Anomalous Interlayer Exciton Diffusion in WS2/WSe2 Moiré Heterostructure.

Stacking van der Waals crystals allows for the on-demand creation of a periodic potential landscape to tailor the transport of quasiparticle excitations. We investigate the diffusion of photoexcited electron-hole pairs, or excitons, at the interface of WS2/WSe2 van der Waals heterostructure over a wide range of temperatures. We observe the appearance of distinct interlayer excitons for parallel and antiparallel stacking and track their diffusion through spatially and temporally resolved photoluminescence spectroscopy from 30 to 250 K. While the measured exciton diffusivity decreases with temperature, it surprisingly plateaus below 90 K. Our observations cannot be explained by classical models like hopping in the moiré potential. A combination of ab initio theory and molecular dynamics simulations suggests that low-energy phonons arising from the mismatched lattices of moiré heterostructures, also known as phasons, play a key role in describing and understanding this anomalous behavior of exciton diffusion. Our observations indicate that the moiré potential landscape is dynamic down to very low temperatures and that the phason modes can enable efficient transport of energy in the form of excitons.

Bidirectional phonon emission in two-dimensional heterostructures triggered by ultrafast charge transfer.

Photoinduced charge transfer in van der Waals heterostructures occurs on the 100 fs timescale despite weak interlayer coupling and momentum mismatch. However, little is understood about the microscopic mechanism behind this ultrafast process and the role of the lattice in mediating it. Here, using femtosecond electron diffraction, we directly visualize lattice dynamics in photoexcited heterostructures of WSe2/WS2 monolayers. Following the selective excitation of WSe2, we measure the concurrent heating of both WSe2 and WS2 on a picosecond timescale-an observation that is not explained by phonon transport across the interface. Using first-principles calculations, we identify a fast channel involving an electronic state hybridized across the heterostructure, enabling phonon-assisted interlayer transfer of photoexcited electrons. Phonons are emitted in both layers on the femtosecond timescale via this channel, consistent with the simultaneous lattice heating observed experimentally. Taken together, our work indicates strong electron-phonon coupling via layer-hybridized electronic states-a novel route to control energy transport across atomic junctions.

Intralayer charge-transfer moiré excitons in van der Waals superlattices.

Moiré patterns of transition metal dichalcogenide heterobilayers have proved to be an ideal platform on which to host unusual correlated electronic phases, emerging magnetism and correlated exciton physics. Whereas the existence of new moiré excitonic states is established1-4 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 (where G and W denote the one-particle Green's function and the screened Coulomb interaction, respectively) plus Bethe-Salpeter calculations and micro-reflection spectroscopy, we identify the nature of the exciton resonances in WSe2/WS2 moiré superlattices, discovering a rich set of moiré excitons that cannot be captured by prevailing continuum models. Our calculations show moiré excitons with distinct characters, including modulated Wannier excitons and previously unidentified intralayer charge-transfer excitons. Signatures of these distinct excitonic characters are confirmed experimentally by the unique carrier-density and magnetic-field dependences of different moiré exciton resonances. Our study highlights the highly non-trivial exciton states that can emerge in transition metal dichalcogenide moiré superlattices, and suggests new ways of tuning many-body physics in moiré systems by engineering excited-states with specific spatial characters.

Dynamic Tuning of Moiré Excitons in a WSe2/WS2 Heterostructure via Mechanical Deformation.

Moiré superlattices in van der Waals (vdW) heterostructures form by stacking atomically thin layers on top of one another with a twist angle or lattice mismatch. The resulting moiré potential leads to a strong modification of the band structure, which can give rise to exotic quantum phenomena ranging from correlated insulators and superconductors to moiré excitons and Wigner crystals. Here, we demonstrate the dynamic tuning of moiré potential in a WSe2/WS2 heterostructure at cryogenic temperature. We utilize the optical fiber tip of a cryogenic scanning near-field optical microscope (SNOM) to locally deform the heterostructure and measure its near-field optical response simultaneously. The deformation of the heterostructure increases the moiré potential, which leads to a red shift of the moiré exciton resonances. We observe the interlayer exciton resonance shifts up to 20 meV, while the intralayer exciton resonances shift up to 17 meV.

Imaging two-dimensional generalized Wigner crystals.

The Wigner crystal1 has fascinated condensed matter physicists for nearly 90 years2-14. Signatures of two-dimensional (2D) Wigner crystals were first observed in 2D electron gases under high magnetic field2-4, and recently reported in transition metal dichalcogenide moiré superlattices6-9. Direct observation of the 2D Wigner crystal lattice in real space, however, has remained an outstanding challenge. Conventional scanning tunnelling microscopy (STM) has sufficient spatial resolution but induces perturbations that can potentially alter this fragile state. Here we demonstrate real-space imaging of 2D Wigner crystals in WSe2/WS2 moiré heterostructures using a specially designed non-invasive STM spectroscopy technique. This employs a graphene sensing layer held close to the WSe2/WS2 moiré superlattice. Local STM tunnel current into the graphene layer is modulated by the underlying Wigner crystal electron lattice in the WSe2/WS2 heterostructure. Different Wigner crystal lattice configurations at fractional electron fillings of n = 1/3, 1/2 and 2/3, where n is the electron number per site, are directly visualized. The n = 1/3 and n = 2/3 Wigner crystals exhibit triangular and honeycomb lattices, respectively, to minimize nearest-neighbour occupations. The n = 1/2 state spontaneously breaks the original C3 symmetry and forms a stripe phase. Our study lays a solid foundation for understanding Wigner crystal states in WSe2/WS2 moiré heterostructures and provides an approach that is generally applicable for imaging novel correlated electron lattices in other systems.

Visualizing electron localization of WS2/WSe2 moiré superlattices in momentum space.

The search for materials with flat electronic bands continues due to their potential to drive strong correlation and symmetry breaking orders. Electronic moirés formed in van der Waals heterostructures have proved to be an ideal platform. However, there is no holistic experimental picture for how superlattices modify electronic structure. By combining spatially resolved angle-resolved photoemission spectroscopy with optical spectroscopy, we report the first direct evidence of how strongly correlated phases evolve from a weakly interacting regime in a transition metal dichalcogenide superlattice. By comparing short and long wave vector moirés, we find that the electronic structure evolves into a highly localized regime with increasingly flat bands and renormalized effective mass. The flattening is accompanied by the opening of a large gap in the spectral function and splitting of the exciton peaks. These results advance our understanding of emerging phases in moiré superlattices and point to the importance of interlayer physics.

Nanoscale Conductivity Imaging of Correlated Electronic States in WSe_{2}/WS_{2} Moiré Superlattices.

We report the nanoscale conductivity imaging of correlated electronic states in angle-aligned WSe_{2}/WS_{2} 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 heterobilayer region, indicative of local disorders in the moiré superlattice potential or electrostatic doping. Our work provides important insights on 2D moiré systems down to the microscopic level.

Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices.

Moiré superlattices can be used to engineer strongly correlated electronic states in two-dimensional van der Waals heterostructures, as recently demonstrated in the correlated insulating and superconducting states observed in magic-angle twisted-bilayer graphene and ABC trilayer graphene/boron nitride moiré superlattices1-4. Transition metal dichalcogenide moiré heterostructures provide another model system for the study of correlated quantum phenomena5 because of their strong light-matter interactions and large spin-orbit coupling. However, experimental observation of correlated insulating states in this system is challenging with traditional transport techniques. Here we report the optical detection of strongly correlated phases in semiconducting WSe2/WS2 moiré superlattices. We use a sensitive optical detection technique and reveal a Mott insulator state at one hole per superlattice site and surprising insulating phases at 1/3 and 2/3 filling of the superlattice, which we assign to generalized Wigner crystallization on the underlying lattice6-11. Furthermore, the spin-valley optical selection rules12-14 of transition metal dichalcogenide heterostructures allow us to optically create and investigate low-energy excited spin states in the Mott insulator. We measure a very long spin relaxation lifetime of many microseconds in the Mott insulating state, orders of magnitude longer than that of charge excitations. Our studies highlight the value of using moiré superlattices beyond graphene to explore correlated physics.

Valley-dependent exciton fine structure and Autler-Townes doublets from Berry phases in monolayer MoSe2.

The Berry phase of Bloch states can have profound effects on electron dynamics1-3 and lead to novel transport phenomena, such as the anomalous Hall effect and the valley Hall effect4-6. Recently, it was predicted that the Berry phase effect can also modify the exciton states in transition metal dichalcogenide monolayers, and lift the energy degeneracy of exciton states with opposite angular momentum through an effective valley-orbital coupling1,7-11. Here, we report the observation and control of the Berry phase-induced splitting of the 2p exciton states in monolayer molybdenum diselenide (MoSe2) using the intraexciton optical Stark spectroscopy. We observe the time-reversal-symmetric analogue of the orbital Zeeman effect resulting from the valley-dependent Berry phase, which leads to energy difference of +14 (-14) meV between the 2p+ and 2p- exciton states in the K (K') valley, consistent with the ordering from our ab initio GW-Bethe-Salpeter equation results. In addition, we show that the light-matter coupling between intraexciton states is remarkably strong, leading to a prominent valley-dependent Autler-Townes doublet under resonant driving. Our study opens up pathways to coherently manipulate the quantum states and excitonic excitation with infrared radiation in two-dimensional semiconductors.

Author Correction: Observation of moiré excitons in WSe2/WS2 heterostructure superlattices.

Change history: In this Letter, the following text has been added to the Acknowledgements section: "the scanning transmission electron microscopy measurements at the Molecular Foundry were supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract number DE-AC02-05CH11231". See accompanying Amendment.

Observation of moiré excitons in WSe2/WS2 heterostructure superlattices.

Moiré superlattices enable the generation of new quantum phenomena in two-dimensional heterostructures, in which the interactions between the atomically thin layers qualitatively change the electronic band structure of the superlattice. For example, mini-Dirac points, tunable Mott insulator states and the Hofstadter butterfly pattern can emerge in different types of graphene/boron nitride moiré superlattices, whereas correlated insulating states and superconductivity have been reported in twisted bilayer graphene moiré superlattices1-12. In addition to their pronounced effects on single-particle states, moiré superlattices have recently been predicted to host excited states such as moiré exciton bands13-15. Here we report the observation of moiré superlattice exciton states in tungsten diselenide/tungsten disulfide (WSe2/WS2) heterostructures in which the layers are closely aligned. These moiré exciton states manifest as multiple emergent peaks around the original WSe2 A exciton resonance in the absorption spectra, and they exhibit gate dependences that are distinct from that of the A exciton in WSe2 monolayers and in WSe2/WS2 heterostructures with large twist angles. These phenomena can be described by a theoretical model in which the periodic moiré potential is much stronger than the exciton kinetic energy and generates multiple flat exciton minibands. The moiré exciton bands provide an attractive platform from which to explore and control excited states of matter, such as topological excitons and a correlated exciton Hubbard model, in transition-metal dichalcogenides.

Ultrafast dynamics in van der Waals heterostructures.

Van der Waals heterostructures are synthetic quantum materials composed of stacks of atomically thin two-dimensional (2D) layers. Because the electrons in the atomically thin 2D layers are exposed to layer-to-layer coupling, the properties of van der Waals heterostructures are defined not only by the constituent monolayers, but also by the interactions between the layers. Many fascinating electrical, optical and magnetic properties have recently been reported in different types of van der Waals heterostructures. In this Review, we focus on unique excited-state dynamics in transition metal dichalcogenide (TMDC) heterostructures. TMDC monolayers are the most widely studied 2D semiconductors, featuring prominent exciton states and accessibility to the valley degree of freedom. Many TMDC heterostructures are characterized by a staggered band alignment. This band alignment has profound effects on the evolution of the excited states in heterostructures, including ultrafast charge transfer between the layers, the formation of interlayer excitons, and the existence of long-lived spin and valley polarization in resident carriers. Here we review recent experimental and theoretical efforts to elucidate electron dynamics in TMDC heterostructures, extending from timescales of femtoseconds to microseconds, and comment on the relevance of these effects for potential applications in optoelectronic, valleytronic and spintronic devices.

Imaging of pure spin-valley diffusion current in WS2-WSe2 heterostructures.

Transition metal dichalcogenide (TMDC) materials are promising for spintronic and valleytronic applications because valley-polarized excitations can be generated and manipulated with circularly polarized photons and the valley and spin degrees of freedom are locked by strong spin-orbital interactions. In this study we demonstrate efficient generation of a pure and locked spin-valley diffusion current in tungsten disulfide (WS2)-tungsten diselenide (WSe2) heterostructures without any driving electric field. We imaged the propagation of valley current in real time and space by pump-probe spectroscopy. The valley current in the heterostructures can live for more than 20 microseconds and propagate over 20 micrometers; both the lifetime and the diffusion length can be controlled through electrostatic gating. The high-efficiency and electric-field-free generation of a locked spin-valley current in TMDC heterostructures holds promise for applications in spin and valley devices.

Direct imaging of isofrequency contours in photonic structures.

The isofrequency contours of a photonic crystal are important for predicting and understanding exotic optical phenomena that are not apparent from high-symmetry band structure visualizations. We demonstrate a method to directly visualize the isofrequency contours of high-quality photonic crystal slabs that show quantitatively good agreement with numerical results throughout the visible spectrum. Our technique relies on resonance-enhanced photon scattering from generic fabrication disorder and surface roughness, so it can be applied to general photonic and plasmonic crystals or even quasi-crystals. We also present an analytical model of the scattering process, which explains the observation of isofrequency contours in our technique. Furthermore, the isofrequency contours provide information about the characteristics of the disorder and therefore serve as a feedback tool to improve fabrication processes.