Prediction of high-temperature quantum anomalous Hall effect in two-dimensional transition-metal oxides

Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect (QAHE), but it is difficult to realize. Here, we predict the two-dimensional (2D) single-atomic-layer ${\mathrm{V}}_2{\mathrm{O}}_3$ with a honeycomb-Kagome structure is a QAH insulator with a large band gap (larger than 0.1 eV) and a high ferromagnetic Curie temperature (about 900 K). Combining the first principles calculations with the effective Hamiltonian analysis, we find that the spin-majority $d_{xy}$ and $d_{yz}$ orbitals of V atoms on the honeycomb lattice form a massless Dirac cone near the Fermi level which becomes massive when the on-site spin-orbit coupling (SOC) is included. Interestingly, we find that the large band gap is caused by a cooperative effect of electron correlation and SOC. Both first principles calculations and the effective Hamiltonian analysis confirm that 2D ${\mathrm{V}}_2{\mathrm{O}}_3$ has a nonzero Chern number (i.e., one). This paper paves a direction toward realizing the QAHE at room temperature.

Figure 1

(a) Lattice structure for the 2D ${\mathrm{V}}_2{\mathrm{O}}_3$ monolayer and schematic representations of FM and Neel AFM orders. (b) The magnetic moment (black) and spin susceptibility (blue) as a function of temperature from the Monte Carlo simulation, indicating that the FM transition temperature is very high (about 900 K).

Figure 2

(a) DOS and partial DOS of ${\mathrm{V}}_2{\mathrm{O}}_3$ calculated at the LDA+$U$ level. From it, one can easily see the bands near the Fermi level are dominated by $d_{xz}$ and $d_{yz}$ orbitals. (b) Electronic configuration of ${\mathrm{V}}^{3+}$ in ${\mathrm{V}}_2{\mathrm{O}}_3$. The spin down $3d$ state is far away from the Fermi level because of the exchange splitting. (c) The schematic illustration of exchange mechanism for the FM coupling. It is clear that the occupation of the low-lying bonding states lowers the total energy.

Figure 3

Dependence of physical properties on the Hubbard $U$ value. (a) Energy difference (eV/f.u.) between AFM and FM states. (b) Energy difference between the FM state with spins along the $x$ axis and that with spins along the $z$ axis, indicating that 2D ${\mathrm{V}}_2{\mathrm{O}}_3$ has an easy-magnetization axis along $z$. (c) Local orbital moments of ${\mathrm{V}}^{3+}$ ion. (d) The global band gap. Note that there is no band gap when the spins are along the in-plane directions.

Figure 4

Band structures of 2D ${\mathrm{V}}_2{\mathrm{O}}_3$ calculated using different methods. (a) LDA+$U$ with $U=4\mathrm{eV}$, (b) LDA+SOC and (c) LDA+$U$+SOC with $U=4\mathrm{eV}$. The bands near the Fermi level consist of the V $3d$ orbitals and the Fermi level is set to zero. (d) Schematic illustration of the band evolution by considering SOC and Hubbard $U$ interaction.

Figure 5

Band structures of 2D ${\mathrm{V}}_2{\mathrm{O}}_3$ calculated using the TB model, (a) and (b) without SOC, (c) and (d) with SOC. The band structures near the $K$ point from the LEEH (solid red) are also shown in (b) and (d). The horizontal dotted lines indicate the Fermi level. The band structure from the TB model agrees with the first principles results [see red circles in Figs. 4 and 4]. One can see the results near $K$ from the TB model and LEEH are in agreement with each other very well.