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 graphene are stacked with a twist angle, is such a tunable moiré system, for which partial filling of its flat band, transport studies have found correlated insulating states. Here we use gate-tuned scanning tunneling spectroscopy (GT-STS) to directly demonstrate the tunability of the band structure of TDBG with an electric field and to show spectroscopic signatures of both electronic correlations and topology for its flat band. Our spectroscopic experiments show excellent agreement with a continuum model of TDBG band structure and reveal signatures of a correlated insulator gap at partial filling of its isolated flat band. The topological properties of this flat band are probed with the application of a magnetic field, which leads to valley polarization and the splitting of Chern bands that respond strongly to the field with a large effective g-factor. Our experiments advance our understanding of the properties of TDBG and set the stage for further investigations of correlation and topology in such tunable moiré systems.
We propose a realization of Kondo-lattice physics in moiré superlattices at the interface between a WX$_2$ homobilayer and MoX$_2$ monolayer (where X=S,Se). Under appropriate gating conditions, the interface-WX$_2$-layer forms a triangular lattice of local moments that couple to itinerant electrons in the other WX$_2$-layer via a gate-tunable Kondo exchange interaction. Using a parton mean-field approach we identify a range of twist-angles which support a gate-tuned quantum phase transition between a heavy-fermion liquid with large anomalous Hall conductance and a fractionalized chiral spin-li…
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 …
Tunable Interlayer Charge-transfer States in MoSe$_2$/WS$_2$ Moiré Superlattices
University of California at Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；National Institute for Materials Science（物质材料研究机构）
Stacking monolayers of transition metal dichalcogenides into a heterostructure with a finite twist-angle gives rise to artificial moiré superlattices with a tunable periodicity. As a consequence, excitons experience a periodic potential, which can be exploited to tailor optoelectronic properties of these materials. While recent experimental studies have confirmed twist-angle dependent optical spectra, the microscopic origin of moiré exciton resonances has not been fully clarified yet. Here, we combine first principle calculations with the excitonic density matrix formalism to study transitions…
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 …
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.
A variety of novel quantum phases have been achieved in twist bilayer graphene (tBLG) and other moire superlattices recently, including correlated insulators, superconductivity, magnetism, and topological states. These phenomena are very sensitive to the moire superlattices, which can hardly be changed rapidly or intensely. Here, we report the experimental realization of a high-order moire pattern (a high-order interference pattern) in graphene-monolayer xenon heterostructure (G/mXe), with moire period in-situ tuned from few nanometers to infinity by changing the lattice constant of Xe through…
Moiré excitons are emergent optical excitations in 2D semiconductors with deep moiré superlattice potentials. While these excitations have been realized in several platforms, a system with dynamically tunable moiré potential to tailor the moiré exciton properties is yet to be realized. Here, we present a continuously tunable moiré potential in a monolayer WSe2 that is enabled by its proximity to twisted bilayer graphene (TBG) near the magic-angle. Due to its flat electronic bands, charge distribution is highly localized and forms a triangular lattice in TBG. Tuning the local charge density via…
Tunable high-Chern-number Chern insulators in rhombohedral tetralayer graphene/hBN moiré superlattices
State Key Laboratory of Micro-nano Engineering Science, Tsung-Dao Lee lnstitute & School of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University（上海交通大学微纳电子工程科学国家重点实验室、李政道研究所及物理与天文学院人工结构与量子控制教育部重点实验室）；Department of Physics, City University of Hong Kong（香港城市大学物理系）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国家材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料研究所材料纳米结构研究中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）；Department of Physics, Hong Kong University of Science and Technology（香港科技大学物理系）
It is well known that stacking domains form in moiré superlattices due to the competition between the interlayer van der Waals forces and intralayer elastic forces, which can be recognized as polar domains due to the local spontaneous polarization in bilayers without centrosymmetry. We propose a theoretical model which captures the effect of an applied electric field on the domain structure. The coupling between the spontaneous polarization and field leads to uneven relaxation of the domains, and a net polarization in the superlattice at nonzero fields, which is sensitive to the moiré period. …
Bandwidth-Limited Critical Currents in Electrically Tunable Moiré Bands
ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学技术研究院）；Massachusetts Institute of Technology（麻省理工学院）；National Graphene Institute, University of Manchester（国家石墨烯研究所，曼彻斯特大学）；Dept. of Physics & Astronomy, University of Manchester（物理与天文学系，曼彻斯特大学）；COMMIT, Department of Physics and NANOlight Center of Excellence, University of Antwerp（安特卫普大学物理系及NANOlight卓越中心）
We construct a van der Waals heterostructure consisting of three graphene layers stacked with alternating twisting angles $\pmθ$. At the average twist angle $θ\sim 1.56^{\circ}$, a theoretically predicted magic angle for the formation of flat electron bands, narrow conduction and valence moiré bands appear together with a linearly dispersing Dirac band. Upon doping the half-filled moiré valence band with holes, or the half-filled moiré conduction band with electrons, displacement field tunable superconductivity emerges, reaching a maximum critical temperature of 2.1 K at optimal doping and dis…
Semiconductor moiré heterostructures exhibit rich correlation-induced many-body phenomena with signatures of emergent magnetism, Mott insulating states or generalized Wigner crystals observed in optical spectroscopy by probing intralayer excitons. However, as the staggered band alignment in the underlying WSe$_2$/WS$_2$ heterobilayer system separates photoexcited electrons and holes to form lowest-energy interlayer excitons, direct access to interactions between correlated charge states and ground state moiré excitons remained elusive. Here, we use MoSe$_2$/WS$_2$ heterostacks with type-I band…
Moiré superlattice-induced sub-bands in twisted van der Waals homo- and hetero-structures govern their optical and electrical properties, rendering additional degrees of freedom such as twist angle. Here, we demonstrate the moiré superlattice effects on the intralayer excitons and trions in a twisted bilayer of MoS$_2$ of H-type stacking at marginal twist angles. We identify the emission from localized and multiple delocalized sub-bands of intralayer moiré excitons and show their electrical modulation by the corresponding trion formation. The electrical control of the oscillator strength of th…
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…
Transition metal dichalcogenide (TMD) moiré heterostructures provide an ideal platform to explore the extended Hubbard model1 where long-range Coulomb interactions play a critical role in determining strongly correlated electron states. This has led to experimental observations of Mott insulator states at half filling2-4 as well as a variety of extended Wigner crystal states at different fractional fillings5-9. Microscopic understanding of these emerging quantum phases, however, is still lacking. Here we describe a novel scanning tunneling microscopy (STM) technique for local sensing and manip…
The spatial texture of internal degree of freedom of electrons has profound effects on the properties of materials. Such texture in real space can manifest as an emergent magnetic field (or Berry curvature), which is expected to induce interesting valley/spin-related transport phenomena. Moiré pattern, which emerges as a spatial variation at the interface of 2D atomic crystals, provides a natural platform for investigating such real space Berry curvature effects. Here we study moiré structures formed in homobilayer transition metal dichalcogenides (TMDs) due to twisting, various uniform strain…
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…
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 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…
Tailoring electron transfer dynamics across solid-liquid interfaces is fundamental to the interconversion of electrical and chemical energy. Stacking atomically thin layers with a very small azimuthal misorientation to produce moiré superlattices enables the controlled engineering of electronic band structures and the formation of extremely flat electronic bands. Here, we report a strong twist angle dependence of heterogeneous charge transfer kinetics at twisted bilayer graphene electrodes with the greatest enhancement observed near the 'magic angle' (~1.1 degrees). This effect is driven by 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 …
The interplay of charge, spin, lattice, and orbital degrees of freedom leads to a wide range of emergent phenomena in strongly correlated systems. In heterobilayer transition metal dichalcogenide moiré systems, recent observations of Mott insulators and generalized Wigner crystals are well described by triangular lattice single-orbital Hubbard models based on K-valley derived moiré bands. Richer phase diagrams, mapped onto multi-orbital Hubbard models, are possible with hexagonal lattices in $Γ$-valley derived moiré bands and additional layer degrees of freedom. Here we report the tunable inte…
Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the n…
Transition metal dichalcogenide heterobilayers offer attractive opportunities to realize lattices of interacting bosons with several degrees of freedom. Such heterobilayers can feature moiré patterns that modulate their electronic band structure, leading to spatial confinement of single interlayer excitons (IXs) that act as quantum emitters with $C_3$ symmetry. However, the narrow emission linewidths of the quantum emitters contrast with a broad ensemble IX emission observed in nominally identical heterobilayers, opening a debate regarding the origin of IX emission. Here we report the continuo…
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…
