Excitonic Quantum Anomalous Hall Effect in Collinear Magnets Without Spin-Orbit Coupling

Abstract

Spin-orbit coupling (SOC) is thought to be necessary in realizing quantum anomalous Hall (QAH) insulators in magnetic materials. In this Letter, we propose an exciton-condensation mechanism to realize QAH effect in collinear magnets with negligible spin-orbit coupling. This mechanism is realized by two steps: first prepare a spin-splitting nodal-ring band structure, and then gap out the nodal-ring via triplet exciton condensation. A nonzero Chern number can be obtained if the in-plane spin texture resulting from the triplet exciton condensation is noncollinear in momentum space. We show that the electron-phonon coupling can switch the spin texture from a colinear pattern to a noncolinear one and plays an essential role in realizing QAH effect. The above mechanism is not only suitable for ferrogmagnets but also applicable for altermagnets. Finally, through first-principles calculations we propose the bilayer material V2SeTeO to be a promising candidate of excitonic QAH insulator.

Figures (8)

• Figure 1: Model for the Ferromagnetism. (a) Illustration of the Hamiltonian in Eq.(\ref{['Eq1-FM']}). (b) Four-band spin-splitting energy dispersion with $t^{d}=1$, $t=0.6$, $m=2$. The red arrow indicates that the spin polarization of the top valence band is spin up, while the blue arrow represents one of the bottom conducting band is spin down. (c) Excitation energies $E_{\pmb{k}}^{\pm}$ of excitonic insulators being gapped.
• Figure 2: (a) The phase diagram based on the mean-field calculation in different parameters $g$ and $V_{\rm ph}$ for FM model. (b) The total ground energy $E_{\rm GS}$ of topological EIs, trivial EIs and metals (no exciton condensation) with various $V_{\rm ph}$ with $g=4$.
• Figure 3: The results of exciton condensation in ferromagnetism for $g=4$. (a) Magnitude of the order parameters $|\Delta_{\pmb{k}}|$ for $V_{\rm ph}=0$, (b) the spontaneous $d$-wave collinear spin textures and (c) the berry curvature with $C=0$. While, (d) magnitude of the order parameters $|\Delta_{\pmb{k}}|$ for $V_{\rm ph}=3$, (e) the spontaneous $(p_x+i p_y)$-wave non-collinear spin textures and (f) the berry curvature with $C=1$.
• Figure 4: Model for the altermagnetism with a $d$-wave symmetry. (a) Illustration of the Hamiltonian in Eq.(\ref{['AMEq1']}). (b) The two middle ones in the eight-band spin-splitting energy dispersion diagram of Hamiltonian in Eq.(\ref{['AMEq1']}) with $t_{1}=0.5$, $t_{2}^{x,y}=1.2$, $t_{3}=0.7$, $t_{4}^{x,y}=0.4$ and $m=4$. (c) The spin-polarization of the top valence band, which is opposite to that of the bottom conducting band. The red solid lines stands for the nodal rings. (d) The energy dispersion, (e) the spin-polarization and (f) excitation energies $E_{\pmb{k}}^{\pm}$ of excitonic insulators after applying applying strain along the $y$-axis.
• Figure 5: (a) Crystal and magnetic structures of bilayer V$_2$SeTeO. The red and blue arrows represent spin-up and spin-down magnetic moments, respectively. The displacement between intra-layer $V^{3+}$ ions is 2.86 Å, the distance between inter-layer $V^{3+}$ ions is 7.5 Å, and the lattice constant in each layer is 4.05Å. (b) The electronic structure along the high-symmetry directions and the contributions from different layers without SOC. (c) The schematic diagram of nodal-line near the Fermi surface for bilayer $\mathrm{V_2SeTeO}$. (d) The electronic structure along the high-symmetry directions when applying uniaxial strain along the y-axis with $b^{\prime}=b(1+0.03)$.