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 interaction. In this work, employing a scanning microwave impedance microscopy technique that is sensitive to local electrical properties, we observe a series of correlated insulating states at fractional fillings of the moiré minibands on both electron- and hole-doped sides in angle-aligned WS2/WSe2 hetero-bilayers, with certain states persisting at temperatures up to 120 K. Monte Carlo simulations reveal that these insulating states correspond to ordering of electrons in the moiré lattice with a periodicity much larger than the moiré unit cell, indicating a surprisingly strong and long-range interaction beyond the nearest neighbors. Our findings usher in unprecedented opportunities in the study of strongly correlated states in two dimensions.
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 …
Layers of two-dimensional materials stacked with a small twist-angle give rise to beating periodic patterns on a scale much larger than the original lattice, referred to as a moiré superlattice. When the stacking involves more than two layers with independent twist angles between adjacent layers, it generates moiré of moiré superlattices, with multiple length scales that control the system's behavior. Here we demonstrate these effects of a high-order moiré superlattice in twisted trilayer graphene with two consecutive small twist angles. We report correlated insulating states near the half fil…
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…
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…
Small-twist-angle transition metal dichalcogenide (TMD) heterobilayers develop isolated flat moiré bands that are approximately described by triangular lattice generalized Hubbard models [PhysRevLett.121.026402]. In this article we explore the metallic and insulating states that appear under different control conditions at a density of one-electron per moiré period, and the transitions between them. By combining fully self-consistent Hartree-Fock theory calculations with strong-coupling expansions around the atomic limit, we identify four different magnetic states and one nonmagnetic state nea…
Emergent electronic insulating states in a one-dimensional moiré superlattice
Zhejiang University（浙江大学）；The University of Osaka（大阪大学）；Dalian University（大连大学）；Inha University（仁荷大学）；National Institute for Materials Science (NIMS)（国立材料研究所）；Stony Brook University（石溪大学）
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…
Moiré superlattices are excellent platforms to realize strongly correlated quantum phenomena, such as Mott insulation and superconductivity. In particular, recent research has revealed stripe phases and generalized Wigner crystals at fractional fillings of moiré superlattices. But these experiments have not focused on the influence of electronic crystallization on the excitonic and valleytronic properties of the superlattices. Here we report excitonic and valleytronic signatures of correlated states at fractional fillings in a WSe$_2$/WS$_2$ moiré superlattice. We observe reflection spectral m…
An unconventional insulating phase and a superconducting phase were recently discovered in the twisted bilayer graphene [Y. Cao et al, Nature {\bf 556}, 80; {\bf 556}, 43 (2018)], but the relevant low-energy electronic states have not been clearly identified yet. In this work, I show that the interlayer hopping induces a spatially modulated Dirac mass term in the continuum Hamiltonian, and leads to a low-energy band formed by Dirac zero modes in the moiré superlattice. This moiré band becomes extremely flat and thus strongly correlated as the Dirac velocity vanishes at the magic angle, and ent…
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 …
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 …
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…
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…
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…
Heterobilayer transition metal dichalcogenide (TMDC) moiré systems provide an ideal framework to investigate strongly correlated physics. Here we theoretically study bosonic many-body phases of excitons in moiré TMDCs. By using two moiré models and cluster mean-field theory, we reveal that, due to non-local Coulomb interactions, moiré excitons can feature exotic supersolid phases, i.e. superfluids of broken translational invariance, and correlated insulating states. The correlated phases exist at experimentally accessible temperatures and are tunable via the twist angle and exciton density.
The dominance of Coulomb interactions over kinetic energy of electrons in narrow, non-trivial moiré bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases such as correlated insulators, superconductivity, orbital ferromagnetism, Chern insulators and nematicity. Most of these phases occur at or near an integer number of carriers per moiré unit cell. Experimental demonstration of ordered states at fractional moiré band-fillings at zero applied magnetic field $B$, is a challenging pursuit. In this letter, we report the observation of states near half-inte…
We report the nanoscale conductivity imaging of correlated electronic states in angle-aligned WSe2/WS2 heterostructures using microwave impedance microscopy. The noncontact microwave probe allows us to observe the Mott insulating state with one hole per moiré unit cell that persists for temperatures up to 150 K, consistent with other characterization techniques. In addition, we identify for the first time a Mott insulating state at one electron per moiré unit cell. Appreciable inhomogeneity of the correlated states is directly visualized in the hetero-bilayer region, indicative of local disord…
The integer quantum Hall state occurs when the Landau levels are fully occupied by the fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by the strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of the hard-core bosons in a multi-band lattice model hosting topological flat bands with high Chern number. The previously proposed $ν=1/3$ fractional Chern insulating state inherited from the high Chern number $C=2$ of the lowest topological flat band is revisited by the infinite density matrix renor…
ABC-stacked trilayer graphene/hBN moiré superlattice (TLG/hBN) has emerged as a playground for correlated electron physics. We report spectroscopy measurements of dual-gated TLG/hBN using Fourier transformed infrared photocurrent spectroscopy. We observed a strong optical transition between moiré mini-bands that narrows continuously as a bandgap is opened by gating, indicating a reduction of the single particle bandwidth. At half-filling of the valence flat band, a broad absorption peak emerges at ~18 meV, indicating direct optical excitation across an emerging Mott gap. Similar photocurrent s…
Moiré superlattices are emerging as a new route for engineering strongly correlated electronic states in two-dimensional van der Waals heterostructures, as recently demonstrated in the correlated insulating and superconducting states in magic-angle twisted bilayer graphene and ABC trilayer graphene/boron nitride moiré superlattices. Transition metal dichalcogenide (TMDC) moiré heterostructures provide another exciting model system to explore correlated quantum phenomena, with the addition of strong light-matter interactions and large spin-orbital coupling. Here we report the optical detection …
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）
Moiré heterostructures are rapidly emerging as a tunable platform to study correlated electronic phenomena. Discovery of exotic quantum phases in moiré systems requires novel probes of charge and spin order. Unlike detection schemes which average over several moiré cells, local sensors can provide richer information with greater sensitivity. We study a WSe$_2$/MoSe$_2$/WSe$_2$ heterotrilayer which hosts excitons and electrons in distinct moiré lattices, and show that localized dipolar excitons are sensitive proximity charge sensors, uncovering numerous correlated electronic states at fractiona…
Robust valley-polarized excitonic Mott states and doublons enabled by stacking-controlled moiré geometry
National Taiwan University（国立台湾大学）；University of Washington（华盛顿大学）；National Institute for Materials Science（国家材料研究所）；Arizona State University（亚利桑那州立大学）
Inspired by the rich physics of twisted 2D bilayer moiré systems, we study Coulomb interacting systems subjected to two overlapping finite 1D lattice potentials of unequal periods through exact numerical diagonalization. Unmatching underlying lattice periods lead to a 1D bichromatic `moiré' superlattice with a large unit cell and consequently a strongly flattened band, exponentially enhancing the effective dimensionless electron-electron interaction strength and manifesting clear signatures of enhanced Mott gaps at discrete fillings. An important non-perturbative finding is a remarkable fine-t…
Superconductivity often occurs close to broken-symmetry parent states and is especially common in doped magnetic insulators. When twisted close to a magic relative orientation angle near 1 degree, bilayer graphene has flat moire superlattice minibands that have emerged as a rich and highly tunable source of strong correlation physics, notably the appearance of superconductivity close to interaction-induced insulating states. Here we report on the fabrication of bilayer graphene devices with exceptionally uniform twist angles. We show that the reduction in twist angle disorder reveals insulatin…
The evolution of a Landau Fermi liquid into a nonmagnetic Mott insulator with increasing electronic interactions is one of the most puzzling quantum phase transitions in physics. The vicinity of the transition is believed to host exotic states of matter such as quantum spin liquids, exciton condensates and unconventional superconductivity. Semiconductor moiré materials realize a highly controllable Hubbard model simulator on a triangular lattice, providing a unique opportunity to drive a metal-insulator transition (MIT) via continuous tuning of the electronic interactions. Here, by electricall…
Collective plasma excitations in moiré flat bands display unique properties reflecting strong electron-electron interactions and unusual carrier dynamics in these systems. Unlike the conventional two-dimensional plasmon modes, dispersing as $\sqrt{k}$ at low frequencies and plunging into particle-hole continuum at higher frequencies, the moiré plasmons pierce through the flat-band continuum and acquire a strong over-the-band character. Due to the complex structure of the moiré superlattice unit cell, the over-the-band plasmons feature several distinct branches connected through zone folding in…
Moiré systems have emerged in recent years as a rich platform to study strong correlations. Here, we will discuss a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of twisted moiré heterostructures -- but without introducing a twist. We consider a monolayer graphene sheet subject to a $C_2$-breaking periodic strain-induced psuedomagnetic field (PMF) with period $L_M \gg a$, along with a scalar potential of the same period. This system has {\it almost ideal} flat bands with valley-resolved Chern number $\pm 1$, where the deviatio…
Moiré superlattices created by the twisted stacking of two-dimensional crystalline monolayers can host electronic bands with flat energy dispersion in which interaction among electrons is strongly enhanced. These superlattices can also create non-trivial electronic band topologies making them a platform for study of many-body topological quantum states. Among the moiré systems realized to date, there are those predicted to have band structures and properties which can be controlled with a perpendicular electric field. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphen…
We show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle flat bands. When the system is insulating at moiré band filling $ν=-3$, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moiré Brillouin zone, one of which couples strongly to THz photons. The low-energy collective modes are faithfully described by a model with a local $SU…
The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, …
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the corre…
