High-Temperature Quantum Anomalous Hall Effect in Buckled Honeycomb Antiferromagnets

Abstract

We propose Néel antiferromagnetic (AF) Mott insulators with a buckled honeycomb structure as potential candidates to host a high-temperature AF Chern insulator (AFCI). Using a generalized Kondo lattice model we show that the staggered potential induced by a perpendicular electric field due to the buckling can drive the AF Mott insulator to an AFCI phase. We address the temperature evolution of the Hall conductance and the chiral edge states. The quantization temperature $T_q$, below which the Hall conductance is quantized, depends essentially on the strength of the spin-orbit coupling and the hopping parameter, independent of the specific details of the model. The deviation of the Hall conductance from the quantized value $e^2/h$ above $T_q$ is found to be accompanied by a spectral broadening of the chiral edge states, reflecting a finite life-time, i.e., a decay. Using parameters typical for heavy transition-metal elements we predict that the AFCI can survive up to room temperature. We suggest Sr$_3$CaOs$_2$O$_9$ as a potential compound to realize a high-$T$ AFCI phase.

Figures (6)

• Figure 1: (a) Side view of the spin-$\mathcal{S}_{\rm tot}$ Heisenberg model with the nearest-neighbor AF interaction $J$ on the buckled honeycomb structure. In the presence of a perpendicular electric field $\vec{E}=E_0\hat{z}$ the system can effectively be described by the generalized Kondo lattice model \ref{['eq:model']} illustrated in (b) for the special case of $\mathcal{S}_{\rm tot}=3/2$.
• Figure 2: Phase diagram of temperature vs the alternating sublattice potential controlled by a perpendicular electric field. The colormap represents the value of the Hall conductance $\sigma_{yx}=-\sigma_{xy}$ given by Eq. \ref{['eq:hall']}. The Néel temperature $T_{\rm N}$ and the crossover quantization temperature $T_{q}$ are specified. The Hall conductance takes the quantized value $e^2/h$ with an error less than $\%1$ below $T_{q}$, characterizing the antiferromagnetic Chern insulator (AFCI). The gray dotted lines separate the metallic region from the insulating regions. The metallic region shrinks rapidly to the two quantum critical points as $T\to 0$. The results are for the model parameters $S=1/2$, $U=12t$, $J_{\rm H}=0.2U$, $J=4t^2/\Delta_0=0.2\bar{7}t$, and $\lambda_{\rm SO}=0.2t$. We recall that the localized spin $S=1/2$ in Eq. \ref{['eq:model']} corresponds to the total spin $\mathcal{S}_{\rm tot}=S+1/2=1$ in Eq. \ref{['eq:heis']}. The number of bath sites $n_b=5$ is used in the ED impurity solver.
• Figure 3: Local magnetizations $m=|\langle s_i^z \rangle|$ and $M=|\langle S_i^z \rangle|$ (a) and the Hall conductance (b) vs $T$. The Néel temperature $T_{\rm N}$ and the crossover quantization temperature $T_{q}$ are specified. (c) Local spectral function averaged over the two sites in the unit cell for the spin component $\alpha$ at different temperatures. The results correspond to the solution with the magnetization on the higher-energy sublattice pointing in the positive $z$ direction. The results are for $S=1/2$, $U=12t$, $J_{\rm H}=0.2U$, $J=4t^2/\Delta_0=0.2\bar{7}t$, $\lambda_{\rm SO}=0.2t$, and $\delta=7t$. The data are for the number of bath sites $n_b=6$ except for the filled gray squares at selective temperatures in (a) and (b) which are for $n_b=7$.
• Figure 4: The brick wall representation of the honeycomb structure with the open boundary condition in $x$ and the periodic boundary condition in $y$ direction. The different sites in the $x$ direction are labeled from $0$ to $N_x-1$. The dashed box specifies the unit cell.
• Figure 5: (a) The momentum-resolved spectral function $A_{\alpha,x}(\omega,k_y)$ for the topological spin component $\alpha=\uparrow$ at the edge $x=0$ at different temperatures. (b) Local spectral function $A_{\uparrow,x}(\omega)$ for $T=0.1t$ at different $x$. The results are for the same model parameters as in Fig. \ref{['fig:del7']}. A cylindrical geometry as illustrated in Fig. \ref{['fig:bw']} with $N_x=80$ is used. The data are for $n_b=6$ bath sites in the ED impurity solver.