Antiferromagnetic topological insulator in stable exfoliated two-dimensional materials

The antiferromagnetic topological insulator (AFM TI) and two-dimensional (2D) magnet constitute two of the most active fields for hosting prominent physical phenomena and significant advances in novel spintronic devices. However, the 2D AFM TI is scarce. Here, we propose a tight-binding model of the 2D AFM square lattice to demonstrate the emergence of the 2D AFM TI protected by a nonsymmorphic symmetry that is a combination of the twofold rotation symmetry and half-lattice translation. Moreover, based on first-principles calculations, we investigate in total 57 tetragonal antiferromagnets in the crystal structure of outstanding AFM CuMnAs to realize our proposal, and nine experimentally feasible candidates are predicted to be intrinsic 2D nonsymmorphic AFM TIs characterized by the nonzero topological invariant ${\mathbb{Z}}_2=1$ and gapless edge states. The presented results not only greatly extend the scope of magnetic topological states in two dimensions but also put forward potential applications in AFM spintronics.

Figure 1

(a) Sketch of the square lattice with antiferromagnetic ordering. Opposite spin directions along the $z$ axis are denoted by arrows. The nonsymmorphic symmetry $S_{2x}=\left\{C_{2x}\right|\frac{1}{2}0\}$, consisting of a twofold rotation $C_{2x}$ and a half of the lattice translation $\left(\frac{1}{2}0\right)$, is illustrated in green. (b) Band structures, (c) Wannier charge centers (WCC), (d) spin berry curvature, and (g) edge states of the antiferromagnetic model with nonsymmorphic symmetry $S_{2x}$, indicating the topological nontrivial character. When $S_{2x}$ is broken, the system becomes a trivial insulator as shown by the band structures, WCC, and edge states in (e), (f), and (h).The same parameters are used for the configurations with and without $S_{2x}$, which are $\mu =1.8$ and $t_{ab}=0.3$.

Figure 2

(a) Top view of $ABC$ quintuple layers, where the unit cell is indicated by solid lines, and the arrows denote the atomic spin moments aligned or antialigned with the $z$ axis. A represents the atoms with relatively stronger spin-orbit coupling (SOC) and B represents that with weaker SOC. (b) The two-dimensional Brillouin zones for the unit cell (black solid lines) and $\sqrt{2}\times \sqrt{2}$ supercell (yellow dash lines), and projected two-dimensional Brillouin zone with marked high symmetry points. (c) Exfoliation energy of RbMnBi quintuple layers. Inset is the side view of bulk RbMnBi and interlayer distance. (d) Phonon dispersion of RbMnBi quintuple layers, indicating that the quintuple layers are dynamically stable.

Figure 3

Orbitally resolved band structures of (a), (b) CaMnPb and (c), (d) RbMnBi quintuple layers (a), (c) without and (b), (d) with SOC, weighted with the $d_{z^2}, d_{xz}$, and $d_{yz}$ orbitals of Mn. The Fermi level is indicated by the black dashed line.

Figure 4

(a) Evolution of WCC for RbMnBi quintuple layers along ${\mathrm{k}}_x$, indicating the ${\mathbb{Z}}_2$ invariant number ${\mathbb{Z}}_2$ = 1. (b) Energy dependence of the spin Hall conductivity ${\sigma }_{xy}^S$ for RbMnBi quintuple layers, showing a quantized value within the energy window of the SOC gap. Inset shows the K-space distribution of spin Berry curvature within theSOC gap.

Figure 5

Topological edge states of semi-infinite (a) KMnSb, (b) RbMnAs, (c) RbMnSb, (d) RbMnBi, (e) CsMnAs, (f) CsMnSb, (g) CaMnPb, and (h) SrMnGe nanoribbons with SOC, showing the nonsymmorphic AFM TIs in two dimensions. Colors ranging from white to red represent the higher LDOS.