To have a fully ab initio description of the Moiré pattern in a transition metal dichalcogenide heterobilayer, we have carried out density functional theory calculations, taking accounts of both atomic registry in and the lattice corrugation out of the monolayers, on a MoTe2(9*9)/MoS2(10*10) system which has a moderate size of superlattice larger than an exciton yet not large enough to justify a continuum model treatment. We find that the local potential in the midplane of the bilayer displays a conspicuous Moiré pattern. It further leads us to reveal that the variation of the average local potential near Mo atoms in both MoTe2 and MoS2 layers make intralayer Moiré potentials. They are the result of mutual modulation and correlate directly with the spatial variation of the valence band maximum and conduction band minimum. The interlayer Moiré potential, defined as the difference between the two intralayer Moiré potentials, has a depth of 0.11 eV and changes roughly in proportion to the band gap variation in the Moiré cell, which has an amplitude of 0.04 eV. We find the lattice corrugation is significant in both MoTe2 (0.30Å) and MoS2 (0.77Å) layers, yet its effect on the electronic properties is marginal. The wrinkling of the MoTe2/MoS2 bilayer enhances the spatial variation of the local band gap by 5 meV, while its influence on the global band gap is within 1 meV. A simple intralayer band-coupling model is proposed to understand the correlation of Moiré potential and spatial variation of the band gap.
Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling $ν=2$ (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling $ν=1$ were observed in AB stacked moiré MoTe$_2$/WSe$_2$ heterobilayers. However, how the topologically nontrivial s…
Van der Waals (vdW) heterostructures formed by 2D atomic crystals provide a powerful approach towards designer condensed matter systems. Incommensurate heterobilayers with small twisting and/or lattice mismatch lead to the interesting concept of Moiré superlattice, where the atomic registry is locally indistinguishable from commensurate bilayers but has local-to-local variation over long range. Here we show that such Moiré superlattice can lead to periodic modulation of local topological order in vdW heterobilayers formed by two massive Dirac materials. By tuning the vdW heterojunction from no…
The formation of interfacial moiré patterns from angular and/or lattice mismatch has become a powerful approach to engineer a range of quantum phenomena in van der Waals heterostructures. For long-lived and valley-polarized interlayer excitons in transition-metal dichalcogenide (TMDC) heterobilayers, signatures of quantum confinement by the moiré landscape have been reported in recent experimental studies. Such moiré confinement has offered the exciting possibility to tailor new excitonic systems, such as ordered arrays of zero-dimensional (0D) quantum emitters and their coupling into topologi…
Layered two-dimensional materials exhibit rich transport and optical phenomena in twisted or lattice-incommensurate heterostructures with spatial variations of interlayer hybridization arising from moiré interference effects. Here, we report experimental and theoretical studies of excitons in twisted heterobilayers and heterotrilayers of transition metal dichalcogenides. Using MoSe$_2$-WSe$_2$ stacks as representative realizations of twisted van der Waals bilayer and trilayer heterostructures, we observe contrasting optical signatures and interpret them in the theoretical framework of interlay…
Moiré patterns with angular mismatch in van der Waals heterostructures composed of atomically thin semiconducting materials are a fascinating platform to engineer the optically generated excitonic properties towards novel quantum phenomena. The moiré pattern as a periodic trap potential can give rise to spatially ordered zero-dimensional (0D) exciton ensembles, which offers the possibility for dense coherent quantum emitters and quantum simulation of many-body physics. The intriguing moiré exciton properties are affected by their dynamics and exciton-phonon interaction. However, the moiré exci…
It has recently been shown that quantum-confined states can appear in epitaxially grown van der Waals material heterobilayers without a rotational misalignment ($θ=0^\circ$), associated with flat bands in the Brillouin zone of the moiré pattern formed due to the lattice mismatch of the two layers. Peaks in the local density of states and confinement in a MoS$_2$/WSe$_2$ system was qualitatively described only considering local stacking arrangements, which cause band edge energies to vary spatially. In this work, we report the presence of large in-plane strain variation across the moiré unit ce…
Moiré Phonons and Emergent Exciton-Phonon Coupling in a Moiré Heterobilayer
University of California, Berkeley（加州大学伯克利分校）；Kavli Energy NanoScience Institute（卡弗里能源纳米科学研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Indian Institute of Science（印度科学学院）；Newcastle University（纽卡斯尔大学）；National Institute for Materials Science（国立材料研究所）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Northeastern University（东北大学）
The moire potential, induced by stacking two monolayer semiconductors with slightly different lattice mismatches, acts as periodic quantum confinement for optically generated excitons, resulting in spatially ordered zero-dimensional quantum systems. However, there are limitations to exploring intrinsic optical properties of moire excitons due to ensemble averaged and broadened emissions from many peaks caused by the inhomogeneity of the moire potential. In this study, we proposed a microfabrication technique based on focused Ga+ ion beams, which enables us to control the number of peaks origin…
Moiré patterns of transition metal dichalcogenide (TMD) heterobilayers have proven to be an ideal platform to host unusual correlated electronic phases, emerging magnetism, and correlated exciton physics. While the existence of novel moiré excitonic states is established through optical measurements, the microscopic nature of these states is still poorly understood, often relying on empirically fit models. Here, combining large-scale first-principles GW-BSE calculations and micro-reflection spectroscopy, we identify the nature of the exciton resonances in WSe$_2$/WS$_2$ moiré superlattices, di…
The nanoscale periodic potentials introduced by moiré patterns in semiconducting van der Waals (vdW) heterostructures provide a new platform for designing exciton superlattices. To realize these applications, a thorough understanding of the localization and delocalization of interlayer excitons in the moiré potentials is necessary. Here, we investigated interlayer exciton dynamics and transport modulated by the moiré potentials in WS$_2$-WSe$_2$ heterobilayers in time, space, and momentum domains using transient absorption microscopy combined with first-principles calculations. Experimental re…
The availability of accessible fabrication methods based on deterministic transfer of atomically thin crystals has been essential for the rapid expansion of research into van der Waals heterostructures. An inherent issue of these techniques is the deformation of the polymer carrier film during the transfer, which can lead to highly non-uniform strain induced in the transferred two-dimensional material. Here, using a combination of optical spectroscopy, atomic force and Kelvin probe force microscopy, we show that the presence of nanometer scale wrinkles formed due to transfer-induced stress rel…
Electric-field-tuned consecutive topological phase transitions between distinct correlated insulators in moire MoTe2/WSe2 heterobilayer
State Key Laboratory of Micro-nano Engineering Science, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院，微纳工程科学国家重点实验室，人工结构与控制教育部重点实验室）；School of Applied and Engineering Physics, Cornell University（康奈尔大学应用与工程物理学院）；Departments of Physics and Applied Physics, Stanford University（斯坦福大学物理与应用物理系）；National Institute for Materials Science（日本物质材料研究机构）；SLAC National Accelerator Laboratory（斯坦福直线加速器国家实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Kavli Institute at Cornell for Nanoscale Science（康奈尔大学卡弗里纳米科学研究所）；Max Planck Institute for the Structure and Dynamics of Matter（德国马普物质结构与动力学研究所）
Topographic scanning tunneling microscopy (STM) images of epitaxial single layer graphene on the Rh(111) surface reveal that extended single crystalline graphene domains are produced without any defects on a large scale. High resolution imaging shows that the moiré structure resulting from the lattice mismatch between the Rh(111) substrate and graphene is highly corrugated, containing regions of an additional spatial modulation in the moiré supercell compared with those previously reported for graphene on Ir(111) or graphene on Ru(0001). These areas, which correspond to the "bridge" regions of…
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…
A major theoretical challenge of studying twisted transition metal dichalcogenide (TMD) bilayers is that the unit cell of such structures is very large and therefore difficult to address using first-principles methods. However, twisted TMD bilayers form moiré patterns, which consist of regions of commensurate stacking, either smoothly interpolated into one another or separated by sharp domain walls. In this paper, we study twisted TMD bilayers by studying the properties of the constituent commensurate structures. Using density functional theory (DFT), we compute band structures for commensurat…
Photo-induced charge separation in transition metal dichalcogenide heterobilayers is being explored for moiré excitons, spin-valley polarization, and quantum phases of excitons/electrons. While different momentum spaces may be critically involved in charge separation dynamics, little is known directly from experiments. Here we determine momentum-resolved electron dynamics in the WS2/MoS2 heterobilayer using time and angle resolved photoemission spectroscopy (TR-ARPES). Upon photoexcitation in the K valleys, we detect electrons in M/2, M, and Q valleys/points on time scales as short as ~70 fs, …
We have studied the incommensurate moiré structure of epitaxial graphene grown on iridium(111) by dynamic low energy electron diffraction [LEED-I(V)] and non-contact atomic force microscopy (AFM) with a CO terminated tip. Our LEED-I(V) results yield the average positions of all the atoms in the surface unit cell and are in qualitative agreement with the structure obtained from density functional theory (DFT). The AFM experiments reveal local variations of the moiré structure: the corrugation varies smoothly over several moiré unit cells between 42 and 56 pm. We attribute these variations to th…
Nearly localized moire flat bands in momentum space, arising at particular twist angles, are the key to achieve correlated effects in transition-metal dichalcogenides. Here, we use angle-resolved photoemission spectroscopy (ARPES) to visualize the presence of a flat band near the Fermi level of van der Waals (vdW) WSe2/MoSe2 heterobilayer grown by molecular beam epitaxy. This flat band is localized near the K point of the Brillouin zone and has a width of several hundred meVs. By combining ARPES measurements with density functional theory (DFT) calculations, we confirm the coexistence of diffe…
Recent experiments on the twisted transition metal dichalcogenide (TMD) material, $\rm WSe_2/WS_2$, have observed insulating states at fractional occupancy of the moiré bands. Such states were conceived as generalized Wigner crystals (GWCs). In this article, we investigate the problem of Wigner crystallization in the presence of an underlying (moiré) lattice. Based on the best estimates of the system parameters, we find a variety of homobilayer and heterobilayer TMDs to be excellent candidates for realizing GWCs. In particular, our analysis based on $r_{s}$ indicates that $\rm MoSe_{2}$ (among…
The properties of van der Waals (vdW) heterostructures are drastically altered by a tunable moiré superlattice arising from periodic variations of atomic alignment between the layers. Exciton diffusion represents an important channel of energy transport in semiconducting transition metal dichalcogenides (TMDs). While early studies performed on TMD heterobilayers have suggested that carriers and excitons exhibit long diffusion lengths, a rich variety of scenarios can exist. In a moiré crystal with a large supercell size and deep potential, interlayer excitons may be completely localized. As the…
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…
We study the electronic and topological properties of fully relaxed twisted bilayer (TBG) and double bilayer (TDBG) graphene under perpendicular pressure. An approach has been proposed to obtain the equilibrium in-plane structural deformation and out-of-plane corrugation in moiré superlattices under pressure. We find that the in-plane relaxation becomes much stronger under higher pressure, while the corrugation height in each layer is maintained. The comparison between band structures of relaxed and rigid structures demonstrates that not only the gaps on the electron and hole sides ($Δ_e$ and …
