We construct a continuum model for the Moiré superlattice of twisted bilayer MnBi$_2$Te$_4$, and study the band structure of the bilayer in both ferromagnetic (FM) and antiferromagnetic (AFM) phases. We find the system exhibits highly tunable Chern bands with Chern number up to $3$. We show that a twist angle of $1^\circ$ turns the highest valence band into a flat band with Chern number $\pm1$ that is isolated from all other bands in both FM and AFM phases. This result provides a promising platform for realizing time-reversal breaking correlated topological phases, such as fractional Chern insulator and $p+ip$ topological superconductor. In addition, our calculation indicates that the twisted stacking facilitates the emergence of quantum anomalous Hall effect in MnBi$_2$Te$_4$.
The intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = -1 evolves into a robust zero Hall resistance…
Recently, the intrinsic magnetic topological insulator MnBi2Te4 has attracted enormous research interest due to the great success in realizing exotic topological quantum states, such as the quantum anomalous Hall effect (QAHE), axion insulator state, high-Chern-number and high-temperature Chern insulator states. One key issue in this field is to effectively manipulate these states and control topological phase transitions. Here, by systematic angle-dependent transport measurements, we reveal a magnetization-tuned topological quantum phase transition from Chern insulator to magnetic insulator w…
The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered antiferromagnetic order was predicted to enable even-odd layer-number dependent topological states, supported by promising edge transport measurements. Furthermore, it becomes a Chern insulator when all spins are aligned by an applied magnetic field. However, the evolution of the bulk electronic structure as the magnetic state is continuously tuned and its dependence…
Chern insulators are two-dimensional magnetic topological materials that conduct electricity along their edges via the one-dimensional chiral modes. The number of these modes is a topological invariant called the first Chern number $C$, that defines the quantized Hall conductance as $S_{xy}= C e^2/h$. Increasing $C$ is pivotal for the realization of low-power-consumption topological electronics, but there has been no clear-cut solution of this problem so far, with the majority of existing Chern insulators showing $C=1$. Here, by using state-of-the-art theoretical methods, we propose an efficie…
Demonstration of Robust Chiral Edge Transport in Field-Induced Chern Insulator MnBi2Te4 Devices with Engineered Geometric Defects
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学北京量子器件重点实验室）；State Key Laboratory of Quantum Functional Materials, and ShanghaiTech Laboratory for Topological Physics, School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院量子功能材料国家重点实验室及拓扑物理上海科技大学实验室）；National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and School of Advanced Manufacturing Engineering, Nanjing University（南京大学先进微结构协同创新中心固体微观结构国家重点实验室先进制造工程学院）；National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and School of Physics, Nanjing University（南京大学固体微观结构国家重点实验室先进微结构协同创新中心物理学院）；Atom Manufacturing Institute（原子制造研究所）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
Axion is a hypothetical elementary particle which was initially postulated to solve the charge conjugation-parity problem in particle physics. Interestingly, the axion state has emerged in effective theory of topological insulators and has attracted extensive attention in condensed matter physics. Time-reversal or inversion symmetry constrains the axion field $θ$ to be quantized. When both the time-reversal and inversion symmetries are broken by, say, an antiferromagnetic order, the axion field $θ$ could become unquantized and dynamical along with magnetic fluctuations, which is termed the dyn…
The recent discovery of antiferromagnetic (AFM) topological insulator (TI) MnBi$_2$Te$_4$ has triggered great research efforts on exploring novel magnetic topological physics. Based on first-principles calculations, we find that the manipulation of magnetic orientation and order not only significantly affects material symmetries and orbital hybridizations, but also results in variant new magnetic topological phases in MnBi$_2$Te$_4$. We thus predict a series of unusual topological quantum phase transitions that are magnetically controllable in the material, including phase transitions from AFM…
The intricate interplay between nontrivial topology and magnetism in two-dimensional (2D) materials has led to the emergence of many novel phenomena and functionalities. An outstanding example is the quantum anomalous Hall (QAH) effect, which was realized in magnetically doped topological insulators (TIs) in the absence of magnetic field. Recently, the layered van der Waals compound MnBi2Te4 has been theoretically predicted and experimentally verified to be a TI with interlayer antiferromagnetic (AFM) order. It is a rare stoichiometric material with coexisting topology and magnetism, thus repr…
Axion, first postulated as a hypothetical particle in high-energy physics, is now extended to describe a novel topological magnetoelectric effect derived from the Chern-Simons theory in condensed matter systems. The recent discovered intrinsic magnetic topological insulators MnBi2Te4 and its derivatives have attracted great attention because of their potential as a material platform to realize such a quantized axion field. Since the magnetic exchange gap can bring the half-quantized anomalous Hall effect at the surface, an axion insulator manifests as quantum anomalous Hall and zero Hall plate…
We derive a general relation between the stacking vector ${\bf u}$ describing the relative shift of two layers of bilayer graphene and the Chern index. We find $C = ν- \text{sign}\left(|V_{AB}|-|V_{BA}|\right)$, where $ν$ is a valley index and $|V_{αβ}|$ the absolute value of stacking potentials that depend on ${\bf u}$ and that uniquely determine the interlayer interaction; AA stacking plays no role in the topological character. With this expression we show that while ideal and relaxed minimally twisted bilayer graphene appear so distinct as to be almost different materials, their Chern index…
We predict twisted double bilayer graphene to be a versatile platform for the realization of fractional Chern insulators readily targeted by tuning the gate potential and the twist angle. Remarkably, these topologically ordered states of matter, including spin singlet Halperin states and spin polarized states in Chern number $\mathcal C=1$ and $\mathcal{C}= 2$ bands, occur at high temperatures and without the need for an external magnetic field.
Here, we propose quantum spin Hall-like phononic states in van der Waals bilayer systems with antiferromagnetic ordering. Antiferromagnetic ordering in bilayer systems with small interlayer interaction makes the total Chern number zero, where the Chern numbers for each layer are opposite to each other. In bilayer CrI3 where antiferromagnetic ordering has been experimentally demonstrated, we show that the quantum spin Hall-like states appear with spatially separated chiral edge modes.
In most cases, to observe quantized Hall plateaux, an external magnetic field is applied in intrinsic magnetic topological insulators $\mathrm{MnBi_2Te_4}$. Nevertheless, whether the nonzero Chern number ($C\neq 0$) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed $C=2$ phase [Deng \textit{et al}., Science \textbf{367}, 895 (2020)]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaux in disordered $\mathrm{MnBi_2Te_4…
Twisting two layers into a magic angle (MA) of ~1.1° is found essential to create low energy flat bands and the resulting correlated insulating, superconducting, and magnetic phases in twisted bilayer graphene (TBG). While most of previous works focus on revealing these emergent states in MA-TBG, a study of the twist angle dependence, which helps to map an evolution of these phases, is yet less explored. Here, we report a magneto-transport study on one non-magic angle TBG device, whose twist angle θ changes from 1.25° at one end to 1.43° at the other. For θ=1.25°, we observe an emergence of to…
We present a field theory of Jain's composite fermion model as generalised to the bilayer quantum Hall systems. We define operators which create composite fermions and write the Hamiltonian exactly in terms of these operators. This is seen to be a complexified version of the familiar Chern Simons theory. In the mean-field approximation, the composite fermions feel a modified effective magnetic field exactly as happens in usual Chern Simons theories, and plateaus are predicted at the same values of filling factors as Lopez and Fradkin and Halperin . But unlike normal Chern Simons theories, we o…
Electronic states at domain walls in bilayer graphene are studied by analyzing their four and two band continuum models, by performing numerical calculations on the lattice, and by using quantum geometric arguments. The continuum theories explain the distinct electronic properties of boundary modes localized near domain walls formed by interlayer electric field reversal, by interlayer stacking reversal, and by simultaneous reversal of both quantities. Boundary mode properties are related to topological transitions and gap closures which occur in the bulk Hamiltonian parameter space. The import…
Quantum anomalous Hall (QAH) multilayers provide a platform of topological materials with high Chern numbers. We investigate the localization routes of bilayer QAH systems with Chern number C = 2 under strong disorder, by numerical simulations on their quantum transport properties and the Chern-Simons axion coupling. Compared to the single layer counterpart with C = 2, the localization trajectories present much richer behaviors, for example, the existence of the stable intermediate state with C = 1 can be tuned by model parameters. This state was always unstable in the single layer case. Furth…
The interplay between band topology and magnetism can give rise to exotic states of matter. For example, magnetically doped topological insulators can realize a Chern insulator that exhibits quantized Hall resistance at zero magnetic field. While prior works have focused on ferromagnetic systems, little is known about band topology and its manipulation in antiferromagnets. Here, we report that MnBi$_2$Te$_4$ is a rare platform for realizing a canted-antiferromagnetic (cAFM) Chern insulator with electrical control. We show that the Chern insulator state with Chern number $C = 1$ appears as soon…
Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe$_2$
Beijing National Laboratory for Condensed Matter Physics and Institute of physics, Chinese academy of sciences（中国科学院物理研究所）；University of Chinese academy of sciences（中国科学院大学）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（巴黎高等师范学院物理实验室）
Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum phase transitions triggered by enhanced electron-electron interactions when its flat-bands are partially filled. However, the phases themselves and their connection to the putative non-trivial topology of the flat bands are largely unexplored. Here we report transport measurements revealing a succession of doping-induced Lifshitz transitions that are accompanied by van Hove singularities (VHS) which facilitate the emergence of correlation-induced gaps and topologically non-trivial sub-bands. In the presence of a magnetic…
We consider magic-angle twisted bilayer graphene (TBG) at filling $ν=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley- and spin-polarized Chern insulating ground state that spontaneously breaks time-reversal symmetry, and is stabilized by a hexagonal boron nitride (hBN) substrate. We identify three different types of domain wall, and study their properties and energetic selection mechanisms via theoretical arguments and Hartree-Fock calculations adapted to deal with inhomogeneous moiré systems. We comment on th…
The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C>1). Here, we report the experimental discovery of high-Chern-number QHE (C=2) without Landau levels and C=1 Cher…
Studies of twisted moiré systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature stable quadratic-band-touching points and find exotic physics different from previously studied twisted moiré systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number ($C=\pm 2$). We further consider the effect of Coulomb interactions in such magic-angle twisted systems an…
Compared with twisted bilayer graphene, twisted double bilayer graphene (TDBG) provides another important platform to realize the moiré flat bands. In this paper, we first calculate the valley Chern number phase diagram of TDBG in the parameter space spanned by the twist angle and the interlayer electric potential. To include the effects of interactions, we then phenomenologically introduce the spin-splitting and valley-splitting. We find that when the valley splitting is larger than the bandwidth of the first conduction band so that a gap is opened and the spin splitting is relatively weak, t…
We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat…
We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions, that are Wannier-like in one direction and Bloch-like in the other. We focus on the active bands as given by the continuum model proposed by Bistritzer and MacDonald, and discuss the properties of corresponding hybrid Wannier functions. We then employ the method for a study of the fillings of $\pm 3$ electrons per moiré cell using the Hartree-Fock method. We discuss at length different regimes under which a quantized anomalous Hall effect is seen in these two fillings.
The real space formalism of orbital magnetization (OM) is an average of the local OM over some appropriate region of the system. Previous studies prefer a bulk average (i.e., without including boundaries). Based on a bilayer model with an adjustable Chern number at half filling, we numerically investigate the effects from boundaries on the real space expressions of OM. The size convergence processes of its three constituent terms $M_{\mathrm{LC}}$, $M_{\mathrm{IC}}$, $M_{\mathrm{BC}}$ are analysed. The topological term $M_{\mathrm{BC}}$ makes a nonnegligible contribution from boundaries as a m…
We perform an extensive exact diagonalization study of interaction driven insulators in spin- and valley-polarized moiré flat bands of twisted bilayer graphene aligned with its hexagonal boron nitride substrate. In addition to previously reported fractional Chern insulator phases, we provide compelling evidence for competing charge-density-wave phases at multiple fractional fillings of a realistic single-band model. A thorough analysis at different interlayer hopping parameters, motivated by experimental variability, and the role of kinetic energy at various Coulomb interaction strengths highl…
We explore the moiré magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moiré bands are extremely flat over a wide range of continuous twist angles; (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle; and (iii) the lowest few topological flat bands in bi…
