We calculate the spectrum of interlayer neutral excitons in transition-metal-dichalcogenide WeSe$_2$/MoSe$_2$ heterobilayers in the $R$-stacking configuration. Most saliently, we show that, similarly to neutral excitons and trions in monolayer transition-metal dichalcogenides, the spectrum is sensitive to the Berry curvature and thus quantum-geometric effects underlying the electron and hole wave functions. Due to the spatial separation between the electron and hole constituting the exciton in different layers, the Berry-curvature-induced splitting of the between the $2p_+$ and the $2p_-$ exciton states is smaller than for monolayer excitons. Furthermore, we investigate the dependence of the exciton spectra on the dielectric environment and the twist angle between the two layers. Finally, the long-lived moiré interlayer exciton ground state ($1s$) enhances the possibility of creating brightened $2p_{\pm}$ states using a circularly polarized medium-infrared probe from the $1s$ ground state. As a result, we determine the polarizability of the $1s-2p_{\pm}$ transition, following by two-level dressed model for the optical Stark effect.
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…
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…
The optical spectra of vertically stacked MoSe$_2$/WSe$_2$ heterostructures contain additional 'interlayer' excitonic peaks that are absent in the individual monolayer materials and exhibit a significant spatial charge separation in out-of-plane direction. Extending on a previous study, we used a many-body perturbation theory approach to simulate and analyse the excitonic spectra of MoSe$_2$/WSe$_2$ heterobilayers with three stacking orders, considering both momentum-direct and momentum-indirect excitons. We find that the small oscillator strengths and corresponding optical responses of the in…
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…
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…
Identifying quantum numbers to label elementary excitations is essential for the correct description of light-matter interaction in solids. In monolayer semiconducting transition metal dichalcogenides (TMDs) such as MoSe$_2$ or WSe$_2$, most optoelectronic phenomena are described well by labelling electron and hole states with the spin projection along the normal to the layer (S$_z$). In contrast, for WSe$_2$/MoSe$_2$ interfaces recent experiments show that taking S$_z$ as quantum number is not a good approximation, and spin mixing needs to be always considered. Here we argue that the correct …
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…
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…
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…
Moiré structures in van der Waals heterostructures lead to emergent phenomena including superconductivity in twisted bilayer graphene and optically accessible strongly-correlated electron states in transition metal dichalcogenide heterobilayers. Dual periodicity moiré structures (DPMS) formed in layered structures with more than two layers have been shown to lead to ferromagnetism and multiple secondary Dirac points in TBG. Whilst in principle it is possible to obtain DPMS in bilayers there has not been clear experimental evidence of this yet. In this paper we present signatures of DPMS in a t…
Charge separated interlayer excitons in transition metal dichalcogenide (TMDC) heterobilayers are being explored for moiré exciton lattices and exciton condensates. The presence of permanent dipole moments and the poorly screened Coulomb interaction make many body interactions particularly strong for interlayer excitons. Here we reveal two distinct phase transitions for interlayer excitons in the MoSe2/WSe2 heterobilayer using time and spatially resolved photoluminescence imaging: from trapped excitons in the moiré-potential to the modestly mobile exciton gas as exciton density increases to ne…
Controlling the Atomic Reconstruction in Twisted MoSe$_2$/WSe$_2$ with a Monolayer hBN Spacer
Walter Schottky Institute and Physics Department, TU Munich（慕尼黑工业大学瓦尔特·肖特基研究所与物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Materials Science and Engineering, Massachusetts Institute of Technology（麻省理工学院材料科学与工程系）；MIT.nano, Massachusetts Institute of Technology（麻省理工学院MIT.nano）；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架构研究中心）
We investigate WSe$_2$-MoSe$_2$ heterobilayers with different twist angles $θ\pm δ$ between the two layers, by low-frequency Raman scattering. In sufficiently aligned samples with $θ=0^\circ$, or $θ=60^\circ$, and $δ\lesssim 3^\circ$, we observe an interlayer shear mode (ISM), which is a clear sign of a commensurate bilayer structure, i.e., the layers must undergo an atomic reconstruction to form R-type or H-type stacking orders. We find slightly different ISM energies of about 18~cm$^{-1}$ and 17~cm$^{-1}$ for H-type and R-type reconstructions, respectively, independent of the exact value of …
We have performed a comprehensive first-principles study of the electronic and magnetic properties of two-dimensional (2D) transition-metal dichalcogenide (TMD) heterobilayers MX2/MoS2 (M = Mo, Cr, W, Fe, V; X = S, Se). For M = Mo, Cr, W; X=S, Se, all heterobilayers show semiconducting characteristics with an indirect bandgap with the exception of the WSe2/MoS2 heterobilayer which retains the direct-band-gap character of the constituent monolayer. For M = Fe, V; X = S, Se, the MX2/MoS2 heterobilayers exhibit metallic characters. Particular attention of this study has been focused on engineerin…
Quantum spin Hall (QSH) insulator with large gap is highly desirable for potential spintronics application. Here we realize electrically tunable QSH insulator with large gap in van der Waals heterobilayer of monolayer transition metal dichalcogenide (TMD) and hexagonal BAs. When the type II band alignment gets inverted in an electric field, the hybridization by interlayer hopping between the spin-valley locked valence band edges in TMD and the BAs conduction band edges leads to a stacking-configuration dependent topological band inversion. In the non-interacting limit, the double spin degenera…
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…
Coherent coupling between excitons is at the heart of many-body interactions with transition metal dichalcogenide (TMD) heterostructures as an emergent platform for the investigation of these interactions. We employ multi-dimensional coherent spectroscopy on monolayer MoSe\textsubscript{2}/WSe\textsubscript{2} heterostructures and observe coherent coupling between excitons spatially localized in monolayer MoSe$_2$ and WSe$_2$. Through many-body spectroscopy, we further observe the absorption state arising from free interlayer electron-hole pairs. This observation yields a spectroscopic measure…
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。
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…
We perform coherent nonlinear spectroscopy of excitons in single-layers of MoSe$_2$ and WSe$_2$ encapsulated between thin films of hexagonal boron nitride. Employing four-wave mixing microscopy we identify virtually disorder free areas, generating exciton optical response at the homogeneous limit. Focussing on such areas, we measure exciton homogeneous broadening as a function of environmental factors, namely temperature and exciton density. Exploiting FWM imaging, we find that at such locations, nonlinear absorption of the exciton excited states and their coherent couplings can be observed. U…
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…
Two-dimensional moiré materials provide a highly tunable platform to investigate strongly correlated electronic states. Such emergent many-body phenomena can be optically probed in moiré systems created by stacking two layers of transition metal dichalcogenide semiconductors: optically injected excitons can interact with itinerant carriers occupying narrow moiré bands to form exciton-polarons sensitive to strong correlations. Here, we investigate the behaviour of excitons dressed by a Fermi sea localised by the moiré superlattice of a molybdenum diselenide (MoSe$_2$) / tungsten diselenide (WSe…
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…
Based on \emph{ab initio} theoretical calculations of the optical spectra of vertical heterostructures of MoSe$_2$ (or MoS$_2$) and WSe$_2$ sheets, we reveal two spin-orbit-split Rydberg series of excitonic states below the \textsl{A} excitons of MoSe$_2$ and WSe$_2$ with a significant binding energy on the order of 250\,meV for the first excitons in the series. At the same time, we predict crystalographically aligned MoSe$_2$/WSe$_2$ heterostructures to exhibit an indirect fundamental band gap. Due to the type-II nature of the MoSe$_2$/WSe$_2$ heterostructure, the indirect transition and the …
Hybridisation of electronic bands of two-dimensional materials, assembled into twistronic heterostructures, enables one to tune their optoelectronic properties by selecting conditions for resonant interlayer hybridisation. Resonant interlayer hybridisation qualitatively modifies the excitons in such heterostructures, transforming these optically active modes into superposition states of interlayer and intralayer excitons. For MoSe$_2$/WSe$_2$ heterostructures, strong hybridization occurs between the holes in the spin-split valence band of WSe$_2$ and in the top valence band of MoSe$_2$, especi…
We propose a new mechanism to explain the quantum anomalous Hall (QAH) effect and the electric-field-induced topological phase transition in AB-stacked MoTe${}_2$/WSe${}_2$ moiré heterobilayers at $ν=1$ hole filling. We suggest that the Chern band of the QAH state is generated from an intrinsic band inversion composed of the highest two moiré hole bands with opposite valley numbers and a gap opening induced by two Coulomb-interaction-driven magnetic orders. These magnetic orders, including an in-plane $120^{\circ}$-Néel order and an in-plane ferromagnetic order, interact with moiré bands via c…
We investigate the twist-angle and gate dependence of the proximity-induced exchange coupling in the monolayer transition-metal dichalcogenides (TMDCs) MoSe$_2$ and WSe$_2$ due to the vdW coupling to the ferromagnetic semiconductor CrI$_3$, from first-principles calculations. A model Hamiltonian, that captures the relevant band edges at the $K/K^{\prime}$ valleys of the proximitized TMDCs, is employed to quantify the proximity-induced exchange. Upon twisting from 0° to 30°, we find a transition of the TMDC valence band (VB) edge exchange splitting from about $-2$ to $2$ meV, while the conducti…
Two-dimensional (2D) materials, such as graphene1, boron nitride2, and transition metal dichalcogenides (TMDs)3-5, have sparked wide interest in both device physics and technological applications at the atomic monolayer limit. These 2D monolayers can be stacked together with precise control to form novel van der Waals heterostructures for new functionalities2,6-9. One highly coveted but yet to be realized heterostructure is that of differing monolayer TMDs with type II band alignment10-12. Their application potential hinges on the fabrication, understanding, and control of bonded monolayers, w…
The emergence of various exciton-related effects in transition metal dichalcogenides (TMDC) and their heterostructures has inspired a significant number of studies and brought forth several possible applications. Often, standard photoluminescence (PL) with microscale lateral resolution is utilized to identify and characterize these excitonic phenomena, including interlayer excitons (IEXs). We studied the local PL signatures of van der Waals heterobilayers composed of exfoliated monolayers of the (Mo,W)(S,Se)$_2$ TMDC family with high spatial resolution (down to 30 nm) using tip-enhanced photol…
We report on the far-field photoluminescence intensity distribution of interlayer excitons in MoSe$_{2}$-WSe$_{2}$ heterostacks as measured by back focal plane imaging in the temperature range between 1.7 K and 20 K. By comparing the data with an analytical model describing the dipolar emission pattern in a dielectric environment, we are able to obtain the relative contributions of the in- and out-of-plane transition dipole moments associated to the interlayer exciton photon emission. We determine the transition dipole moments for all observed interlayer exciton transitions to be (99 $\pm$ 1)%…
