Intercalation of lithium atoms between layers of 2D materials can alter their atomic and electronic structure. We investigate effects of Li intercalation in twisted bilayers of the transition metal dichalcogenide MoS$_2$ through first-principles calculations, tight-binding parameterization based on the Wannier transformation, and analysis of moiré band structures through an effective continuum model. The energetic stability of different intercalation sites for Li between layers of MoS$_2$ are classified according to the local coordination type and the number of vertically aligned Mo atoms, suggesting that the Li atoms will cluster in certain regions of the moiré superlattice. The proximity of a Li atom has a dramatic influence on the interlayer interaction between sulfur atoms, deepening the moiré potential well and leading to better isolation of the flat bands in the energy spectrum. These results point to the usefulness for the use of chemical intercalation as a powerful means for controlling moiré flat-band physics in 2D semiconductors.
Stepwise deposition of Li atoms onto hexagonal boron nitride (hBN) monolayer on Ir(111) is investigated by means of angle-resolved photoemission spectroscopy and low-energy electron diffraction. Sequential Li deposition progressively shifts the band structure of hBN to higher binding energies due to the induction of a variable electric potential originating from electronic charge donation by alkali atoms. At small coverages, Li atoms preferably intercalate under the hBN layer, where they are highly charged and give rise to a large initial shift of the band structure. Additionally, intercalated…
We investigate the effects of lithium intercalation in twisted bilayers of graphene, using first-principles electronic structure calculations. To model this system we employ commensurate supercells that correspond to twist angles of 7.34$^\circ$ and 2.45$^\circ$. From the energetics of lithium absorption we demonstrate that for low Li concentration the intercalants cluster in the AA regions with double the density of a uniform distribution. The charge donated by the Li atoms to the graphene layers results in modifications to the band structure that can be qualitatively captured using a continu…
The intercalation of Eu underneath Gr on Ir(111) is comprehensively investigated by microscopic, magnetic, and spectroscopic measurements, as well as by density functional theory. Depending on the coverage, the intercalated Eu atoms form either a $(2 \times 2)$ or a $(\sqrt{3} \times \sqrt{3})$R$30^{\circ}$ superstructure with respect to Gr. We investigate the mechanisms of Eu penetration through a nominally closed Gr sheet and measure the electronic structures and magnetic properties of the two intercalation systems. Their electronic structures are rather similar. Compared to Gr on Ir(111), t…
We perform a comprehensive first-principles study of the electronic properties of van der Waals (vdW) trilayers via intercalating a two-dimensional (2D) monolayer (ML = BN, MoSe2, WS2, or WSe2) between MoS2 bilayer to form various MoS2/ML/MoS2 sandwich trilayers. We find that the BN monolayer is the most effective sheet to decouple the interlayer vdW coupling of the MoS2 bilayer, and the resulting sandwich trilayer can recover the electronic structures of the MoS2 monolayer, particularly the direct-gap character. Further study of the MoS2/BN superlattices confirms the effectiveness of the BN m…
The possibility of tuning the vibrational properties and the thermal conductivity of layered van der Waals materials either chemically or mechanically paves the way to significant advances in nanoscale heat management. Using first-principles calculations we investigate the modulation of heat transport in MoS2 by lithium intercalation and cross-plane strain. We find that both the in-plane and cross-plane thermal conductivity (kr, kz) of MoS2 are extremely sensitive to both strain and electrochemical intercalation. Combining lithium intercalation and strain, the in-plane and cross-plane thermal …
In moiré crystals formed by stacking van der Waals (vdW) materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are also renormalized in MoS$_2$ twisted bilayers, adding a new perspective to moiré physics. Over a range of small twist angles, the phonon spectra evolve rapidly due to ultra-strong coupling between different phonon modes and atomic reconstructions of the moiré pattern. We develop a new low-energy continuum model for phonons that overcomes the outstanding challe…
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 …
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…
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…
Previous experimental observations for H intercalation under graphene on SiC surfaces motivate clarification of configuration stabilities and kinetic processes related to intercalation. From first-principles density-functional-theory (DFT) calculations, we analyze H adsorption and intercalation for graphene on a 6H-SiC(0001) surface, where the system includes two single-atom-thick graphene layers: the top-layer graphene (TLG) and the underling buffer-layer graphene (BLG) above the terminal Si layer. Our chemical potential analysis shows that, in the low-H coverage regime (described by a single…
Magnetic adatoms on surfaces are exchange coupled to their environment, inducing fast relaxation of excited spin states and decoherence. These interactions can be suppressed by inserting decoupling layers between the magnetic adsorbate and the metallic substrate. Using low-temperature scanning tunneling microscopy and spectroscopy, we investigate the magnetic properties of single Fe atoms on Au(111) covered by a monolayer of MoS$_2$ and explore the influence of the moiré structure on the spin excitation spectra. Fe adatoms absorbed at minima of the moiré structure exhibit almost pure inelastic…
A two-dimensional (2D) hetero-bilayer system consisting of MoS2 on WSe2, deposited on epitaxial graphene, is studied by scanning tunneling microscopy and spectroscopy at temperatures of 5 and 80 K. A moiré pattern is observed, arising from lattice mismatch of 3.7% between the MoS2 and WSe2. Significant energy shifts are observed in tunneling spectra observed at the maxima of the moiré corrugation, as compared with spectra obtained at corrugation minima, consistent with prior work. Furthermore, at the minima of the moiré corrugation, sharp peaks in the spectra at energies near the band edges ar…
Monolayer islands of molybdenum disulfide (MoS$_2$) on Au(111) form a characteristic moiré structure, leading to locally different stacking sequences at the S-Mo-S-Au interface. Using low-temperature scanning tunneling microscopy (STM) and atomic force microscopy (AFM), we find that the moiré islands exhibit a unique orientation with respect to the Au crystal structure. This indicates a clear preference of MoS$_2$ growth in a regular stacking fashion. We further probe the influence of the local atomic structure on the electronic properties. Differential conductance spectra show pronounced feat…
Layer-Hybridized Wigner Crystals in MoSe2/WS2 Moiré Superlattice
Carnegie Mellon University（卡内基梅隆大学）；Arizona State University（亚利桑那州立大学）；National Institute for Materials Science（国立材料研究所）；The University of Texas at Dallas（德克萨斯大学达拉斯分校）；University of California at Riverside（加州大学河滨分校）
We present results of atomic-force-microscopy-based friction measurements on Re-doped molybdenum disulfide (MoS2). In stark contrast to the widespread observation of decreasing friction with increasing number of layers on two-dimensional (2D) materials, friction on Re-doped MoS2 exhibits an anomalous, i.e., inverse dependence on the number of layers. Raman spectroscopy measurements combined with ab initio calculations reveal signatures of Re intercalation. Calculations suggest an increase in out-of-plane stiffness that inversely correlates with the number of layers as the physical mechanism be…
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 …
We present a linear stability analysis to demonstrate that a flat coherent phase boundary formed by the (de)intercalation of solutes into a compound is unstable against perturbations with wavelengths larger than a critical wavelength. This critical wavelength is controlled by the competition between the interface energy and the elastic strain energy caused by the misfit between the solute-rich and solute-poor phases. It increases with the distance between the phase boundary and free surface of the compound, and so the instability is most pronounced when the boundary is close to the surface at …
Transition metal dichalcogenides exhibit rich phase diagrams dominated by the interplay of superconductivity and charge density waves, which often result in anomalies in the electric transport properties. Here, we employ the ionic gating technique to realize a tunable, non-volatile organic ion intercalation in bulk single crystals of molybdenum disulphide (MoS$_{2}$). We demonstrate that this gate-driven organic ion intercalation induces a strong electron doping in the system without changing the pristine $2H$ crystal symmetry and triggers the emergence of a re-entrant insulator-to-metal trans…
We propose a new current-driven mechanism for achieving significant plasmon dispersion nonreciprocity in systems with narrow, strongly hybridized electron bands. The magnitude of the effect is controlled by the strength of electron-electron interactions $α$, which leads to its particular prominence in moiré materials, characterized by $α\gg 1$. Moreover, this phenomenon is most evident in the regime where Landau damping is quenched and plasmon lifetime is increased. The synergy of these two effects holds a great promise for novel optoelectronic applications of moiré materials.
Moiré patterns on Highly Oriented Pyrolytic Graphite surfaces due to dislocated graphene layers were studied. We observed that the apparent corrugations of the moiré patterns in scanning tunnelling microscopy images change as a function of tunnel junction bias. A simple geometric investigation of the atomic structure of the graphene layers generating moiré patterns revealed that different atomic arrangements due to different twist angles can result in similar geometric moiré periods such that, only a small fraction of the observed moiré periodicities may coincide with the real atomic periodici…
Mo$X_2$ ($X$=S or Se) is a semiconductor family with two-dimensional structure. And a recent calculation predicted the superconductivity in electron doped MoS$_2$ monolayer. In this work, the electronic structure and lattice dynamics of Mo$X_2$ bilayers with monolayer Na intercalated, have been calculated. According to the electron-phonon interaction, it is predicted that these bilayers can be transformed from indirect-gap semiconductors to a superconductors by Na intercalation. More interestingly, the biaxial tensile strain can significantly enhance the superconducting temperature up to $\sim…
Twistronic van der Waals heterostrutures offer exciting opportunities for engineering optoelectronic properties of nanomaterials. Here, we use multiscale modeling to study trapping of charge carriers and excitons by ferroelectric polarisation and piezoelectric charges by domain structures in twistronic WX$_2$/MoX$_2$ bilayers (X=S,Se). For almost aligned 2H-type bilayers, we find that holes and electrons are trapped in the opposite -- WMo and XX (tungsten over molybdenum {\it versus} overlaying chalcogens) -- corners of the honeycomb domain wall network, swapping their position at a twist angl…
Layer-tunable Hubbard bands probed via moiré excitons in MoSe$_2$/WS$_2$ heterostructures
University of California, Riverside（加州大学河滨分校）；University of Southern California（南加州大学）；Tamkang University（淡江大学）；National Institute for Materials Science（日本国立材料研究所）
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…
The moiré pattern observed in stacked non-commensurate crystal lattices, such as hetero-bilayers of transition metal dichalcogenides, produces a periodic modulation of their bandgap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasi-particle dubbed moiré exciton. In the case of MoS$_2$/WSe$_2$ hetero-bilayers, the moiré trapping potential has honeycomb symmetry and, consequently, the moiré exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we…
We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moiré patterns. By using an extended continuum model incorporating non-uniform lattice distortion, we find that the local density of states of the flat band is hardly broadened, but splits into upper and lower subbands in most places. The spatial dependence of the splitting energy is almost exclusively determined by the local value of the effective vector potential induced by heterostrain, whereas the variation of local twist angle and local moiré period give relatively minor effects on the …
Two-dimensional (2D) layered materials, demonstrating significantly different properties from their bulk counterparts, offer a materials platform with potential applications from energy to information processing devices. Although some single- and few-layer forms of materials such as graphene and transition metal dichalcogenides have been realized and thoroughly studied, the space of arbitrarily layered assemblies is still mostly unexplored. The main goal of this work is to demonstrate precise control of layered materials' electronic properties through careful choice of the constituent layers, …
Electrochemical intercalation is a powerful method for tuning the electronic properties of layered solids. In this work, we report an electro-chemical strategy to controllably intercalate lithium ions into a series of van der Waals (vdW) heterostructures built by sandwiching graphene between hexagonal boron nitride (h-BN). We demonstrate that encapsulating graphene with h-BN eliminates parasitic surface side reactions while simultaneously creating a new hetero-interface that permits intercalation between the atomically thin layers. To monitor the electrochemical process, we employ the Hall eff…
In graphene moiré superlattices, electronic interactions between layers are mostly hidden as band structures get crowded because of folding, making their interpretation cumbersome. Here, the evolution of the electronic band structure as a function of the interlayer rotation angle is studied using Density Functional Theory followed by unfolding bands and then comparing them to their corresponding individual components. We observe interactions at regions not theoretically elucidated so far, where for small interlayer angles, gaps turn into discrete-like states that are evenly spaced in energy. W…
Sliding of two-dimensional materials is critical for their application as solid lubricants for space, and also relevant for strain engineering and device fabrication. Dopants such as Ni surprisingly improve lubrication in MoS$_2$, despite formation of interlayer bonds by intercalated Ni, and the mechanism has remained unclear. While sliding on the atomistic level has been theoretically investigated in pristine 2D materials, there has been little work on doped forms, especially for the complicated case of intercalation. We use density functional theory to study sliding of Ni-doped MoS$_2$, cons…
Moiré superlattice-induced sub-bands in twisted van der Waals homo- and hetero-structures govern their optical and electrical properties, rendering additional degrees of freedom such as twist angle. Here, we demonstrate the moiré superlattice effects on the intralayer excitons and trions in a twisted bilayer of MoS$_2$ of H-type stacking at marginal twist angles. We identify the emission from localized and multiple delocalized sub-bands of intralayer moiré excitons and show their electrical modulation by the corresponding trion formation. The electrical control of the oscillator strength of th…
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…
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…
Phase transitions of two-dimensional materials and their heterostructures enable many applications including electrochemical energy storage, catalysis, and memory; however, the nucleation pathways by which these transitions proceed remain underexplored, prohibiting engineering control for these applications. Here, we demonstrate that the lithium intercalation-induced 2H-1T' phase transition in MoS2 proceeds via nucleation of the 1T' phase at a heterointerface by monitoring the phase transition of MoS2/graphene and MoS2/hexagonal boron nitride (hBN) heterostructures with Raman spectroscopy in s…
Two dimensional materials and their heterostructures constitute a promising platform to study correlated electronic states as well as many body physics of excitons. Here, we present experiments that unite these hitherto separate efforts and show how excitons that are dynamically screened by itinerant electrons to form exciton-polarons, can be used as a spectroscopic tool to study interaction-induced incompressible states of electrons. The MoSe$_2$/hBN/MoSe$_2$ heterostructure that we study exhibits a long-period Moiré superlattice as evidenced by coherent-hole tunneling mediated avoided crossi…
The valence band edge in tiny angle twist bilayers of MoS$_2$ and phosphorene is shown to consist of highly localized energy levels created by a `moiré quantum well', i.e. trapped by the interlayer moiré potential. These approximately uniformly spaced energy levels exhibit a richly modulated charge density, becoming ultra-localized at the valence band maximum. The number and spacing of such levels is controllable by the twist angle and interlayer interaction strength, suggesting the possibility of `moiré engineering' ordered arrays of quantum dots in 2d twist semi-conductors.
The intercalation-induced phase transition of MoS2 from the semiconducting 2H to the semimetallic 1T' phase has been studied in detail for nearly a decade; however, the effects of a heterointerface between MoS2 and other two-dimensional (2D) crystals on the phase transition have largely been overlooked. Here, ab initio calculations show that intercalating Li at a MoS2-hexagonal boron nitride (hBN) interface stabilizes the 1T phase over the 2H phase of MoS2 by ~ 100 mJ m-2, suggesting that encapsulating MoS2 with hBN may lower the electrochemical energy needed for the intercalation-induced phas…
We predict that in a twisted homobilayer of transition-metal dichalcogenide MoS$_2$, spin-orbit coupling in the conduction band states from $\pm K$ valleys can give rise to moiré flat bands with nonzero Chern numbers in each valley. The nontrivial band topology originates from a unique combination of angular twist and local mirror symmetry breaking in each individual layer, which results in unusual skyrmionic spin textures in momentum space with skyrmion number $\mathcal{S} = \pm 2$. Our Hartree-Fock analysis further suggests that density-density interactions generically drive the system at $1…
Highly nonlinear Moiré exciton and trion polaritons
Laboratory for Physical Sciences, University of Maryland（马里兰大学物理科学实验室）；University of Rochester（罗切斯特大学）；University of Notre Dame（圣母大学）；The Institute of Optics, University of Rochester（罗切斯特大学光学研究所）
Moiré superlattices serve as a playground for emerging phenomena, such as localization of band states, superconductivity, and localization of excitons. These superlattices are large and are often modeled in the zero angle limit, which obscures the effect of finite twist angles. Here, by means of first-principles calculations we quantify the twist-angle dependence of the moiré potential in the MoS$_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…
We fabricate ion-gated field-effect transistors (iFET) on mechanically exfoliated multilayer MoS$_2$. We encapsulate the flake by Al$_2$O$_3$, leaving the device channel exposed at the edges only. A stable Li$^+$ intercalation in the MoS$_2$ lattice is induced by gating the samples with a Li-based polymeric electrolyte above $\sim$ 330 K and the doping state is fixed by quenching the device to $\sim$ 300 K. This intercalation process induces the emergence of anomalies in the temperature dependence of the sheet resistance and its first derivative, which are typically associated with structural/…
We investigate the physics of photonic band structures of the moiré patterns that emerged when overlapping two uni-dimensional (1D) photonic crystal slabs with mismatched periods. The band structure of our system is a result of the interplay between intra-layer and inter-layer coupling mechanisms, which can be fine-tuned via the distance separating the two layers. We derive an effective Hamiltonian that captures the essential physics of the system and reproduces all numerical simulations of electromagnetic solutions with high accuracy. Most interestingly, \textit{magic distances} corresponding…
