 rue Lhomond, 75005 Paris, France
⁶Department of Physics, MIT, Cambridge, Massachusetts 02139, USA
⁷Francis Bitter Magnet Laboratory, MIT, Cambridge, Massachusetts 02139, USA

^*vincent.callewaert@uantwerpen.be

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Vol. 94, Iss. 11 — 15 September 2016

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Images

Figure 1
(a) Schematic of the PAES mechanism. In the first step, a positron (blue) annihilates with an electron (red) occupying a core level and creates a highly unstable hole. In the second step, an electron from a higher level fills this hole and transfers the energy difference between the two levels to a second electron. If the energy difference is sufficiently large and the second electron is close enough to the surface, it can traverse the surface dipole and escape from the sample. The measured outgoing electron energy corresponds with the transferred energy in the Auger process minus the energy difference between the second electron's state and the vacuum level. (b) Results of the PAES measurements on the ${Bi}_{2} {Te}_{2} Se$ sample in which Auger signals from the different elements are indicated.
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Figure 2
(a) Schematic of the AMPS mechanism. The left part of the diagram shows the incident positron (blue) that drops in the image potential well. In this process, the positron transfers an energy $Δ E$ , determined by the incident kinetic-energy $E_{p}$ and the binding energy of the SS $E_{b}$ , to an electron of the system through a virtual photon as indicated in the right part of the figure. If the energy difference is larger than the electronic work-function $ϕ^{-}$ , the electron can escape to the vacuum. (b) The measured low-energy Auger signals for the ${Bi}_{2} {Te}_{2} Se$ sample. The outgoing electron energy is determined by the transferred energy $Δ E$ minus the required energy to escape from the sample. The different lines show the result for varying energies of the incident positrons. (c) The integrated peak amplitudes of the low-energy Auger signal associated with the AMPS mechanism as a function of the incident positron energy.
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Figure 3
Potential obtained for the Ps model with the values for $C, z_{0}, λ$ , and $ϕ^{+}$ mentioned in the discussion. For the electronic work function, we took $ϕ^{-} = 4.612 eV$ , which gives a Ps work function of $ϕ^{Ps} = 0.2 eV$ and lies in the middle of the range of values for which the model gives an activation energy in good agreement with the experimental result.
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Figure 4
Overlap of the positron SS with the Dirac states. (a) Planar average of the positron (blue) and electron (red/yellow) densities associated with the Dirac states below the Fermi energy for two different values of the chemical potential $μ^{-}$ . (b) Density of the topological surface state and the positron in the same spatial region as panel (a). The progressively lighter blue isosurfaces show the positron density at 80%, 20%, and 2% of the maximum value, respectively, and the red isosurfaces show the electronic charge density associated with the electron states on the Dirac cone below the Fermi level at 10% of the maximum value. The Bi, Te, and Se atoms are shown in purple, brown, and green colors, respectively.
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Figure 5
Theoretical momentum densities. (a) LCW map with the chemical potential located at the Fermi level. (b) LCW map with the chemical potential raised by 0.2 eV. The dashed lines denote the location of the Fermi surface as derived from the electronic band structure. (c) High-resolution cuts through the LCW map along the $Γ - M$ direction for different values of the chemical potential. The inset shows the band structure near the Fermi level $(E_{F} = 0.0 eV)$ .
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Figure 6
Difference between the LCW maps obtained with different doping levels of the Dirac cone: $μ^{-} = E_{F} + 0.2 eV$ and $μ^{-} = E_{F}$ . The top left pane of the figure shows the total amplitude of the LCW map. The top right, bottom left, and bottom right figures show the magnetization components along the $x, y$ , and $z$ axes, respectively. We only show the result zoomed in around the $Γ$ point as the difference between the LCW maps is exactly zero in the rest of the Brillouin zone. The inner and othermost edges of the nonzero part in the plots correspond with the dashed lines shown in Figs. 5 and 5, respectively. The length of the reciprocal axes is $| b | = 1.688 Å^{- 1}$ , and the amplitudes are given in ${{ps}^{- 1} Å}^{2}$ . (It is readily seen that the units of the LCW map are in ${{ps}^{- 1} Å}^{2}$ by realizing that the integral over the LCW map yields the positron's annihilation rate, or in the case of the magnetic LCW maps, the difference in annihilation rate between two measurements with opposite spin polarizations for the positron.)
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