Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials

Abstract

The interplay of magnetism and topology is a key research subject in condensed matter physics, which offers great opportunities to explore emerging new physics, such as the quantum anomalous Hall (QAH) effect, axion electrodynamics, and Majorana fermions. However, these exotic physical effects have rarely been realized experimentally because of the lack of suitable working materials. Here, we predict a series of van der Waals layered MnBi₂Te₄-related materials that show intralayer ferromagnetic and interlayer antiferromagnetic exchange interactions. We find extremely rich topological quantum states with outstanding characteristics in MnBi₂Te₄, including an antiferromagnetic topological insulator with the long-sought topological axion states on the surface, a type II magnetic Weyl semimetal with one pair of Weyl points, as well as a collection of intrinsic axion insulators and QAH insulators in even- and odd-layer films, respectively. These notable predictions, if proven experimentally, could profoundly change future research and technology of topological quantum physics.

Fig. 1. The MB₂T₄-family materials (MB₂T₄: M = transition-metal or rare-earth element, B = Bi or Sb, T = Te, Se, or S) using MnBi₂Te₄ as an example.

(A) Monolayer MB₂T₄ with an FM M layer, whose easy axis is out of plane for MB₂T₄. The monolayer is predicted to be an FM insulator for varying element M (blue panels). It is metallic and possibly unstable for other elements (gray panels). The total magnetic moments per unit cell and their orientations (out of plane or in plane) of MBi₂Te₄ are depicted by the numbers and red arrows, respectively, in the bottom panel. Note that the magnetic easy axis is unknown for M = Ti. (B) Rich topological quantum states in MB₂T₄ thin films (2D) and bulks (3D) of different magnetic states that are tunable from AFM to FM or PM. AI, axion insulator; QSH, quantum spin Hall; DSM, Dirac semimetal. (C) Schematic diagram showing that magnetism and topology in MnBi₂Te₄ are induced by Mn d-bands and Bi-Te p-bands, respectively. (D) Band structure of monolayer MnBi₂Te₄, which is an FM insulator.

Fig. 2. AFM MnBi₂Te₄ bulk.

(A) Crystal structure (top left) and Brillouin zones of bulk, (111), and (110) surfaces (bottom) of ABC-stacked MnBi₂Te₄ with an A-type AFM ordering (top right). O₁ and O₂ represent inversion centers, and T_1/2 denotes a lattice translation. (B and C) Band structures excluding (B) and including (C) SOC. Parities of Bloch wave functions at Γ are labeled by “+” and “–.” (D) Band gap at Γ as a function of the SOC strength. The system would vary from normal insulator (NI) to AFM TI if gradually turning on SOC. (E) Evolution of WCCs in the k_z = 0 plane, which implies a nonzero topological invariant. (F and G) Surface states of the semi-infinite (111) (F) and (110) (G) surfaces, which are gapped and gapless, respectively.

Fig. 3. FM MnBi₂Te₄ bulk.

Crystal structure (A) and band structure (B) of the FM bulk. (C) Zoom-in band structures along the out-of-plane Γ-Z and nearly in-plane F-W-L directions. There is a pair of Weyl points at W and W′ = −W. (D) Motion of the sum of WCCs on a small sphere centered at W in momentum space. (E) Surface states of the ($1\overline{1}0$) termination on the isoenergy plane of the Weyl points, demonstrating the existence of Fermi arcs.

Fig. 4. AFM MnBi₂Te₄ films.

Band structure (A), Hall conductance σ_xy (B), and edge states (C) of the five-layer film. (D and E) Illustration of intrinsic axion insulators in even layers and QAH insulators in odd layers. The intrinsically gapped surfaces on the top and bottom sides have half-quantized Hall conductances, whose signs are opposite (the same) in even (odd) layers, leading to C = 0 (C = 1). In even layers, an electric field could induce magnetization effects identical to the depicted circulating Hall current, showing quantized magnetoelectric effects. (F) Schematic diagram showing chiral edge states on step edges between even (2N) and odd (2N + 1) layers.