Hinged quantum spin Hall effect in antiferromagnetic topological insulators

Rapid Communication

Hinged quantum spin Hall effect in antiferromagnetic topological insulators

Yue-Ran Ding, Dong-Hui Xu, Chui-Zhen Chen, and X. C. Xie

Phys. Rev. B 101, 041404(R) – Published 13 January 2020

Abstract

In this work, we predict a hinged quantum spin Hall (HQSH) effect featured by a pair of counterpropagating chiral hinge modes in antiferromagnetic (AFM) topological insulator (TI) multilayers. This pair of chiral hinge modes are localized on the hinges of the top and bottom surfaces of the AFM TI multilayers. Unlike the conventional QSH effect, the HQSH effect survives the breaking of time-reversal symmetry (TRS) and thus represents a different kind of topological phenomenon. The pair of counterpropagating chiral hinge modes are sustainable to inelastic scattering and TRS-breaking disorder, which can be observed in macroscopic samples. We show that this HQSH effect can be understood as a three-dimensional generalization of the Su-Schrieffer-Heeger model. At last, we propose that the HQSH effect can be realized in newly found intrinsic AFM TI materials $({MnBi}_{2} {Te}_{4})_{m} {({Bi}_{2} {Te}_{3})}_{n}$ or magnetic-doped TI multilayers by current experimental setups.

Received 26 November 2019

DOI:https://doi.org/10.1103/PhysRevB.101.041404

Physics Subject Headings (PhySH)

Hall effect Topological insulators Transport phenomena

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yue-Ran Ding¹, Dong-Hui Xu ², Chui-Zhen Chen ^1,*, and X. C. Xie^3,4,5,†

¹Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou 215006, China
²Department of Physics, Hubei University, Wuhan 430062, China
³International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
⁴CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
⁵Beijing Academy of Quantum Information Sciences, West Bld.3, No.10 Xibeiwang East Rd., Haidian District, Beijing 100193, China

^*czchen@suda.edu.cn
^†xcxie@pku.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 101, Iss. 4 — 15 January 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic plots of alternatively stacked AFM TIs and the phase diagram. Two adjacent magnetic TI layers in opposite magnetization carrying chiral states with opposite chirality (marked by red and black arrows) form a composite layer. (a) Magnetic TIs between two adjacent composite layers are hybridized pairwise when the interlayer coupling $t_{2}$ dominates over the intralayer coupling $t_{1}$ , leaving two chiral edge modes localized on the top and bottom layers. They are equivalent to a pair of helical edge modes in the QSH effect. On the contrary, (b) all the chiral edge modes within the composite layers hybridize in pairs if $t_{1}$ dominates. (c) Phase diagram of AFM TIs on the plane of $t_{2} / t_{1}$ and $t_{3} / t_{1}$ , with $t_{2, 3}$ hopping between two adjacent composite layers. The two red stars on red line $(t_{3} = 0)$ indicate the parameter region studied in Fig. 2.
Reuse & Permissions
Figure 2
The energy band structure of AFM TI multilayers with the width $N_{y} = 16$ , thickness $N_{z}$ , and intralayer coupling $t_{1}$ and interlayer coupling $t_{2}$ . (a) The two chiral edge modes are hybridized and gapped out for $N_{z} = 1$ . (b),(c) For $t_{1} = 0.04 < t_{2} = 0.1$ , the chiral edge modes in different composite layers are hybridized and gapped out in pairs, leaving two isolated chiral edge modes [see the dashed red and black lines in (b) $N_{z} = 2$ and (c) $N_{z} = 6]$ localized on the top and bottom layers. (e) Local density of state with $N_{x} \times N_{y} \times N_{z} = 32 \times 16 \times 6$ at $E = 0.01$ . (d) For $t_{1} = 0.08 > t_{2} = 0.04$ , all the chiral edge modes with opposite chirality in same composite layers are coupled and gapped out in pairs with $N_{z} = 6$ .
Reuse & Permissions
Figure 3
Plots of (a)–(c) the two-terminal conductance $G_{12, 12}$ and (d) nonlocal conductance $G_{14, 23}$ versus the Fermi energy $E$ for different thickness (a) $N_{z} = 1$ , (b) 2, and [(c),(d)] 6 at various disorder strength $W$ . The error bar denotes conductance fluctuation. The three sets of model parameters are the same as those in Figs. 2–2, respectively, with the sample size $N_{x} \times N_{y} \times N_{z} = 64 \times 16 \times N_{z}$ in Figs. 3–3 and $96 \times 16 \times 6$ in Fig. 3. The insets of (b) and (d) show a two-terminal device and a $π$ -bar device, respectively.
Reuse & Permissions
Figure 4
(a) Two-terminal conductance $G_{12, 12}$ of the HQSH versus the Fermi energy $E$ for various dephasing strength $Γ$ . (b) Phase coherent length $L_{ϕ}$ as a function of $Γ$ . (c) $G_{12, 12}$ of the conventional QSH in the Bernevig-Hughes-Zhang (BHZ) model versus $E$ for various $Γ$ . (d) $G_{12, 12}$ versus $Γ$ for the HQSH and the conventional QSH at $E = 0.02$ . The parameters of the Dirac Hamiltonian in the BHZ model are the same as the $h_{D}$ in the HQSH model. The sample size is $N_{x} \times N_{y} \times N_{z} = 32 \times 16 \times 6$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics