Atomically dispersed tungsten on metal halide monolayer as a ferromagnetic Chern insulator

Although the quantum anomalous Hall (QAH) effect has been experimentally observed in several magnetically doped topological insulators, up to now, it only survives at a very low temperature. More suitable candidate QAH insulators that can work at high temperature are much desired. Here, we propose an experimentally feasible way to realize a robust QAH insulator: atomically dispersed transition metals (e.g., W) on a two-dimensional porous metal halide normal insulator (e.g., ${\mathrm{InI}}_3$), which has been developed as a state-of-the-art chemical technology broadly adopted for homogeneous catalysis. Based on the first-principles calculations, we predict that the atomic W embedded in an ${\mathrm{InI}}_3$ monolayer forms an intrinsic ferromagnetic QAH insulator, which exhibits robust uniform out-of-plane ferromagnetic order up to $\sim 160\mathrm{K}$ and a topologically nontrivial band gap of 56 meV with a nonzero Chern number $\left(\left|C\right|=2\right)$. We also study its magneto-optical Kerr effect and collective plasma excitation modes, which may help for further experimental verifications and measurement of interesting physical features of Dirac-like electronic dispersion. Our results introduce a feasible method to obtain the QAH effect, which may motivate intensive experimental interest in this field.

Figure 1

(a) Four absorption sites (A1, A2, B, and C) of W in the ${\mathrm{InI}}_3$ monolayer. (b) Relative energy per W for each adsorption configuration. (c) Top and side view of the optimized $\mathrm{W}@\mathrm{In}{\mathrm{I}}_3$ monolayer. Green, gray, and orange balls represent W, In, and I atoms, respectively. (d) Phonon dispersion along a high-symmetry $k$ path. (e) Total energy as a function of time from ab initio molecular dynamics simulation at 300 K. (f) Atomic geometry after molecular dynamics simulation for 3000 fs.

Figure 2

(a) Average magnetization ($M$) and specific heat ($C_{\mathrm{v}}$) as a function of temperature from Monte Carlo simulations. Insets: ferromagnetic (FM) and antiferromagnetic (AFM) spin orders. (b) Magnon dispersion. (c) Projected density of states. The Fermi level is set to 0. Inset: charge difference of W on ${\mathrm{InI}}_3$ monolayer. Yellow and cyan isosurfaces represent charge accumulation and depletion, respectively.

Figure 3

Band dispersion along the high-symmetry $k$ path, (a) without and (b) with SOC interactions. The symmetry representation is also shown in panel (a). The color map shows the out-of-plane spin component $\langle s_z\rangle$ of each state.

Figure 4

(a) Berry curvature in the $k$ space. (b) MLWF based tight-binding band structure of nanoribbon, where blue to red colors represent left edge to right edge state contributions, respectively. (c) Local density of state (LDOS) distribution at $k=1/4\times (\overline{\mathrm{\Gamma }}\to \overline{M})$ of the nanoribbon. One clearly sees a localized edge state inside the bulk band gap, which is indicated in (b) as a white circled cross.

Figure 5

(a) Integrated anomalous Hall conductance ${\sigma }_{xy}$ as function of chemical potential, where a terrace of $\sigma =2e^2/h$ appears around the Fermi level. (b) Calculated MOKE with respect to incident energy.

Figure 6

(a) EELS $\mathcal{L}\left(q,\omega \right)$ dispersion of $n$-doped system with chemical potential $\mu =E_F+0.2\mathrm{eV}$. The area below the white dashed line $\left(v_{g}q\right)$ is the single-particle excitation damping region. (b) Calculated EELS $\mathcal{L}\left(q,\omega \right)$ with fixed $q=0.018{\AA }^{-1}$ under different chemical potential relative to Fermi level.