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/h ~ 1011 cm-2 and from the exciton gas to the highly mobile charge separated electron/hole plasma for ne/h > 1012 cm-2. The latter is the Mott transition and is confirmed in photoconductivity measurements. These findings set fundamental limits for achieving quantum states of interlayer excitons.
We reveal by first-principles calculations that the interlayer binding in a twisted MoS2/MoTe2 heterobilayer decreases with increasing twist angle, due to the increase of the interlayer overlapping degree, a geometric quantity describing well the interlayer steric effect. The binding energy is found to be a Gaussian-like function of twist angle. The resistance to rotation, an analogue to the interlayer sliding barrier, can also be defined accordingly. In sharp contrast to the case of MoS2 homobilayer, here the energy band gap reduces with increasing twist angle. We find a remarkable interlayer…
We present theoretical results for the radiative rates and doping-dependent photoluminescence spectrum of interlayer excitonic complexes localized by donor impurities in MoSe$_2$/WSe$_2$ twisted heterobilayers, supported by quantum Monte Carlo calculations of binding energies and wave-function overlap integrals. For closely aligned layers, radiative decay is made possible by the momentum spread of the localized complexes' wave functions, resulting in few $μ$s$^{-1}$ radiative rates. For strongly misaligned layers, the short-range interaction between the carriers and impurity provides a finite …
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…
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…
We show that, because of the inevitable twist and lattice mismatch in heterobilayers of transition metal dichalcogenides, interlayer excitons have six-fold degenerate light cones anomalously located at finite velocities on the parabolic energy dispersion. The photon emissions at each light cone are elliptically polarized, with major axis locked to the direction of exciton velocity, and helicity specified by the valley indices of the electron and the hole. These finite-velocity light cones allow unprecedented possibilities to optically inject valley polarization and valley current, and the obse…
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…
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…
Due to their unique two-dimensional nature, charge carriers in semiconducting transition metal dichalcogenides (TMDs) exhibit strong unscreened Coulomb interactions and sensitivity to defects and impurities. The versatility of van der Waals layer stacking allows spatially separating electrons and holes between different TMD layers with staggered band structure, yielding interlayer few-body excitonic complexes whose nature is still debated. Here we combine quantum Monte Carlo calculations with spectrally and temporally resolved photoluminescence measurements on a top- and bottom-gated MoSe2/WSe…
We investigate the optical properties of spin-triplet interlayer excitons in heterobilayer transition metal dichalcogenides in comparison with the spin-singlet ones. Surprisingly, the optical transition dipole of the spin-triplet exciton is found to be in the same order of magnitude to that of the spin-singlet exciton, in sharp contrast to the monolayer excitons where the spin triplet species is considered as dark compared to the singlet. Unlike the monolayer excitons whose spin-conserved (spin-flip) transition dipole can only couple to light of in-plane (out-of-plane) polarization, such restr…
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 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…
The valence flat bands in transition metal dichalcogenide (TMD) heterobilayers are shown to exhibit strong intralayer spin-orbit coupling. This is reflected in a simple tight-binding model with spin-dependent complex hoppings based on the continuum model. A perpendicular electric field causes interlayer hybridization, such that the effective model is equivalent to the Kane-Mele model of topological insulators. The proposed model can be used as a starting point to understand interactions and the experimentally observed topological phases.
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 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…
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, …
Stacking two-dimensional (2D) van der Waals materials with different interlayer atomic registry in a heterobilayer causes the formation of a long-range periodic superlattice that may bestow the heterostructure with exotic properties such as new quantum fractal states [1-3] or superconductivity [4, 5]. Recent optical measurements of transition metal dichalcogenide (TMD) heterobilayers have revealed the presence of hybridized interlayer electron-hole pair excitations at energies defined by the superlattice potential [6-10]. The corresponding quasiparticle band structure, so-called minibands, hav…
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…
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…
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…
Van der Waals heterostructures of 2D materials provide a powerful approach towards engineering various quantum phases of matters. Examples include topological matters such as quantum spin Hall (QSH) insulator, and correlated matters such as exciton superfluid. It can be of great interest to realize these vastly different quantum matters on a common platform, however, their distinct origins tend to restrict them to material systems of incompatible characters. Here we show that heterobilayers of two-dimensional valley semiconductors can be tuned through interlayer bias between an exciton superfl…
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…
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。
Valley selective hybridization and residual coupling of electronic states in commensurate van der Waals heterobilayers enable the control of the orbital character of interlayer excitons. We demonstrate electric field control of layer index, orbital character, lifetime and emission energy of indirect excitons in MoS2/WS2 heterobilayers embedded in an vdW field effect structure. Different excitonic dipoles normal to the layers are found to stem from bound electrons and holes located in different valleys of MoS2/WS2 with a valley selective degree of hybridization. For the energetically lowest emi…
Interlayer excitons, or bound electron-hole pairs whose constituent quasiparticles are located in distinct stacked semiconducting layers, are being intensively studied in heterobilayers of two dimensional semiconductors. They owe their existence to an intrinsic type-II band alignment between both layers that convert these into p-n junctions. Here, we unveil a pronounced interlayer exciton (IX) in heterobilayers of metal monochalcogenides, namely gamma-InSe on epsilon-GaSe, whose pronounced emission is adjustable just by varying their thicknesses given their number of layers dependent direct ba…
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 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…
Moiré patterns with a superlattice potential can be formed by vertically stacking two layered materials with a relative twist or lattice constant mismatch. The moiré superlattice can generate flat bands that result in new correlated insulating, superconducting, and topological states. Strong electron correlations, tunable by the fractional filling, have been observed in both graphene and transition metal dichalcogenide (TMD) based systems. In addition, in TMD based systems, the moiré potential landscape can trap interlayer excitons (IX) at specific atomic registries. Here we report that spatia…
