Using a realistic band structure for twisted WSe$_2 $ materials, we develop a theory for the interaction-driven correlated insulators to conducting metals transitions through the tuning of the filling factor around commensurate fractional fillings of the moiré unit cell in the 2D honeycomb lattice, focusing on the dominant half-filled Mott insulating state, which exists for both long- and short-range interactions. We find metallic states slightly away from half-filling, as have recently been observed experimentally. We discuss the stabilities and the magnetic properties of the resulting insulating and metallic phases, and comment on their experimental signatures. We also discuss the nature of the correlated insulator states at the rational fractional fillings.
We propose a phenomenological understanding of the recently discovered weak Mott insulator in the moiré superlattice of twisted bilayer graphene, especially the emergent superconductivity at low temperature within the weak Mott insulator phase, namely while lowering temperature, the longitudinal resistivity first grows below temperature $T_m$, but then rapidly drops to zero at even lower temperature $T_c$. An emergent superconductor in an insulator phase is very unusual. Here we propose that this phenomenon is due to the pure two-dimensional nature of the bilayer graphene moiré superlattice. W…
One salient feature of systems with Moiré superlattice is that, Chern number of "minibands" originating from each valley of the original graphene Brillouin zone becomes a well-defined quantized number because the miniband from each valley can be isolated from the rest of the spectrum due to the Moiré potential. Then a Moiré system with a well-defined valley Chern number can become a nonchiral topological insulator with $U(1) \times Z_3 $ symmetry and a $\mathbb{Z}$ classification at the free fermion level. Here we demonstrate that the strongly interacting nature of the Moiré system reduces the…
Recently, correlated physics such as superconductivity and insulator at commensurate fractional electron fillings has been discovered in several different systems with Moire superlattice and narrow electron bands near charge neutrality. Before we learn more experimental details and the accurate microscopic models describing the insulators, some general conclusions can already be made about these systems, simply based on their symmetries and electron fillings. The insulator in the Moire superlattice is described by an effective spin-orbital model with approximate higher symmetries than ordinary…
Moiré superlattices formed in two-dimensional semiconductor heterobilayers provide a new realization of Hubbard model physics in which the number of electrons per effective atom can be tuned at will. We report on an exact diagonalization study of the electronic properties of half-filled narrow moiré bands in which correlation strengths are varied by changing twist angles or interaction strengths. We construct a phase diagram for the bilayer, identifying where the metal-insulator phase transition occurs, estimating the sizes of the charge gaps in the insulating phase, and commenting on the natu…
Two-dimensional (2D) moire materials provide a new solid-state platform with unprecedented controllability for studies of correlated quantum phenomena. To date, experimental studies have focused on the correlated electronic states; the correlated bosonic states in moire materials have remained practically unexplored. Here, we report a correlated dipolar excitonic insulator, a charge insulating state driven by the formation of excitons, in a Coulomb-coupled WSe2 monolayer and WSe2/WS2 moire bilayer at total hole doping density equal to the moire density. The system is a Mott insulator when all …
Moiré bilayer materials have recently attracted much attention following the discovery of various correlated insulating states at specific band fillings. Here we discuss the metal-insulator transitions (MITs) that have been observed in the same devices, but at fillings far from the strongly correlated regime dominated by Mott-like physics, displaying many similarities to other examples of disorder-dominated MITs. We propose a minimal theoretical model describing the interplay of interactions and disorder, which able to capture most experimental trends observed on several devices.
Band mixing and particle-hole asymmetry in moiré fractional Chern insulators
Center for Computational Quantum Physics, Flatiron Institute（Flatiron研究所计算量子物理中心）；Materials Science Division, Argonne National Laboratory（阿贡国家实验室材料科学部）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学学院）；Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University（尼古拉·哥白尼大学物理、天文学和信息学学院物理学研究所）；Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文学系）
Moiré superlattices of van der Waals materials, such as twisted graphene and transitional metal dichalcogenides, have recently emerged as a fascinating platform to study strongly correlated states in two dimensions, thanks to the strong electron interaction in the moiré minibands. In most systems, the correlated states appear when the moiré lattice is filled by integer number of electrons per moiré unit cell. Recently, correlated states at fractional fillings of 1/3 and 2/3 holes per moiré unit cell has been reported in the WS2/WSe2 heterobilayer, hinting the long range nature of the electron …
We propose a new mechanism for quantum anomalous Hall (QAH) effect in the AB stacked MoTe$_2$/WSe$_2$ system. Based on the observation that the inter-layer tunneling is suppressed in the AB stacking, we consider a model with two layers coupled through the Coulomb interaction. The moiré lattices of the two layers are shifted to form a honeycomb lattice together. Initially, the system is in a layer-polarized Mott insulator at $ν_T=1$. But with a displacement field, an equal number of holes and electrons are doped into the two layers respectively and they form inter-layer exciton condensation. Th…
Entangled Moire Chern Insulator in Rhombohedral Graphene
Peking University（北京大学）；National Institute of Material Sciences（国立材料研究所）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Hefei National Laboratory（合肥国家实验室）
Continuous correlated states and dual-flatness in a moiré heterostructure
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Department of Physics and Astronomy, University of Manchester（曼彻斯特大学物理与天文学系）；National Graphene Institute, University of Manchester（曼彻斯特大学国家石墨烯研究所）；The Institute for Functional Intelligent Materials, National University of Singapore（新加坡国立大学功能智能材料研究所）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（日本物质材料研究机构电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（日本物质材料研究机构材料纳米结构研究中心）；Henry Royce Institute for Advanced Materials（亨利·罗伊斯先进材料研究所）；Department of Physics, Washington University in St. Louis（华盛顿大学圣路易斯分校物理系）；Department of Materials Science and Engineering, National University of Singapore（新加坡国立大学材料科学与工程系）；Department of Physics, Sogang University（西江大学物理系）
Motivated by the recent observation of evidences of ferromagnetism in correlated insulating states in systems with Moiré superlattices, we study a two-orbital quantum antiferromagnetic model on the triangular lattice, where the two orbitals physically correspond to the two valleys of the original graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$ symmetry, where the two SU(2) symmetries correspond to the rotation within the spin and valley space respectively. Through analytical argument, Schwinger boson analysis and also DMRG simulation, we find that even though all th…
Quantum particles on a lattice with competing long-range interactions are ubiquitous in physics. Transition metal oxides, layered molecular crystals and trapped ion arrays are a few examples out of many. In the strongly interacting regime, these systems often exhibit a rich variety of quantum many-body ground states that challenge theory. The emergence of transition metal dichalcogenide moiré heterostructures provides a highly controllable platform to study long-range electronic correlations. Here we report an observation of nearly two-dozen correlated insulating states at fractional fillings …
Strongly correlated quantum matter exhibits a rich variety of remarkable properties, but the organizing principles that underlie the behavior remain to be established. Graphene heterostructures, which can host narrow moire electron bands that amplify the correlation effect, represent a new setting to make progress on this overarching issue. In such correlated moire systems, an insulating state is a prominent feature of the phase diagram and may hold the key to understanding the basic physics. Here we advance the notion of a fragile insulator, a correlation-driven insulating state that is on th…
The flat bands resulting from moiré superlattices in magic-angle twisted bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated electron phenomena such as correlated insulators and superconductivity. More recently, orbital magnetism associated with correlated Chern insulators was found in this class of layered structures centered at integer multiples of n0, the density corresponding to one electron per moiré superlattice unit cell. Here we report the experimental observation of ferromagnetism …
We theoretically study a generalized Hubbard model on moiré superlattices of twisted bilayers, and find very rich filling-factor-dependent quantum phase diagrams tuned by interaction strength and twist angle. Strong long-range Coulomb interaction in the moiré-Hubbard model induces Wigner crystals at a series of fractional filling factors. The effective lattice of the Wigner crystal is controlled by the filling factor, and can be triangle, rectangle, honeycomb, kagome, etc, providing a single platform to realize many different spin models on various lattices by simply tuning carrier density. In…
Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron-electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report scanning tunneling microscopy (STM) measurements that reveal the existence of threefold rotational (C3) symmetry breaking in twisted double bilayer graphene (tDBG). Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry br…
Moir{é} superlattice realized in two-dimensional heterostructures offers an exciting platform to access strongly-correlated electronic states. In this work, we study transition metal dichalcogenides (TMD) Moir{é} superlattices with time-reversal-symmetry and nontrivial spin{/valley}-Chern numbers. Utilizing realistic material parameters and the method of exact diagonalization, we find that at a certain twisting angle and fractional filling, gapped fractional topological states, i.e., fractional Chern insulators, are naturally {stabilized} by simply introducing the Coulomb repulsion. In contras…
Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
Anisotropic Moiré Fractional Chern Insulators and Their Phase Transitions
Nanyang Technological University（南洋理工大学）；Hong Kong University of Science and Technology（香港科技大学）；Center for Theoretical Condensed Matter Physics, The Hong Kong University of Science and Technology（香港科技大学理论凝聚态物理中心）
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and Hofstadter bands; in both cases, a large magnetic field is required to engineer the underlying flat band. The recent observation of quantum anomalous Hall effects (QAH) in narrow band moiré systems has led to the theoretical prediction that such phases may be realized even at zero magnetic field. Here we report the experimental observation of insulators with Chern…
We present a combined experimental and theoretical study of twisted double bilayer graphene with twist angles between 1° and 1.35°. Consistent with moiré band structure calculations, we observe insulators at integer moiré band fillings one and three, but not two. An applied transverse electric field separates the first moiré conduction band from neighbouring bands, and favors the appearance of correlated insulators at 1/4, 1/2, and 3/4 band filling. Insulating states at 1/4 and 3/4 band filling emerge only in a parallel magnetic field (B_{||}), whereas the resistance at half band filling is we…
Emergence of a symmetry-broken Chern insulator near a moiré Kondo breakdown
Shanghai Jiao Tong University（上海交通大学）；Cornell University（康奈尔大学）；Kavli Institute at Cornell for Nanoscale Science（康奈尔纳米科学卡弗里研究所）；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凝聚态物理国家实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；National Institute for Materials Science（国立材料研究所）；Hefei National Laboratory（合肥国家实验室）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构动力学研究所）
Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological …
Chern-Textured Exciton Insulators with Valley Spiral Order in Moiré Materials
Rudolf Peierls Centre for Theoretical Physics（鲁道夫·皮尔斯理论物理中心）；Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论科学中心）；Department of Physics, University of Zurich（苏黎世大学物理系）；Department of Physics, Ghent University（根特大学物理系）
Exciton-roton mode in moiré fractional Chern insulators
Tsinghua University（清华大学）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Frontier Science Center for Quantum Information, Beijing（北京量子前沿科学中心）
We investigate few- and many-body states in half-filled maximally symmetric topological insulator flat bands realized by two degenerate Landau levels which experience opposite magnetic fields. This serves as a toy model of flat bands in moiré materials in which valleys have Chern numbers $C= \pm 1$. We argue that although the spontaneously polarized Ising Chern magnet is a natural ground state for repulsive Coulomb interactions, it can be in reasonable energetic competition with correlated states which can be viewed as Laughlin states of excitons when short distance corrections to the interact…
Studies on two-dimensional electron systems in a strong magnetic field first revealed the quantum Hall (QH) effect, a topological state of matter featuring a finite Chern number (C) and chiral edge states. Haldane later theorized that Chern insulators with integer QH effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (TLG/hBN) moiré superlattice provides an attractive platform to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent electrically tunable …
Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions. One representative example is the copper-oxide superconductors, where stripe order is thought to be relevant to the mechanism of high-temperature superconductivity. Identifying and studying the stripe phases in conventional strongly correlated systems are, however, challenging due to the complexity and limited tunability of these materials. Here we uncover stripe phases in WSe2/WS2 moiré superlattices with continuously gate-tunable ch…
Emergent magnetism and spin liquids in an extended Hubbard description of moiré bilayers
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Cologne（科隆大学）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara（法国美国理论科学中心，CNRS，KITP，圣塔芭芭拉）；Canadian Institute for Advanced Research（加拿大高级研究院）；Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）
Electrons in moiré flat band systems can spontaneously break time reversal symmetry, giving rise to a quantized anomalous Hall effect. Here we use a superconducting quantum interference device to image stray magnetic fields in one such system composed of twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap consistent with …
Van der Waals moiré materials have emerged as a highly controllable platform to study the electronic correlation phenomena. In particular, robust correlated insulating states have recently been discovered at both integer and fractional filling factors of the semiconductor moiré systems. Here, we reveal the thermodynamic properties of these states by measuring the gate capacitance of MoSe2/WS2 moiré superlattices. We observe a series of incompressible states for filling factor 0 - 8 and anomalously large capacitance (nearly 60% above the device's geometrical capacitance) in the intervening comp…
We study the Hubbard-Holstein model, which includes both the electron-electron and electron-phonon interactions characterized by $U$ and $g$, respectively, employing the dynamical mean-field theory combined with Wilson's numerical renormalization group technique. A zero temperature phase diagram of metal-insulator and insulator-insulator transitions at half-filling is mapped out which exhibits the interplay between $U$ and $g$. As $U$ ($g$) is increased, a metal to Mott-Hubbard insulator (bipolaron insulator) transition occurs, and the two insulating states are distinct and can not be adiabati…
Transition metal dichalcogenide (TMD) bilayers have recently emerged as a robust and tunable moiré system for studying and designing correlated electron physics. In this work, by combining large-scale first principle calculation and continuum model approach, we provide an electronic structure theory that maps long-period heterobilayer TMD superlattices onto diatomic crystals with cations and anions. We find that the interplay between moiré potential and Coulomb interaction leads to filling-dependent charge transfer between MM and MX regions several nanometers apart. We show that the insulating…
