Origins of electronic bands in the antiferromagnetic topological insulator ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$

Letter

Origins of electronic bands in the antiferromagnetic topological insulator ${MnBi}_{2} {Te}_{4}$

Chenhui Yan, Sebastian Fernandez-Mulligan, Ruobing Mei, Seng Huat Lee, Nikola Protic, Rikuto Fukumori, Binghai Yan, Chaoxing Liu, Zhiqiang Mao, and Shuolong Yang

Phys. Rev. B 104, L041102 – Published 6 July 2021

Abstract

Despite the rapid progress in understanding the first intrinsic magnetic topological insulator ${MnBi}_{2} {Te}_{4}$ , its electronic structure remains a topic under debates. Here we perform a thorough spectroscopic investigation into the electronic structure of ${MnBi}_{2} {Te}_{4}$ via laser-based angle-resolved photoemission spectroscopy. Through quantitative analysis, we estimate an upper bound of 3 meV for the gap size of the topological surface state. Furthermore, our circular dichroism measurements reveal band chiralities for both the topological surface state and quasi-2D bands, which can be well reproduced in a band hybridization model. A numerical simulation of energy-momentum dispersions based on a four-band model with an additional step potential near the surface provides a promising explanation for the origin of the quasi-2D bands. Our study represents a solid step forward in reconciling the existing controversies in the electronic structure of ${MnBi}_{2} {Te}_{4}$ , and provides an important framework to understand the electronic structures of other relevant topological materials ${MnBi}_{2 n} {Te}_{3 n + 1}$ .

Received 14 May 2021
Accepted 29 June 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L041102

Physics Subject Headings (PhySH)

Electronic structure Surface states Topological materials

Antiferromagnets Topological insulators

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chenhui Yan ¹, Sebastian Fernandez-Mulligan¹, Ruobing Mei², Seng Huat Lee², Nikola Protic¹, Rikuto Fukumori ¹, Binghai Yan ³, Chaoxing Liu², Zhiqiang Mao², and Shuolong Yang ^1,*

¹Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
²Department of Physics, Pennsylvania State University, University Park, State College, Pennsylvania 16802, USA
³Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel

^*yangsl@uchicago.edu

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Vol. 104, Iss. 4 — 15 July 2021

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Figure 1
Observation of the topological surface state and quasi-2D bands in ${MnBi}_{2} {Te}_{4}$ . (a) ARPES constant energy maps at different binding energies. [(b),(c)] Band dispersions cutting through the $Γ$ point taken with a photon energy of (b) 6.04 eV and (c) 21.2 eV, at 15 K. [(d),(e)] Zoomed-in spectra marked by the green dashed box in (b). The overlaid white crossing marks are extracted by fitting momentum distribution curves. The blue and green dashed lines represent fitting curves using (d) linear extrapolation and (e) a more complex model incorporating the band curvatures [28], respectively.
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Figure 2
Temperature-dependent band dispersions and circular dichroism in ${MnBi}_{2} {Te}_{4}$ . [(a),(b)] Band dispersions taken with a photon energy of 6.04 eV at temperatures of (a) 30 K and (b) 12 K. The energy-momentum maps are obtained by adding the spectra taken with LCP and RCP to reduce the polarization matrix element effect. [(c),(d)] Second derivative maps of the spectra in (a) and (b), respectively. The dashed line highlights the “ $S_{2}$ ” band. [(e),(f)] Circular dichroism maps of the ARPES spectra at (e) 30 K and (f) 12 K (the dashed line is a guide to the eyes), respectively. The lower branch of the Dirac cone is plotted using a different color scale as its intensity is much lower than that near the Fermi level. We adopt a two-dimensional color map, where the red-blue color contrast represents circular dichroism and the darkness represents the band intensity [30].
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Figure 3
Simulation of hybridization between the TSS and quasi-2D bands. (a) TSS and one quasi-2D band without hybridization. (b) Formed new bands after hybridization. The hybridization energy is 20 meV. (c) The chiral CD pattern of the resulting bands overlaid on the experimental CD map taken at 30 K. (d) TSS and two quasi-2D bands without hybridization. (e) Formed new bands after hybridization. The hybridization energy is 20 meV. (f) The chiral CD pattern of the resulting bands overlaid on the experimental CD map taken at 12 K. The simulated band structures are obtained by solving 2-band or 3-band Hamiltonians with hybridization terms, as discussed in the main text. The simulated CD patterns are obtained by using the proportionate contributions from the unhybridized bands. The proportions are computed in the Hamiltonian diagonalization procedure.
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Figure 4
Slab calculations of the TSS and quantum-well states (QWS) in ${MnBi}_{2} {Te}_{4}$ . (a) Illustration of the model for a ${MnBi}_{2} {Te}_{4}$ slab. The total thickness of the slab is $L$ , and the thickness of each monolayer is $d$ . $V_{0}$ , $g$ , and $Γ$ stand for the surface potential, the antiferromagnetic coupling strength, and the scattering rate, respectively. The magnetic moments are represented by red and blue arrows, which flip directions in each neighboring layer. A step potential with length $l$ and depth $V_{0}$ is invoked to achieve QWS. (b) Density of states (DOS) plot for $V_{0} = 0.1$ eV, $g = 0$ eV with momentum-dependent $Γ = 0.025 + 2 k_{| |}^{2}$ . Around four surface layers are considered. There is a quasi-2D band between the surface state and conduction bands. (c) Energy distribution curves taken at $k_{| |} = 0$ [the red and blue ones correspond to the theoretical spectra in (b) and (d), respectively]. (d) DOS plot for $V_{0} = 0.1$ eV, $g = 0.15$ eV with momentum-dependent $Γ = 0.025 + 2 k_{| |}^{2}$ . The quasi-2D band splits into two subbands and the surface state is gapless.
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Physical Review B

covering condensed matter and materials physics

Origins of electronic bands in the antiferromagnetic topological insulator ${MnBi}_{2} {Te}_{4}$

Chenhui Yan, Sebastian Fernandez-Mulligan, Ruobing Mei, Seng Huat Lee, Nikola Protic, Rikuto Fukumori, Binghai Yan, Chaoxing Liu, Zhiqiang Mao, and Shuolong Yang

Phys. Rev. B 104, L041102 – Published 6 July 2021

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Physical Review B

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Origins of electronic bands in the antiferromagnetic topological insulator MnBi2Te4

Chenhui Yan, Sebastian Fernandez-Mulligan, Ruobing Mei, Seng Huat Lee, Nikola Protic, Rikuto Fukumori, Binghai Yan, Chaoxing Liu, Zhiqiang Mao, and Shuolong Yang

Phys. Rev. B 104, L041102 – Published 6 July 2021

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Origins of electronic bands in the antiferromagnetic topological insulator ${MnBi}_{2} {Te}_{4}$