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The interplay between non-trivial topology and strong electron interaction can generate a variety of exotic quantum matter. Here we theoretically propose that monolayer transition metal trihalides MoF$_3$ and W$X_3$ ($X$= Cl, Br, I) have isolated nearly flat band near the Fermi level with higher Chern number $\mathcal{C}=+3$ and $\mathcal{C}=-2$, respectively. The nontrivial topology of these flat Chern bands originates from the effective $sd^2$ hybridization of transition metal atom, which transform the apparent atomic $d$ orbitals on a hexagonal lattice into $(s, p_+, p_-)$ orbitals on a triangular lattice. Interestingly, the quantum geometry of flat Chern bands in these materials are comparable with those in moir\'e systems exhibiting fractional Chern insulator state. The Hofstadter butterfly of such flat Chern bands are further studied. These natural materials, if realized experimentally, could offer new platforms to explore correlated phenomena driven by flat Chern band with higher Chern number., Comment: 7 pages, 4 figures

Intrinsic magnetic topological insulators offers an ideal platform to explore exotic topological phenomena, such as axion electrodynamics, quantum anomalous Hall (QAH) effect and Majorana edge modes. However, these emerging new physical effects have rarely been experimentally observed due to the limited choice of suitable materials. Here, we predict the van der Waals layered V$_2$WS$_4$ and its related materials show intralayer ferromagnetic and interlayer antiferromagnetic exchange interactions. We find extremely rich magnetic topological states in V$_2$WS$_4$, including an antiferromagnetic topological insulator, the axion state with the long-sought quantized topological magnetoelectric effect, three-dimensional QAH state, as well as a collection of QAH insulators and intrinsic axion insulators in odd- and even-layer films, respectively. Remarkably, the N\'eel temperature of V$_2$WS$_4$ is predicted to be much higher than that of MnBi$_2$Te$_4$. These interesting predictions, if realized experimentally, could greatly promote the topological quantum physics research and application., Comment: 7 pages, 4 figures

We propose a general theory of anisotropic band flattening in moir\'e systems at the $\Gamma$ valley. For a two-dimensional semiconductor with a rectangular unit cell of $C_{2z}$ or mirror symmetries, we find that a larger effective mass anisotropy $\eta=m_y/m_x$ of the valence or conduction bands in the monolayer will have a stronger tendency to be further enhanced in its twisted bilayer. This gives rise to strong anisotropic band flattening and correlated physics in one dimension effectively. We predict twisted bilayer black phosphorus (tBBP) has giant anisotropic flattened moir\'e bands ($\eta\sim10^4$) from ab initio calculations and continuum model, where the low energy physics is described by the weakly coupled array of one-dimensional wires. We further calculate the phase diagram based on the sliding Luttinger liquid by including the screened Coulomb interactions in tBBP, and find a large parameter space may host the non-Fermi liquid phase. We thus establish tBBP as a promising and experimentally accessible platform for exploring correlated physics in low dimensions., Comment: 5 pages, 4 figures

Topological materials with unconventional electronic properties have been investigated intensively for both fundamental and practical interests. Thousands of topological materials have been identified by symmetry-based analysis and ab initio calculations. However, the predicted magnetic topological insulators with genuine full band gaps are rare. Here we employ this database and supervisedly train neural networks to develop a heuristic chemical rule for electronic topology diagnosis. The learned rule is interpretable and diagnoses with a high accuracy whether a material is topological using only its chemical formula and Hubbard $U$ parameter. We next evaluate the model performance in several different regimes of materials. Finally, we integrate machine-learned rule with ab initio calculations to high-throughput screen for magnetic topological insulators in 2D material database. We discover 6 new classes (15 materials) of Chern insulators, among which 4 classes (7 materials) have full band gaps and may motivate for experimental observation. We anticipate the machine-learned rule here can be used as a guiding principle for inverse design and discovery of new topological materials., Comment: 7 pages, 4 figures

We theoretically propose that the van der Waals layered ternary transition metal chalcogenide V$_2 MX_4$ ($M=$ W, Mo; $X=$ S, Se) is a new family of quantum anomalous Hall insulators with sizable bulk gap and Chern number $\mathcal{C}=-1$. The large topological gap originates from the \emph{deep} band inversion between spin up bands contributed by $d_{xz},d_{yz}$ orbitals of V and spin down band from $d_{z^2}$ orbital of $M$ at Fermi level. Remarkably, the Curie temperature of monolayer V$_2 MX_4$ is predicted to be much higher than that of monolayer MnBi$_2$Te$_4$. Furthermore, the thickness dependence of the Chern number for few multilayers shows interesting oscillating behavior. The general physics from the $d$-orbitals here applies to a large class of ternary transition metal chalcogenide such as Ti$_2$W$X_4$ with the space group $P$-$42m$. These interesting predictions, if realized experimentally, could greatly promote the research and application of topological quantum physics., Comment: 7 pages, 4 figures

We theoretically propose that the monolayer $A$Ti$X$ family (KTiSb, KTiBi, RbTiSb, SrTiSn) are potential candidates for large-gap quantum anomalous Hall insulators with high Chern number $\mathcal{C}=2$. Both of the topology and magnetism in these materials are from $3d$-orbitals of Ti. We construct the tight-binding model with symmetry analysis to reveal the origin of topology. Remarkably, quite different from the conventional $s$-$d$ band inversion, here the topological band inversion within $3d$ orbitals is due to the crystal field and electron hopping, while spin-orbit coupling only trivially gaps out the Dirac cone at Fermi level. The general physics from the $3d$ orbitals here applies to a large class of transition metal compounds with the space group $P4/nmm$ or $P$-$42m$ and their subgroups., Comment: 6 pages, 4 figures

Topological flat bands at the Fermi level offer a promising platform to study a variety of intriguing correlated phase of matter. Here we present band engineering in the twisted orbital-active bilayers with spin-orbit coupling. The symmetry constraints on the interlayer coupling that determines the effective potential for low-energy physics of moir\'e electrons are exhaustively derived for two-dimensional point groups. We find the line graph or biparticle sublattice of moir\'e pattern emerge with a minimal $C_3$ symmetry, which exhibit isolated electronic flat bands with nontrivial topology. The band flatness is insensitive to the twist angle since they come from the interference effect. Armed with this guiding principle, we predict that twisted bilayers of 2H-PbS$_2$ and CdS realize the salient physics to engineer two-dimensional topological quantum phases. At small twist angles, PbS$_2$ heterostructures give rise to an emergent moir\'e Kagom\'e lattice, while CdS heterostructures lead to an emergent moir\'e honeycomb lattice, and both of them host moir\'e quantum spin Hall insulators with almost flat topological bands. We further study superconductivity of these two systems with local attractive interactions. The superfluid weight and Berezinskii-Kosterlitz-Thouless temperature are determined by multiband processes and quantum geometry of the band in the flat-band limit when the pairing potential exceeds the band width. Our results demonstrate twisted bilayers with multi-orbitals as a promising tunable platform to realize correlated topological phases., Comment: 8 pages, 4 figures

We investigate the role of disorder in the edge transport of axion insulator films. We predict by first-principles calculations that even-number-layer MnBi$_2$Te$_4$ have gapped helical edge states. The random potential will dramatically modify the edge spectral function to become gapless. However, such gapless helical state here is fundamentally different from that in quantum spin Hall insulator or topological Anderson insulator. We further study the edge transport in this system by Landauer-B\"{u}ttiker formalism, and find such gapless edge state is dissipative and not immune to backscattering, which would explain the dissipative nonlocal transport in the axion insulator state observed in six septuple layer MnBi$_2$Te$_4$ experimentally. Several transport experiments are proposed to verify our theory on the dissipative helical edge channels. In particular, the longitudinal resistance can be greatly reduced by adding an extra floating probe even if it is not used. These results will facilitate the observsation of long-sought topological magnetoelectric effect in axion insulators., Comment: 7pages,4 figures

The unoccupied part of the band structure in the magnetic topological insulator MnBi$_2$Te$_4$ is studied by first-principles calculations. We find a second, unoccupied topological surface state with similar electronic structure to the celebrated occupied topological surface state. This state is energetically located approximate $1.6$ eV above the occupied Dirac surface state around $\Gamma$ point, which permit it to be directly observed by the two-photon angle-resolved photoemission spectroscopy. We propose a unified effective model for the occupied and unoccupied surface states. Due to the direct optical coupling between these two surface states, we further propose two optical effects to detect the unoccupied surface state. One is the polar Kerr effect in odd layer from nonvanishing ac Hall conductance $\sigma_{xy}(\omega)$, and the other is higher-order terahertz-sideband generation in even layer, where the non-vanishining Berry curvature of the unoccupied surface state is directly observed from the giant Faraday rotation of optical emission., Comment: 7 pages, 3 figures

The interplay between band topology and magnetic order could generate a variety of time-reversal-breaking gapped topological phases with exotic topological quantization phenomena, such as quantum anomalous Hall (QAH) insulators and axion insulators (AxI). Here by combining analytic models and first-principles calculations, we predict QAH and AxI phases can be realized in thin film of an intrinsic antiferromagnetic van der Waal material Mn$_2$Bi$_2$Te$_5$. The phase transition between QAH and AxI is tuned by the layer magnetization, which would provide a promising platform for chiral superconducting phases. We further present a simple and unified continuum model that captures the magnetic topological features, and is generic for Mn$_2$Bi$_2$Te$_5$ and MnBi$_2$Te$_4$ family materials., Comment: 6 pages, 4 figures, 1 table