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Visualizing band structure hybridization and superlattice effects in twisted MoS$_2$/WS$_2$ heterobilayers

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 Added by S{\\o}ren Ulstrup
 Publication date 2021
  fields Physics
and research's language is English




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A mismatch of atomic registries between single-layer transition metal dichalcogenides (TMDs) in a two dimensional van der Waals heterostructure produces a moire superlattice with a periodic potential, which can be fine-tuned by introducing a twist angle between the materials. This approach is promising both for controlling the interactions between the TMDs and for engineering their electronic band structures, yet direct observation of the changes to the electronic structure introduced with varying twist angle has so far been missing. Here, we probe heterobilayers comprised of single-layer MoS$_2$ and WS$_2$ with twist angles of $(2.0 pm 0.5)^{circ}$, $(13.0 pm 0.5)^{circ}$, and $(20.0 pm 0.5)^{circ}$ and investigate the differences in their electronic band structure using micro-focused angle-resolved photoemission spectroscopy. We find strong interlayer hybridization between MoS$_2$ and WS$_2$ electronic states at the $bar{mathrm{Gamma}}$-point of the Brillouin zone, leading to a transition from a direct bandgap in the single-layer to an indirect gap in the heterostructure. Replicas of the hybridized states are observed at the centre of twist angle-dependent moire mini Brillouin zones. We confirm that these replica features arise from the inherent moire potential by comparing our experimental observations with density functional theory calculations of the superlattice dispersion. Our direct visualization of these features underscores the potential of using twisted heterobilayer semiconductors to engineer hybrid electronic states and superlattices that alter the electronic and optical properties of 2D heterostructures.



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It has recently been shown that quantum-confined states can appear in epitaxially grown van der Waals material heterobilayers without a rotational misalignment ($theta=0^circ$), associated with flat bands in the Brillouin zone of the moire 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 moire unit cell of a $theta=0^circ$ MoS$_2$/WSe$_2$ heterobilayer, and show that inclusion of strain variation and out-of-plane displacement in density functional theory calculations greatly improves their agreement with the experimental data. We further explore the role of twist-angle by showing experimental data for a twisted MoS$_2$/WSe$_2$ heterobilayer structure with twist angle of $theta=15^circ$, that exhibits a moire pattern but no confinement.
Twisted bilayers of two-dimensional materials, such as twisted bilayer graphene, often feature flat electronic bands that enable the observation of electron correlation effects. In this work, we study the electronic structure of twisted transition metal dichalcogenide (TMD) homo- and heterobilayers that are obtained by combining MoS$_2$, WS$_2$, MoSe$_2$ and WSe$_2$ monolayers, and show how flat band properties depend on the chemical composition of the bilayer as well as its twist angle. We determine the relaxed atomic structure of the twisted bilayers using classical force fields and calculate the electronic band structure using a tight-binding model parametrized from first-principles density-functional theory. We find that the highest valence bands in these systems can derive either from $Gamma$-point or $K$/$K$-point states of the constituent monolayers. For homobilayers, the two highest valence bands are composed of monolayer $Gamma$-point states, exhibit a graphene-like dispersion and become flat as the twist angle is reduced. The situation is more complicated for heterobilayers where the ordering of $Gamma$-derived and $K$/$K$-derived states depends both on the material composition and also the twist angle. In all systems, qualitatively different band structures are obtained when atomic relaxations are neglected.
Accurately described excitonic properties of transition metal dichalcogenide heterobilayers (HBLs) are crucial to comprehend the optical response and the charge carrier dynamics of them. Excitons in multilayer systems posses inter or intralayer character whose spectral positions depend on their binding energy and the band alignment of the constituent single-layers. In this study, we report the electronic structure and the absorption spectra of MoS$_2$/WS$_2$ and MoSe$_2$/WSe$_2$ HBLs from first-principles calculations. We explore the spectral positions, binding energies and the origins of inter and intralayer excitons and compare our results with experimental observations. The absorption spectra of the systems are obtained by solving the Bethe-Salpeter equation on top of a G$_0$W$_0$ calculation which corrects the independent particle eigenvalues obtained from density functional theory calculations. Our calculations reveal that the lowest energy exciton in both HBLs possesses interlayer character which is decisive regarding their possible device applications. Due to the spatially separated nature of the charge carriers, the binding energy of inter-layer excitons might be expected to be considerably smaller than that of intra-layer ones. However, according to our calculations the binding energy of lowest energy interlayer excitons is only $sim$ 20% lower due to the weaker screening of the Coulomb interaction between layers of the HBLs. Therefore, it can be deduced that the spectral positions of the interlayer excitons with respect to intralayer ones are mostly determined by the band offset of the constituent single-layers. By comparing oscillator strengths and thermal occupation factors, we show that in luminescence at low temperature, the interlayer exciton peak becomes dominant, while in absorption it is almost invisible.
We discuss here the effect of band nesting and topology on the spectrum of excitons in a single layer of MoS$_2$, a prototype transition metal dichalcogenide material. We solve for the single particle states using the ab initio based tight-binding model containing metal $d$ and sulfur $p$ orbitals. The metal orbitals contribution evolving from $K$ to $Gamma$ points results in conduction-valence band nesting and a set of second minima at $Q$ points in the conduction band. There are three $Q$ minima for each $K$ valley. We accurately solve the Bethe-Salpeter equation including both $K$ and $Q$ points and obtain ground and excited exciton states. We determine the effects of the electron-hole single particle energies including band nesting, direct and exchange screened Coulomb electron-hole interactions and resulting topological magnetic moments on the exciton spectrum. The ability to control different contributions combined with accurate calculations of the ground and excited exciton states allows for the determination of the importance of different contributions and a comparison with effective mass and $kcdot p$ massive Dirac fermion models.
275 - Luqing Wang , Alex Kutana , 2014
Monolayer transition metal dichalcogenides are promising materials for photoelectronic devices. Among them, molybdenum disulphide (MoS$_2$) and tungsten disulphide (WS$_2$) are some of the best candidates due to their favorable band gap values and band edge alignments. Here we consider various perturbative corrections to the DFT electronic structure, e.g. GW, spin-orbit coupling, as well as many-body excitonic and trionic effects, and calculate accurate band gaps as a function of homogeneous strain in these materials. We show that all of these corrections are of comparable magnitudes and need to be included in order to obtain an accurate electronic structure. We calculate the strain at which the direct-to-indirect gap transition occurs. After considering all contributions, the direct to indirect gap transition strain is found to be at 2.7% in MoS$_2$ and 3.9% in WS$_2$. These values are generally higher than the previously reported theoretical values.
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