Model Hamiltonian for the Quantum Anomalous Hall State in Iron-Halogenide

Abstract

We examine quantum anomalous Hall (QAH) insulators with intrinsic magnetism displaying quantized Hall conductance at zero magnetic fields. The spin-momentum locking of the topological edge stats promises QAH insulators with great potential in device applications in the field of spintronics. Here, we generalize Haldane’s model on the honeycomb lattice to a more realistic two-orbital case without the artificial real-space complex hopping. Instead, we introduce an intraorbital coupling, stemming directly from the local spin-orbit coupling (SOC). Our dxy /d x 2–y 2 model may be viewed as a generalization of the bismuthene px /py -model for correlated d-orbitals. It promises a large SOC gap, featuring a high operating temperature. This two-orbital model nicely explains the low-energy excitation and the topology of two-dimensional ferromagnetic iron-halogenides. Furthermore, we find that electronic correlations can drive the QAH states to a c = 0 phase, in which every band carries a nonzero Chern number. Our work not only provides a realistic QAH model, but also generalizes the nontrivial band topology to correlated orbitals, which demonstrates an exciting topological phase transition driven by Coulomb repulsions. Both the model and the material candidates provide excellent platforms for future study of the interplay between electronic correlations and nontrivial band topology.

Designing light-element materials with large effective spin-orbit coupling

“…As a bonus, we systematically obtain nine materials with nontrivial SOC-induced bandgap (see Table I), rendering them large-gap QAH insulators against the thermal excitation [21] and local disorder [43]. While some materials in Table I, as well as certain artificial structures, are occasionally predicted as large-gap QAH insulators [44][45][46][47][48][49][50][51][52][53], the comprehensive understanding of the such over-room-temperature nontrivial gaps as well as systematic material search are still lacking. In our framework, however, the large-gap QAH insulators can be well understood and exhaustively collected from our material candidates (Supplementary Table S4) by performing more delicate GGA+U Wannier-representation tight-binding calculations [54][55][56][57] (see Methods).…”

Tunable Topological States in Stacked Chern Insulator Bilayers

“…To explore the origin of the nontrivial band topology and the Dirac fermions in MnBr 3 systems, a tight-binding model on the basis of a hexagonal lattice comprising two localized d orbitals (d xy and d x 2 – y 2 ) of each magnetic atom is proposed. − All nearest-neighbor hopping terms are taken into consideration, and we thus build a 4-band TB Hamiltonian with calculated four symmetrical bands at the Fermi level, as shown in Supplementary Figure 8. The Dirac fermions at the K point, as well as degenerate bands at the Γ point in the BZ, are qualitatively in accord with the corresponding density functional theory (DFT) results, thereby indicating that our 4-band d orbital model can reproduce the electronic properties of MnBr 3 monolayer nicely.…”

Controllable Chirality and Band Gap of Quantum Anomalous Hall Insulators

“…The quantum anomalous Hall (QAH) insulator (QAHI) is a novel two-dimensional (2D) magnetic topological phase that possesses Berry flux monopoles in the momentum space and displays quantized Hall conductance (σ xy ) robust against disorder. , QAHIs offer a versatile playground for exploring emerging quantum physics such as dissipationless currents, topological magnetoelectric effects, Majorana Fermions, etc. , Despite intensive research effort, − very few candidate materials are available experimentally, and all of them must work at quite low temperatures. ,− Optimizing material properties of the QAHI, especially the band gap, is of critical importance to experiment and applications, which demand in-depth research. For instance, the QAH gap of MnBi 2 Te 4 predicted by theory is sizable and robust, , whereas the gap detected by experiments is much smaller or even surprisingly vanishes. − …”

“…Type-III QAHIs are understood in a different scenario. Figure c displays a few candidate materials including monolayer transition metal trihalides MY 3 ( M = transition metal element, Y = halogen element) . − As illustrated in Figure d, the low-energy topological physics are described by a Haldane-like model (see SI Section S1 ) with an SOC-induced Dirac mass m = −λ SOC ⟨ s z ⟩, where λ SOC denotes the effective SOC of transition metal d orbitals and ⟨ s z ⟩ is the expectation value of out-of-plane spin component of Dirac bands. The QAH gap is 2| m | and chirality χ = sgn­( m ).…”