Photon antibunching, a hallmark of quantum light, has been observed in the correlations of light from isolated atomic and atomic-like solid-state systems. Two-dimensional semiconductor heterostructures offer a unique method to create a quantum light source: a small lattice mismatch or relative twist in a heterobilayer can create moiré trapping potentials for excitons which are predicted to create arrays of quantum emitters. While signatures of moiré trapped excitons have been observed, their quantum nature has yet to be confirmed. Here we report photon antibunching from single moiré trapped interlayer excitons in a heterobilayer. Via polarization resolved magneto-optical spectroscopy, we demonstrate the discrete anharmonic spectra arise from bound band-edge electron-hole pairs trapped in moiré potentials. Finally, using an out-of-plane electric field, we exploit the large permanent dipole of interlayer excitons to achieve large DC Stark tuning, up to 40 meV, of the quantum emitters. Our results confirm the quantum nature of moiré confined excitons and open opportunities to investigate their inhomogeneity and interactions between the emitters or tune single emitters into resonance with cavity modes or other emitters.
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…
Moiré superlattices provide a powerful way to engineer properties of electrons and excitons in two-dimensional van der Waals heterostructures. The moiré effect can be especially strong for interlayer excitons, where electrons and holes reside in different layers and can be addressed separately. In particular, it was recently proposed that the moiré superlattice potential not only localizes interlayer exciton states at different superlattice positions, but also hosts an emerging moiré quasi-angular momentum (QAM) that periodically switches the optical selection rules for interlayer excitons at …
We investigate the optical properties of interlayer excitons in heterobilayer transition metal dichalcogenides where moiré pattern is introduced by heterostrain, in comparison with that introduced by twisting (and/or lattice mismatch). Besides being a cause of the moiré texture, strain also effectively introduces a constant gauge potential on either electron or hole, which shifts the dispersion of kinetic energy with respect to the excitonic crystal momenta in the moiré superlattices.This leads to distinct exciton mini-band dispersions and light coupling properties from the twisting induced mo…
Moiré superlattices provide a powerful tool to engineer novel quantum phenomena in two-dimensional (2D) heterostructures, where 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 can emerge in different types of graphene/boron nitride moiré superlattices, while correlated insulating states and superconductivity have been reported in twisted bilayer graphene moiré superlattices. In addition to their dramatic effects on the single pa…
Moiré patterns are common in Van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moiré potential, and iii) the valle…
Moiré exciton features tunable Dirac dispersion and spatially dependent optical selection rules. With the long lifetime due to its interlayer nature, it is promising to realize a Bose-Einstein condensation of moiré excitons. Here we study the properties of moiré exciton condensate within the mean-field theory, with special focus on exciton-exciton interaction effect on the nonlinear Bloch band and Bloch waves of exciton condensate in moiré potential. We find the nonlinear dispersion of the moiré exciton condensate exhibits complex loop structure induced by exciton-exciton interaction. A nonlin…
Cascade transition between energy levels has important applications, such as in quantum information protocols and quantum cascade lasers. In two-dimensional heterostructure, the moiré superlattice potential can result in multiple interlayer exciton (IX) energy levels. We demonstrate the cascade transitions between such moiré IXs by performing time- and energy-resolved photoluminescence measurements. We show that the lower-energy moiré IX can be excited to higher-energy ones, facilitating IX population inversion.
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…
Moiré superlattices formed in van der Waals bilayers have enabled the creation and manipulation of new quantum states, as is exemplified by the discovery of superconducting and correlated insulating states in twisted bilayer graphene near the magic angle. Twisted bilayer semiconductors may lead to tunable exciton lattices and topological states, yet signatures of moiré excitons have been reported only in closely angularly-aligned bilayers. Here we report tuning of moiré lattice in WS$_{2}$ /MoSe$_{2}$ bilayers over a wide range of twist angles, leading to the continuous tuning of moiré lattice…
Stacking transition metal dichalcogenides (TMDs) to form moiré superlattices has provided exciting opportunities to explore many-body correlation phenomena of the moiré trapped carriers. TMDs bilayers, on the other hand, host long-lived interlayer exciton (IX), an elementary excitation of long spin-valley lifetime that can be optically or electrically injected. Here we find that, through the Coulomb exchange between mobile IXs and carriers, the IX bath can mediate both Heisenberg and Dzyaloshinskii-Moriya type spin interactions between moiré trapped carriers, controllable by exciton density an…
Moiré lattices formed from semiconductor bilayers host tightly localised excitons that can simultaneously couple strongly to light and possess large electric dipole moments. This facilitates the realization of new forms of polaritons that are very strongly interacting and that have been predicted to lead to strong optical nonlinearities controlled by multi-photon resonances. Here, we investigate the role of the non-local component of the exciton-exciton (dipolar) interactions on the optical response of these strongly-interacting moiré exciton-polaritons under conditions of strong optical drivi…
In van der Waals (vdW) heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice. While it is widely recognized that a moiré superlattice can modulate the electronic band structure and lead to novel transport properties including unconventional superconductivity and insulating behavior driven by correlations, its influence on optical properties has not been investigated experimentally. We present spectroscopic evidence that interlayer excitons are confined by the moiré potential in a high-quality MoSe…
In twisted homobilayer transition metal dichalcogenides, intra- and inter-layer valley excitons hybridize with the layer configurations spatially varying in the moiré. The ground state valley excitons are trapped at two high-symmetry points with opposite electric dipoles in a moiré supercell, forming a honeycomb superlattice of nearest-neighbor dipolar attraction. We find that the spatial texture of layer configuration results in a luminescence anomaly of the moiré trapped excitons, where a tiny displacement by interactions dramatically increases the brightness and changes polarization from ci…
Transition-metal dichalcogenide heterostructures exhibit moiré patterns that spatially modulate the electronic structure across the material's plane. For certain material pairs, this modulation acts as a potential landscape with deep, trigonally symmetric wells capable of localizing interlayer excitons, forming periodic arrays of quantum emitters. Here, we study these moiré localized exciton states and their optical properties. By numerically solving the two-body problem for an interacting electron-hole pair confined by a trigonal potential, we compute the localized exciton spectra for differe…
Moiré superlattices in van der Waals heterostructures have emerged as a powerful tool for engineering novel quantum phenomena. Here we report the observation of a correlated interlayer exciton insulator in a double-layer heterostructure composed of a WSe2 monolayer and a WS2/WSe2 moiré bilayer that are separated by an ultrathin hexagonal boron nitride (hBN). The moiré WS2/WSe2 bilayer features a Mott insulator state at hole density p/p0 = 1, where p0 corresponds to one hole per moiré lattice site. When electrons are added to the Mott insulator in the WS2/WSe2 moiré bilayer and an equal number …
Moiré superlattices in twisted van der Waals materials constitute a promising platform for engineering electronic and optical properties. However, a major obstacle to fully understanding these systems and harnessing their potential is the limited ability to correlate the local moiré structure with optical properties. By using a recently developed scanning electron microscopy technique to image twisted WSe$_2$/WSe$_2$ bilayers, we directly correlate increasing moiré periodicity with the emergence of two distinct exciton species. These can be tuned individually through electrostatic gating, and …
The propagation of excitons in TMD monolayers has been intensively studied revealing interesting many-particle effects, such as halo formation and non-classical diffusion. Initial studies have investigated how exciton transport changes in twisted TMD bilayers, including Coulomb repulsion and Hubbard-like exciton hopping. In this work, we investigate the twist-angle-dependent transition of the hopping regime to the dispersive regime of effectively free excitons. Based on a microscopic approach for excitons in the presence of a moiré potential, we show that the hopping regime occurs up to an ang…
Recent advances in the field of vertically stacked 2D materials have revealed a rich exciton landscape. In particular, it has been demonstrated that out-of-plane electrical fields can be used to tune the spectral position of spatially separated interlayer excitons. Other studies have shown that there is a strong hybridization of exciton states, resulting from the mixing of electronic states in both layers. However, the connection between the twist-angle dependent hybridization and field-induced energy shifts has remained in the dark. Here, we investigate on a microscopic footing the interplay …
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…
The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe$_2$ bilayers. In particular, we show that the strong hybridization of electrons at the $Λ$ point leads to a drastic reds…
Spatially periodic structures with a long range period, referred to as moiré pattern, can be obtained in van der Waals bilayers in the presence of a small stacking angle or of lattice mismatch between the monolayers. Theoretical predictions suggest that the resulting spatially periodic variation of the band structure modifies the optical properties of both intra and interlayer excitons of transition metal dichalcogenides heterostructures. Here, we report on the impact of the moiré pattern formed in a MoSe$_2$/MoS$_2$ heterobilayer encapsulated in hexagonal boron nitride. The periodic in-plane …
(Sub)nanoscale Visualization of Reconstruction-Driven Moiré Exciton Localization and Delocalization
Molecular Foundry, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室分子发现中心）；School for Engineering of Matter, Transport and Energy, Arizona State University（亚利桑那州立大学物质、运输与能源工程学院）；Department of Physics, University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）；National Institute for Materials Science（日本国立材料研究所）；Center for Nanophase Materials Sciences, Oak Ridge National Laboratory（橡树岭国家实验室纳米材料科学中心）；Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学学院）；McKetta Department of Chemical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校麦凯塔化学工程系）；Kavli Energy NanoScience Institute, University of California Berkeley（加州大学伯克利分校卡弗里能源纳米科学研究所）；Jawaharlal Nehru Centre for Advanced Scientific Research（贾瓦哈拉尔·尼赫鲁高级科学研究中心）
Unveiling the Spin-Valley Structure of Dipolar Exciton Ladders in R-stacked WSe$_2$/WS$_2$ Moiré Heterobilayers
Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University（赫瑞-瓦特大学光子与量子科学研究所）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料纳米结构研究中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（电子与光学材料研究中心）
研究 R 堆叠 WSe₂/WS₂ 莫尔异质双层中偶极激子阶梯的自旋-谷结构，用螺旋度分辨磁光致发光确定其微观起源，明确不同电荷填充时各激子态情况，建立超越简单占据数物理的自旋-谷分辨图像。
Moire superlattices in van der Waals (vdW) heterostructures could trap strongly bonded and long lived interlayer excitons. Assumed to be localized, these moire excitons could form ordered quantum dot arrays, paving the way for novel optoelectronic and quantum information applications. Here we perform first principles simulations to shed light on moire excitons in twisted MoS2/WS2 heterostructures. We provide the direct evidence of localized interlayer moire excitons in vdW heterostructures. The moire potentials are mapped out based on spatial modulations of energy gaps. Nearly flat valence ban…
The creation of moiré patterns in crystalline solids is a powerful approach to manipulate their electronic properties, which are fundamentally influenced by periodic potential landscapes. In 2D materials, a moiré pattern with a superlattice potential can form by vertically stacking two layered materials with a twist and/or finite lattice constant difference. This unique approach has led to emergent electronic phenomena, including the fractal quantum Hall effect, tunable Mott insulators, and unconventional superconductivity. Furthermore, theory predicts intriguing effects on optical excitations…
The optical properties of weakly-doped two-dimensional materials are dominated by strong exciton and trion absorption and luminescence features. In this article we examine the influence of moiré patterns in semiconductor heterobilayers on exciton and trion states in the limit of strong moiré modulation potentials, commenting on similarities and differences compared to the case of excitons and trions in semiconductor quantum dots. We discuss strategies for using optical properties as quantitative probes of moiré materials, and the prospects for exploiting moiré materials to design unique light …
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）
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.
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…
Controlling matter-light interactions with cavities is of fundamental importance in modern science and technology. It is exemplified in the strong-coupling regime, where matter-light hybrid modes form, with properties controllable via the photon component on the optical-wavelength scale. In contrast, matter excitations on the nanometer scale are harder to access. In two-dimensional van der Waals heterostructures, a tunable moiré lattice potential for electronic excitations may form, enabling correlated electron gases in lattice potentials. Excitons confined in moiré lattices have also been rep…
Geometrical moiré patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moiré superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band ed…
Moiré superlattices in atomically thin van-der-Waals heterostructures hold great promise for an extended control of electronic and valleytronic lifetimes, the confinement of excitons in artificial moiré lattices, and the formation of novel exotic quantum phases. Such moiré-induced emergent phenomena are particularly strong for interlayer excitons, where the hole and the electron are localized in different layers of the heterostructure. In order to exploit the full potential of correlated moiré and exciton physics, a thorough understanding of the ultrafast interlayer exciton formation process a…
We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moiré pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moiré Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the excito…
