Fabricating van der Waals (vdW) bilayer heterostructures (BL-HS) by stacking the same or different two-dimensional (2D) layers, offers a unique physical system with rich electronic and optical properties. Twist-angle between component layers has emerged as a remarkable parameter that can control the period of lateral confinement, and nature of the exciton (Coulomb bound electron-hole pair) in reciprocal space thus creating exotic physical states including moiré excitons. In this review article, we focus on opto-electronic properties of excitons in transition metal dichalcogenide (TMD) semiconductor twisted BL-HS. We look at existing evidence of moiré excitons in localized and strongly correlated states, and at nanoscale mapping of moiré superlattice and lattice-reconstruction. This review will be helpful in guiding the community as well as motivating work in areas such as near-field optical measurements and controlling the creation of novel physical states.
Recent experimental progresses have demonstrated the great potential of electronic and excitonic moiré superlattices in transition metal dichalcogenides (TMDs) for quantum many-body simulations and quantum optics applications. Here we reveal that the moiré potential landscapes in the TMDs heterostructures have an electrostatic origin from the spontaneous charge transfer across the heterointerfaces dependent on the atomic registry. This allows engineering tunable multi-chromatic superlattices through the interference of moiré potentials from independently configurable heterointerfaces in multil…
Moiré superlattices serve as a playground for emerging phenomena, such as localization of band states, superconductivity, and localization of excitons. These superlattices are large and are often modeled in the zero angle limit, which obscures the effect of finite twist angles. Here, by means of first-principles calculations we quantify the twist-angle dependence of the moiré potential in the MoS$_2$ homobilayer and identify the contributions from the constituent elements of the moiré potential. Furthermore, by considering the zero-angle limit configurations, we show that the moiré potential i…
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…
In bilayers of semiconducting transition metal dichalcogenides, the twist angle between layers can be used to introduce a highly regular periodic potential modulation on a length scale that is large compared to the unit cell. In such structures, correlated states can emerge, in which excitons in the heterostructure are strongly localized to the potential minima due to exciton-exciton interactions. We explore the transition between Mott and extended exciton phases in terms of a moiré-Bose-Hubbard Hamiltonian. Hopping and on-site interaction parameters are obtained from a Wannier representation …
Moiré superlattices of van der Waals heterostructures provide a powerful new way to engineer the electronic structures of two-dimensional (2D) materials. Many novel quantum phenomena have emerged in different moiré heterostructures, such as correlated insulators, superconductors, and Chern insulators in graphene systems and moiré excitons in transition metal dichalcogenide (TMDC) systems. Twisted phosphorene offers another attractive system to explore moiré physics because phosphorene features an anisotropic rectangular lattice, different from the isotropic hexagonal lattice in graphene and TM…
Flexible long period moir\' e superlattices form in two-dimensional van der Waals crystals containing layers that differ slightly in lattice constant or orientation. In this Letter we show theoretically that isolated flat moir\' e bands described by generalized triangular lattice Hubbard models are present in twisted transition metal dichalcogenide heterobilayers. The hopping and interaction strength parameters of the Hubbard model can be tuned by varying the twist angle and the three-dimensional dielectric environment. When the flat moiré bands are partially filled, candidate many-body ground…
Moiré materials have become one of the most active fields in material science in recent years due to their high tunability, and their unique properties emerge from the Moiré-scale structure modulation. Here, we propose twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ as a new Moiré material where the Moiré-scale modulation induces a topological phase transition. We show, in twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$, a topological insulator domain and a normal insulator domain coexist in the Moiré lattice structure, and edge states on the domain boundary make nearly flat bands that dominate the …
We study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity. We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit. The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moire patterns.
In two-dimensional (2D) twisted bilayers, the van der Waals (vdW) interlayer interaction introduces atomic-scale reconstruction at interface by locally rotating lattice to form strain-field vortex networks in their moiré superlattice. However, direct imaging the tiny local lattice rotation of the strain-field vortex requires extremely high spatial resolution and is an outstanding challenge in experiment. Here, a topmost small-period graphene moiré pattern is introduced to magnify sub-Angstrom distortions of the lattice and tiny local lattice rotation in underlying twisted bilayer graphene (TBG…
In this paper a systematic examination of graphene/hexagonal boron nitride (g/hBN) bilayers is presented, through a recently developed two-dimensional phase field crystal model that incorporates out-of-plane deformations. The system parameters are determined by closely matching the stacking energies and heights of graphene/hBN bilayers to those obtained from existing quantum-mechanical density functional theory calculations. Out-of-plane deformations are shown to reduce the energies of inversion domain boundaries in hBN, and the coupling between graphene and hBN layers leads to a bilayer defec…
Moiré excitons are emergent optical excitations in 2D semiconductors with deep moiré superlattice potentials. While these excitations have been realized in several platforms, a system with dynamically tunable moiré potential to tailor the moiré exciton properties is yet to be realized. Here, we present a continuously tunable moiré potential in a monolayer WSe2 that is enabled by its proximity to twisted bilayer graphene (TBG) near the magic-angle. Due to its flat electronic bands, charge distribution is highly localized and forms a triangular lattice in TBG. Tuning the local charge density via…
In twisted bilayers of semiconducting transition metal dichalcogenides (TMDs), a combination of structural rippling and electronic coupling gives rise to periodic moiré potentials that can confine charged and neutral excitations. Here, we report experimental measurements of the structure and spectroscopic properties of twisted bilayers of WSe2 and MoSe2 in the H-stacking configuration using scanning tunneling microscopy (STM). Our experiments reveal that the moiré potential in these bilayers at small angles is unexpectedly large, reaching values of above 300 meV for the valence band and 150 me…
We develop a minimal theory for the recently observed metal-insulator transition (MIT) in two-dimensional (2D) moiré multilayer transition metal dichalcogenides (mTMD) using Coulomb disorder in the environment as the underlying mechanism. In particular, carrier scattering by random charged impurities leads to an effective 2D MIT approximately controlled by the Ioffe-Regel criterion, which is qualitatively consistent with the experiments. We find the necessary disorder to be around $5$-$10\times10^{10}$cm$^{-2}$ random charged impurities in order to quantitatively explain much, but not all, of …
Traditional ferroelectrics undergo thermally-induced phase transitions whereby their structural symmetry increases. The associated higher-symmetry structure is dubbed {\em paraelectric}. Ferroelectric transition metal dichalcogenide bilayers have been recently shown to become paraelectric, but not much has been said of the atomistic configuration of such a phase. As discovered through numerical calculations that include molecular dynamics here, their paraelectricity can only be ascribed to a time average of ferroelectric phases with opposing intrinsic polarizations, whose switching requires ma…
Transition metal dichalcogenide (TMD) bilayers have recently emerged as a robust and tunable moiré system for studying and designing correlated electron physics. In this work, by combining large-scale first principle calculation and continuum model approach, we provide an electronic structure theory that maps long-period heterobilayer TMD superlattices onto diatomic crystals with cations and anions. We find that the interplay between moiré potential and Coulomb interaction leads to filling-dependent charge transfer between MM and MX regions several nanometers apart. We show that the insulating…
Small-twist-angle transition metal dichalcogenide (TMD) heterobilayers develop isolated flat moiré bands that are approximately described by triangular lattice generalized Hubbard models [PhysRevLett.121.026402]. In this article we explore the metallic and insulating states that appear under different control conditions at a density of one-electron per moiré period, and the transitions between them. By combining fully self-consistent Hartree-Fock theory calculations with strong-coupling expansions around the atomic limit, we identify four different magnetic states and one nonmagnetic state nea…
Moire-Engineered Excitonic Landscape and Phonon-Mediated Recombination in Twisted WSe2 Bilayers
Indian Institute of Technology Mandi（印度技术学院曼迪分校）；CSIR-National Physical Laboratory（印度科学工业研究理事会国家物理实验室）；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）；Indian Institute of Science（印度科学学院）；National Institute of Material Science（国家物质科学研究所）
One-Dimensional Electronic States in a Moiré Superlattice of Twisted Bilayer WTe2
Osaka University（大阪大学）；Kyushu University（九州大学）；The University of Tokyo（东京大学）；Stony Brook University（石溪大学）；Japan Advanced Institute of Science and Technology（日本科学技术高级学院）
We explore the moiré magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moiré bands are extremely flat over a wide range of continuous twist angles; (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle; and (iii) the lowest few topological flat bands in bi…
Artificially twisted heterostructures of semiconducting transition metal dichalcogenides (TMDs) offer unprecedented control over their electronic and optical properties via the spatial modulation of interlayer interactions and structural reconstruction. Here we study twisted MoS2 bilayers in a wide range of twist angles near 0° using Scanning Tunneling Microscopy/Spectroscopy. We investigate the twist angle-dependence of the moiré pattern which is dominated by lattice reconstruction for small angles (<2°) leading to large triangular domains with rhombohedral stacking. Local spectroscopy measur…
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…
The interlayer couplings in commensurate and incommensurate bilayer structures of transition metal dichalcogenides are investigated with perturbative treatment. The interlayer coupling in \pm K valleys can be decomposed into a series of hopping terms with distinct phase factors. In H-type and R-type commensurate bilayers, the interference between the three main terms leads to a sensitive dependence of the interlayer coupling strength on the translation. The magnitudes of the main hopping terms are found to some dozen of meV by fitting to the ab initio results. The interlayer couplings in Γvall…
Van der Waals layered materials, such as transition metal dichalcogenides (TMDs), are an exciting class of materials with weak interlayer bonding which enables one to create van der Waals heterostructures (vdWH). Recent work has shown that control of the twist angle between layers can have a dramatic effect on vdWH properties. For TMD vdWH, twist angle has been treated solely through the use of rigid-lattice moiré patterns. No atomic reconstruction, i.e. any rearrangement of atoms within the individual layers, has been reported experimentally to date. Here we demonstrate that vdWH of MoSe2/WSe…
Using a multiscale computational approach, we probe the origin and evolution of ultraflatbands in moiré superlattices of twisted bilayer MoS$_2$, a prototypical transition metal dichalcogenide. Unlike twisted bilayer graphene, we find no unique magic angles in twisted bilayer MoS$_2$ for flatband formation. Ultraflatbands form at the valence band edge for twist angles ($θ$) close to 0$^\circ$ and at both the valence and conduction band edges for $θ$ close to 60$^\circ$, and have distinct origins. For$ θ$ close to 0$^\circ$, inhomogeneous hybridization in the reconstructed moiré superlattice is…
Spontaneous order of layer pseudospins in two-dimensional bilayers is common in quantum Hall systems, where it is responsible for hysteretic responses to gate fields in states with Ising order, and giant drag voltages in states with XY (spontaneous inter-layer phase coherence) order. In this article we predict that layer pseudospin order will also occur in double-moiré strongly correlated two-dimensional electron systems. We comment on similarities and differences in the competition between the two types of order in quantum Hall and double-moiré systems, and relate our findings to previous wor…
In twisted bilayer graphene (TBG) a moiré pattern forms that introduces a new length scale to the material. At the 'magic' twist angle of 1.1°, this causes a flat band to form, yielding emergent properties such as correlated insulator behavior and superconductivity [1-4]. In general, the moiré structure in TBG varies spatially, influencing the local electronic properties [5-9] and hence the outcome of macroscopic charge transport experiments. In particular, to understand the wide variety observed in the phase diagrams and critical temperatures, a more detailed understanding of the local moiré …
Recently, the topological flat bands and spin Hall effect have been experimentally observed in the AB-stacked MoTe$_2$/WSe$_2$ heterostructures. In this work, we systematically study the Berry curvature effects in moiré transition metal dichalcogenide (TMD) heterobilayers. We point out that the moiré potential of the remote conduction bands would induce a sizable periodic pseudo-magnetic field (PMF) on the valence band. This periodic PMF creates net Berry curvature flux in each valley of the moiré Brillouin zone. The combination of the effect of the Berry curvature and the spin-valley locking …
The valence band maxima of most group-VI transition metal dichalcogenide thin films remain at the $Γ$-point all the way from bulk to bilayer. In this paper we develop a continuum theory of the moirè minibands that are formed in the valence bands of $Γ$-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent $D_6$ symmetry we find that low-energy $Γ$-valley moirè holes differ qualitatively from their K-valley counterparts addressed previ…
Moir{é} superlattice realized in two-dimensional heterostructures offers an exciting platform to access strongly-correlated electronic states. In this work, we study transition metal dichalcogenides (TMD) Moir{é} superlattices with time-reversal-symmetry and nontrivial spin{/valley}-Chern numbers. Utilizing realistic material parameters and the method of exact diagonalization, we find that at a certain twisting angle and fractional filling, gapped fractional topological states, i.e., fractional Chern insulators, are naturally {stabilized} by simply introducing the Coulomb repulsion. In contras…
We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relatively slid with respect to the other layer, the edge states are transferred from a single band to another across the band gap, and the number of the edge states pumped in a sliding cycle is shown to be …
We predict that twisted bilayers of 1T-ZrS$_2$ realize a novel and tunable platform to engineer two-dimensional topological quantum phases dominated by strong spin-orbit interactions. At small twist angles, ZrS$_2$ heterostructures give rise to an emergent and twist-controlled moiré Kagomé lattice, combining geometric frustration and strong spin-orbit coupling to give rise to a moiré quantum spin Hall insulator with highly controllable and nearly-dispersionless bands. We devise a generic pseudo-spin theory for group-IV transition metal dichalcogenides that relies on the two-component character…
The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, …
By using the first-principles method based on density of functional theory, we study the electronic properties of twisted bilayer graphene with some specific twist angles and interlayer spacings. With the decrease of the twist angle(the unit cell becomes larger), the energy band becomes narrower and Coulomb repulsion increases, leading to the enhancement of electronic correlation; On the other hand, as the interlayer spacing decreases and the interlayer coupling becomes stronger, the correlation becomes stronger. By tuning the interlayer coupling, we can realize the strongly correlated state w…
The spatial texture of internal degree of freedom of electrons has profound effects on the properties of materials. Such texture in real space can manifest as an emergent magnetic field (or Berry curvature), which is expected to induce interesting valley/spin-related transport phenomena. Moiré pattern, which emerges as a spatial variation at the interface of 2D atomic crystals, provides a natural platform for investigating such real space Berry curvature effects. Here we study moiré structures formed in homobilayer transition metal dichalcogenides (TMDs) due to twisting, various uniform strain…
Moiré superlattice created by twist stacking has multiple physical properties. These physical properties depend on the twist angle, hence investigation of the twist angle dependency is important for the deep understanding of physical phenomena in moiré superlattice. In this work, negative magnetoresistance owing to weak localization (WL) was investigated in twisted double bilayer graphene (TDBG) as a function of the twist angle. The ratio of the intervalley scattering time to the intravalley scattering time, estimated using the WL formula for bilayer graphene, tended to decrease as the twist a…
