Giant Stark splitting of an exciton in bilayer MoS$_2$
Nadine Leisgang, Shivangi Shree, Ioannis Paradisanos, Lukas Sponfeldner, Cedric Robert, Delphine Lagarde, Andrea Balocchi, Kenji Watanabe, Takashi Taniguchi, Xa… 展开作者
Nadine Leisgang, Shivangi Shree, Ioannis Paradisanos, Lukas Sponfeldner, Cedric Robert, Delphine Lagarde, Andrea Balocchi, Kenji Watanabe, Takashi Taniguchi, Xavier Marie, Richard J. Warburton, Iann C. Gerber, Bernhard Urbaszek
Transition metal dichalcogenides (TMDs) constitute a versatile platform for atomically thin optoelectronics devices and spin-valley memory applications. In monolayers optical absorption is strong, but the transition energy is not tunable as the neutral exciton has essentially no out-of-plane electric dipole. In contrast, interlayer exciton transitions in heterobilayers are widely tunable in applied electric fields, but their coupling to light is considerably reduced. Here, we show tuning over 120 meV of interlayer excitons with high oscillator strength in bilayer MoS2. These shifts are due to the quantum confined Stark effect, here the electron is localised to one of the layers yet the hole is delocalised across the bilayer. We optically probe the interaction between intra- and interlayer excitons as they are energetically tuned into resonance. This allows studying their mixing supported by beyond standard density functional theory calculations including excitonic effects. In MoS2 trilayers our experiments uncover two types of interlayer excitons with and without in-built electric dipoles, respectively. Highly tunable excitonic transitions with large oscillator strength and in-built dipoles, that lead to considerable exciton-exciton interactions, hold great promise for non-linear optics with polaritons.
In 1H monolayer transition metal dichalcogenide, the inversion symmetry is broken, while the reflection symmetry is maintained. On the contrary, in the bilayer, the inversion symmetry is restored, but the reflection symmetry is broken. As a consequence of these contrasting symmetries, here we show that bilayer WS$_2$ exhibits a quantum confined Stark effect (QCSE) that is linear with the applied out-of-plane electric field, in contrary to a quadratic one for a monolayer. The interplay between the unique layer degree of freedom in the bilayer and the field driven partial inter-conversion betwee…
The band gap of two-dimensional (2D) semiconductors can be efficiently tuned by gate electric field, which is so called the Stark effect. We report that doping, which is essential in realistic devices, will substantially change the Stark effect of few-layer transition metal dichalcogenides in unexpected ways. Particularly in bilayer structures, because of the competition between strong quantum confinement and intrinsic screening length, electron and hole dopings exhibit surprisingly different Stark effects: doped electrons actively screen the external field and result in a nonlinear Stark effe…
Electronic properties of zigzag boron-carbon-nitride (BCN) nanoribbons, where the outermost C atoms on the edges of graphene nanoribbons are replaced by B or N atoms, are theoretically studied using the first-principles calculations. We show that BCN nanoribbons are metallic, since several bands cross the Fermi level. For BCN nanoribbons in a rich H$_2$ environment, the so-called nearly free electron state appears just above the Fermi level because of the intrinsic giant Stark effect due to the internal electric field of a transverse dipole moment. The position of the nearly free electron stat…
We report the direct observation of intervalley exciton between the Q conduction valley and $Γ$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Γ$ exciton lies at ~18 meV below the QK exciton and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton spectra at gate-tunable electric field, we reveal different interlayer electric dipole moments and Stark shifts between Q$Γ$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Γ$ and QK excitons. Both Q$Γ$ and QK excitons exhibit pronounced phonon re…
Photoexcited intralayer excitons in van der Waals heterostructures (vdWHs) with type-II band alignment have been observed to tunnel into interlayer excitons on ultrafast timescales. Such interlayer excitons have sufficiently long lifetimes that inducing dissociation with external in-plane electric fields becomes an attractive option of improving efficiency of photocurrent devices. In the present paper, we calculate interlayer exciton binding energies, Stark shifts, and dissociation rates for six different transition metal dichalcogenide (TMD) vdWHs using a numerical procedure based on exterior…
Van der Waals heterostructures formed by stacking two-dimensional atomic crystals are a unique platform for exploring new phenomena and functionalities. Interlayer excitons, bound states of spatially separated electron-hole pairs in van der Waals heterostructures, have demonstrated potential for rich valley physics and optoelectronics applications, and been proposed to facilitate high-temperature superfluidity. Here, we demonstrate highly tunable layer-polarized excitons by an out-of-plane electric field in homo-bilayers of transition metal dichalcogenides. Continuous tuning from negative to p…
We present a comprehensive study of the electronic structures of 192 configurations of 39 stable, layered, transition-metal dichalcogenides using density-functional theory. We show detailed investigations of their monolayer, bilayer, and trilayer structures' valence-band maxima, conduction-band minima, and band gap responses to transverse electric fields. We also report the critical fields where semiconductor-to-metal phase transitions occur. Our results show that band gap engineering by applying electric fields can be an effective strategy to modulate the electronic properties of transition-m…
We theoretically investigate excitons in MoS$_2$ monolayers in an applied in-plane electric field. Tight-binding and Bethe-Salpeter equation calculations predict a quadratic Stark shift, of the order of a few meV for fields of 10 V/$μ$m, in the linear absorption spectra. The spectral weight of the main exciton peaks decreases by a few percent with an increasing electric field due to the exciton field ionization into free carriers as reflected in the exciton wave functions. Subpicosecond exciton decay lifetimes at fields of a few tens of V/$μ$m could be utilized in solar energy harvesting and p…
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
We use a theoretical approach to reveal the electronic and structural properties of molybdenum impurities between MoS$_{2}$ bilayers. We find that interstitial Mo impurities are able to reverse the well-known stability order of the pristine bilayer, because the most stable form of stacking changes from AA' (undoped) into AB (doped). The occurrence of Mo impurities in different positions shows their split electronic levels in the energy gap, following octahedral and tetrahedral crystal fields. The energy stability is related to the accommodation of Mo impurities compacted in hollow sites betwee…
While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster time scale in MoSe$_2$ bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the $K$ va…
Excitons in bilayer transition metal dichalcogenides (2L-TMDs) are Coulomb-bound electron/hole pairs that can be viewed as broadly tunable analogs of atomic or molecular systems. Here, we study the properties of 2L-TMD excitons under strong electric field. To overcome the field limit, reached in previous experiments, we developed a new organic/inorganic molecular gating technique. Our approach allows reaching the field > 0.27 V nm-1, about twice higher than previously available. Under this field inter and intra-layer excitonic are brought into an energetic resonance, allowing us to discover ne…
Spatially indirect excitons with displaced wavefunctions of electrons and holes play a pivotal role in a large portfolio of fascinating physical phenomena and emerging optoelectronic applications, such as valleytronics, exciton spin Hall effect, excitonic integrated circuit and high-temperature superfluidity. Here, we uncover three types of spatially indirect excitons (including their phonon replicas) and their quantum-confined Stark effects in hexagonal boron nitride encapsulated bilayer WSe2, by performing electric field-tunable photoluminescence measurements. Because of different out-of-pla…
Moiré superlattices in twistronic heterostructures are a powerful tool for materials engineering. In marginally twisted (small misalignment angle, $θ$) bilayers of nearly lattice-matched two-dimensional (2D) crystals moiré patterns take the form of domains of commensurate stacking, separated by a network of domain walls (NoDW) with strain hot spots at the NoDW nodes. Here, we show that, for type-II transition metal dichalcogenide bilayers MoX$_2$/WX$_2$ (X=S, Se), the hydrostatic strain component in these hot spots creates quantum dots for electrons and holes. We investigate the electron/hole …
We demonstrate electrical control of the A-exciton interband transition in mono- and few-layer $MoS_{2}$ crystals embedded into photocapacitor devices via the DC Stark effect. Electric field dependent low-temperature photoluminescence spectroscopy reveals a significant tuneability of the A-exciton transition energy, up to $\sim 16 meV$, from which we extract the mean DC exciton polarisability $<\barβ>_{N} = (0.58 \pm 0.25) \cdot 10^{-8} DmV^{-1}$. The exciton polarisability is shown to be layer-independent, indicating a strong localisation of both electron and hole wave functions in each indiv…
Van der Waals (vdW) coupling is emerging as a powerful method to engineer and tailor physical properties of atomically thin two-dimensional (2D) materials. In graphene/graphene and graphene/boron-nitride structures it leads to interesting physical phenomena ranging from new van Hove singularities1-4 and Fermi velocity renormalization5, 6 to unconventional quantum Hall effects7 and Hofstadter's butterfly pattern8-12. 2D transition metal dichalcogenides (TMDCs), another system of predominantly vdW-coupled atomically thin layers13, 14, can also exhibit interesting but different coupling phenomena…
Two-dimensional layered materials offer the possibility to create artificial vertically stacked structures possessing an additional degree of freedom - $the$ $interlayer$ $twist$. We present a comprehensive optical study of artificially stacked bilayers (BLs) MoS$_2$ encapsulated in hexagonal BN with interlayer twist angle ranging from 0 to 60 degrees using Raman scattering and photoluminescence spectroscopies. It is found that the strength of the interlayer coupling in the studied BLs can be estimated using the energy dependence of indirect emission versus the A$_\textrm{1g}$-E$_\textrm{2g}^1…
Coulomb bound electron-hole pairs, excitons, govern the optical properties of semi-conducting transition metal dichalcogenides like MoS$_2$ and WSe$_2$. We study optical transitions at the K-point for 2H homobilayer MoS$_2$ in Density Functional Theory (DFT) including excitonic effects and compare with reflectivity measurements in high quality samples encapsulated in hexagonal BN. In both calculated and measured spectra we find a strong interlayer exciton transition in energy between A and B intralayer excitons, observable for T$=4 -300$ K, whereas no such transition is observed for the monola…
Twisted bilayer transition metal dichalcogenides are ideal platforms to study flat-band phenomena. In this paper, we investigate flat-band plasmons in the hole-doped twisted bilayer MoS$_2$ (tb-MoS$_2$) by employing a full tight-binding model and the random phase approximation. When considering lattice relaxations in tb-MoS$_2$, the flat band is not separated from remote valence bands, which makes the contribution of interband transitions in transforming the plasmon dispersion and energy significantly different. In particular, low-damped and quasi-flat plasmons emerge if we only consider intra…
We investigate the valley depolarization dynamics and valley Hall effect of exciton due to the electron-hole exchange interaction in mono- and bilayer MoS$_2$ by solving the kinetic spin Bloch equations. The effect of the exciton energy spectra by the electron-hole exchange interaction is explicitly considered. For the valley depolarization dynamics, in the monolayer MoS$_2$, it is found that in the strong scattering regime, the conventional motional narrowing picture is no longer valid, and a novel valley depolarization channel is opened. For the valley Hall effect of exciton, in both the mon…
We demonstrate pronounced electric-field-induced second-harmonic generation in naturally inversion symmetric 2H stacked bilayer MoS$_{2}$ embedded into microcapacitor devices. By applying strong external electric field perturbations ($|F| = \pm 2.6 MVcm^{-1}$) perpendicular to the basal plane of the crystal we control the inversion symmetry breaking and, hereby, tune the nonlinear conversion efficiency. Strong tunability of the nonlinear response is observed throughout the energy range ($E_ω \sim 1.25 eV - 1.47 eV$) probed by measuring the second-harmonic response at $E_{2ω}$, spectrally detun…
Excitons in thin layers of semiconducting transition metal dichalcogenides are highly subject to the strongly modified Coulomb electron-hole interaction in these materials. Therefore, they do not follow the model system of a two-dimensional hydrogen atom. We investigate experimentally and theoretically excitonic properties in both the monolayer (ML) and the bilayer (BL) of MoSe$_2$ encapsulated in hexagonal BN. The measured magnetic field evolutions of the reflectance contrast spectra of the MoSe$_2$ ML and BL allow us to determine $g$-factors of intralayer A and B excitons, as well as the $g$…
The temperature evolution of the resonant Raman scattering from high-quality bilayer 2H-MoS$_{2}$ encapsulated in hexagonal BN flakes is presented. The observed resonant Raman scattering spectrum as initiated by the laser energy of 1.96 eV, close to the A excitonic resonance, shows rich and distinct vibrational features that are otherwise not observed in non-resonant scattering. The appearance of 1$^{st}$ and 2$^{nd}$ order phonon modes is unambiguously observed in a broad range of temperatures from 5 K to 320 K. The spectrum includes the Raman-active modes, $i.e.$ E$_\textrm{1g}^{2}$($Γ$) and…
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…
We report the multi-scale modeling and design of a gate-defined single-electron transistor in a MoS$_{2}$ bilayer. By combining density-functional theory and finite-element analysis, we design a surface gate structure to electrostatically define and tune a quantum dot and its associated tunnel barriers in the MoS$_{2}$ bilayer. Our approach suggests new pathways for the creation of novel quantum electronic devices in two-dimensional materials.
We explore the collective electronic excitations of bilayer molybdenum disulfide (MoS$_2$) using the density functional theory together with the random phase approximation. The many-body dielectric function and electron energy-loss spectra are calculated using an {\it ab initio} based model involving material-realistic physical properties. The electron energy-loss function of bilayer MoS$_2$ system is found to be sensitive to either electron or hole doping and it is owing to the fact that the Kohn-Sham band dispersions are not symmetric for energies above and below the zero Fermi level. Three …
University of Warsaw（华沙大学）；Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；Peking University Shenzhen Graduate School（北京大学深圳研究生院）；CNRS（法国国家科学研究中心）
The magnetic field dependence of energy levels in gapped single- and bilayer graphene quantum dots (QDs) defined by electrostatic gates is studied analytically in terms of the Dirac equation. Due to the absence of sharp edges in these types of QDs, the valley degree of freedom is a good quantum number. We show that its degeneracy is efficiently and controllably broken by a magnetic field applied perpendicular to the graphene plane. This opens up a feasible route to create well-defined and well controlled spin- and valley-qubits in graphene QDs. We also point out the similarities and difference…
With exceptional electrical and mechanical properties and at the same time air-stability, layered MoSi2N4 has recently draw great attention. However, band structure engineering via strain and electric field, which is vital for practical applications, has not yet been explored. In this work, we show that the biaxial strain and external electric field are effective ways for the band gap engineering of bilayer MoSi$_2$N$_4$ and WSi$_2$N$_4$. It is found that strain can lead to indirect band gap to direct band gap transition. On the other hand, electric field can result in semiconductor to metal t…
In Bernal stacked bilayer graphene interlayer coupling significantly affects the electronic bandstructure compared to monolayer graphene. Here we present magnetotransport experiments on high-quality $n$-doped bilayer MoS$_{2}$. By measuring the evolution of the Landau levels as a function of electron density and applied magnetic field we are able to investigate the occupation of conduction band states, the interlayer coupling in pristine bilayer MoS$_{2}$, and how these effects are governed by electron-electron interactions. We find that the two layers of the bilayer MoS$_{2}$ behave as two in…
We report on the theoretical and experimental investigation of valley-selective optical Stark and Bloch-Siegert shifts of exciton resonances in monolayers WSe$_2$ and MoS$_2$ induced by strong circularly polarized nonresonant optical fields. We predict and observe transient shifts of both 1sA and 1sB exciton transitions in the linear interaction regime. The theoretical description is based on semiconductor Bloch equations. The solutions of the equations are obtained with a modified perturbation technique, which takes into account many-body Coulomb interaction effects. These solutions allow to …
We investigate the semiclassical electronic transport properties of the bilayer silicene-like system in the presence of charged impurity. The trigonal warping due to the interlayer hopping, and its effect to the band structure of bilayer silicene is discussed. Besides the trigonal warping, the external field also gives rise to the anisotropic effect of the mobility (at finite temperature) which can be explored by the Boltzmann theory. The dynamical polarization as well as the scattering wave vector-dependent screening within random phase approximation are very important in determining the scat…
The optics of dangling-bond-free van der Waals heterostructures containing transition metal dichalcogenides are dominated by excitons. A crucial property of a confined exciton is the quantum confined Stark effect (QCSE). Here, such a heterostructure is used to probe the QCSE by applying a uniform vertical electric field across a molybdenum disulfide (MoS$_2$) monolayer. The photoluminescence emission energies of the neutral and charged excitons shift quadratically with the applied electric field provided the electron density remains constant, demonstrating that the exciton can be polarized. St…
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…
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 $\sim…
Moiré patterns are known to confine electronic states in transition metal dichalcogenide bilayers, thus generalizing the notion of magic angles discovered in twisted bilayer graphene to semiconductors. Here, we present a revised Slater-Koster tight-binding model that facilitates the first reliable and systematic studies of such states in twisted bilayer MoS$_2$ for the whole range of rotation angles $θ$. We show that isolated bands appear at low energy for $θ\lesssim 5 - 6^\circ$. Moreover, these bands become "flatbands", characterized by a vanishing average velocity, for the smallest angles $…
The chirality of electronic Bloch bands is responsible for many intriguing properties of layered two-dimensional materials. We show that in bilayers of transition metal dichalcogenides (TMDCs), unlike in few-layer graphene and monolayer TMDCs, both intra-layer and inter-layer couplings give important contributions to the Berry-curvature in the $K$ and $-K$ valleys of the Brillouin zone. The inter-layer contribution leads to the stacking dependence of the Berry curvature and we point out the differences between the commonly available 3R type and 2H type bilayers. Due to the inter-layer contribu…
We present measurements of weak localization on hexagonal boron nitride encapsulated bilayer MoS$_2$. From the analysis we obtain information regarding the phase-coherence and the spin diffusion of the electrons. We find that the encapsulation with boron nitride provides higher mobilities in the samples, and the phase-coherence shows improvement, while the spin relaxation does not exhibit any significant enhancement compared to non-encapsulated MoS$_2$. The spin relaxation time is in the order of a few picoseconds, indicating a fast intravalley spin-flip rate. Lastly, the spin-flip rate is fou…
We investigate and compare experimental and numerical excitonic spectra of the yellow series in cuprous oxide Cu$_2$O in the Voigt configuration and thus partially extend the results from Schweiner et al. [Phys. Rev. B 95, 035202 (2017)], who only considered the Faraday configuration. The main difference between the configurations is given by an additional effective electric field in the Voigt configuration, caused by the motion of the exciton through the magnetic field. This Magneto-Stark effect was already postulated by Gross et al. and Thomas et al. in 1961 [Sov. Phys. Solid State 3, 221 (1…
Bilayer MoS2 is a centrosymmetric semiconductor with degenerate spin states in the six valleys at the corners of the Brillouin zone. It has been proposed that breaking of this inversion symmetry by an out-of-plane electric field breaks this degeneracy, allowing for spin and valley lifetimes to be manipulated electrically in bilayer MoS2 with an electric field. In this work, we report phase-coherent transport properties of double-gated mono-, bi-, and tri-layer MoS2. We observe a similar crossover from weak localization to weak anti-localization, from which we extract the spin relaxation time a…
The interlayer coupling is emerging as a new parameter for tuning the physical properties of two-dimensional (2D) van der Waals materials. When two identical semiconductor monolayers are stacked with a twist angle, the periodic interlayer coupling modulation due to the moiré superlattice may endow exotic physical phenomena, such as moiré excitons and correlated electronic phases. To gain insight into these new phenomena, it is crucial to unveil the underlying coupling between atomic layers. Recently, the rhombohedral-stacked transition metal dichalcogenide (TMD) bilayer has attracted significa…
Structural engineering of van der Waals heterostructures via stacking and twisting has recently been used to create moiré superlattices, enabling the realization of new optical and electronic properties in solid-state systems. In particular, moiré lattices in twisted bilayers of transition metal dichalcogenides (TMDs) have been shown to lead to exciton trapping, host Mott insulating and superconducting states, and act as unique Hubbard systems whose correlated electronic states can be detected and manipulated optically. Structurally, these twisted heterostructures also feature atomic reconstru…
We show how the excitonic features of biaxial MoS2 flakes are very sensitive to biaxial strain. We find a lower bound for the gauge factors of the A exciton and B exciton of (-41 +- 2) meV/% and (-45 +- 2) meV/% respectively, which are larger than those found for single-layer MoS2. Interestingly, the interlayer exciton feature also shifts upon biaxial strain but with a gauge factor that is systematically larger than that found for the A exciton, (-48 +- 4) meV/%. We attribute this larger gauge factor for the interlayer exciton to the strain tunable van der Waals interaction due to the Poisson …
Realizing nonlinear optical response in the low photon density limit in solid-state systems has been a long-standing challenge. Semiconductor microcavities in the strong coupling regime hosting exciton-polaritons have emerged as attractive candidates in this context. However, the weak interaction between these quasiparticles has been a hurdle in this quest. Dipolar excitons provide an attractive strategy to overcome this limitation but are often hindered by their weak oscillator strength. The interlayer dipolar excitons in naturally occurring homobilayer MoS$_2$ alleviates this issue owing to …
We apply a multiscale modeling approach to study lattice reconstruction in marginally twisted bilayers of transition metal dichalcogenides (TMD). For this, we develop DFT-parametrized interpolation formulae for interlayer adhesion energies of MoSe$_2$, WSe$_2$, MoS$_2$, and WS$_2$, combine those with elasticity theory, and analyze the bilayer lattice relaxation into mesoscale domain structures. Paying particular attention to the inversion asymmetry of TMD monolayers, we show that 3R and 2H stacking domains, separated by a network of dislocations develop for twist angles $θ^{\circ}<θ^{\circ}_P\…
The interaction of intralayer and interlayer excitons is studied in a two-dimensional semiconductor, homobilayer MoS$_2$. It is shown that the measured optical susceptibility reveals both the magnitude and the sign of the coupling constants. The interlayer exciton interacts capacitively with the intralayer B-exciton (positive coupling constant) consistent with hole tunnelling from one monolayer to the other. Conversely, the interlayer exciton interacts inductively with the intralayer A-exciton (negative coupling constant). First-principles many-body calculations show that this coupling arises …
Intercalation of lithium atoms between layers of 2D materials can alter their atomic and electronic structure. We investigate effects of Li intercalation in twisted bilayers of the transition metal dichalcogenide MoS$_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, sug…
