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Hybridized intervalley moire excitons and flat bands in twisted WSe$_2$ bilayers

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 Added by Samuel Brem
 Publication date 2020
  fields Physics
and research's language is English




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The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe$_2$ bilayers. In particular, we show that the strong hybridization of electrons at the $Lambda$ point leads to a drastic redshift of the momentum-dark K-$Lambda$ exciton, accompanied by the emergence of flat moire exciton bands at small twist angles. We directly compare theoretically predicted and experimentally measured optical spectra allowing us to identify photoluminescence signals stemming from phonon-assisted recombination of layer-hybridized dark excitons. Moreover, we predict the emergence of additional spectral features resulting from the moire potential of the twisted bilayer lattice.



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Lattice reconstruction in twisted transition-metal dichalcogenide (TMD) bilayers gives rise to piezo- and ferroelectric moire potentials for electrons and holes, as well as a modulation of the hybridisation across the bilayer. Here, we develop hybrid $mathbf{k}cdot mathbf{p}$ tight-binding models to describe electrons and holes in the relevant valleys of twisted TMD homobilayers with parallel (P) and anti-parallel (AP) orientations of the monolayer unit cells. We apply these models to describe moire superlattice effects in twisted WSe${}_2$ bilayers, in conjunction with microscopic emph{ab initio} calculations, and considering the influence of encapsulation, pressure and an electric displacement field. Our analysis takes into account mesoscale lattice relaxation, interlayer hybridisation, piezopotentials, and a weak ferroelectric charge transfer between the layers, and describes a multitude of possibilities offered by this system, depending on the choices of P or AP orientation, twist angle magnitude, and electron/hole valley.
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 moire 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 moire superlattice. The proximity of a Li atom has a dramatic influence on the interlayer interaction between sulfur atoms, deepening the moire 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 moire flat-band physics in 2D semiconductors.
We report the direct observation of intervalley exciton between the Q conduction valley and $Gamma$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Gamma$ 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$Gamma$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Gamma$ and QK excitons. Both Q$Gamma$ and QK excitons exhibit pronounced phonon replicas, in which two-phonon replicas outshine the one-phonon replicas due to the existence of (nearly) resonant exciton-phonon scatterings and numerous two-phonon scattering paths. We can simulate the replica spectra by comprehensive theoretical modeling and calculations. The good agreement between theory and experiment for the Stark shifts and phonon replicas strongly supports our assignment of Q$Gamma$ and QK excitons.
Excitons and trions (or exciton-polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer WSe$_2$. We observe the intervalley dark excitons, which can recombine by the assistance of defect scattering or chiral-phonon emission. We also reveal that a trion can decay in two distinct paths - through intravalley or intervalley electron-hole recombination - into two different final valley states. Although these two paths are energy degenerate, we can distinguish them by lifting the valley degeneracy under a magnetic field. In addition, the intra- and inter-valley trion transitions are coupled to zone-center and zone-corner chiral phonons, respectively, to produce distinct phonon replicas. The observed multipath optical decays of dark excitons and trions provide much insight into the internal quantum structure of trions and the complex excitonic interactions with defects and chiral phonons in monolayer valley semiconductors.
The creation of moire 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 moire 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 by a moire potential in 2D valley semiconductors, but these signatures have yet to be experimentally detected. Here, we report experimental evidence of interlayer valley excitons trapped in a moire potential in MoSe$_2$/WSe$_2$ heterobilayers. At low temperatures, we observe photoluminescence near the free interlayer exciton energy but with over 100 times narrower linewidths. The emitter g-factors are homogeneous across the same sample and only take two values, -15.9 and 6.7, in samples with twisting angles near 60{deg} and 0deg, respectively. The g-factors match those of the free interlayer exciton, which is determined by one of two possible valley pairing configurations. At a twist angle near 20deg, the emitters become two orders of magnitude dimmer, but remarkably, they possess the same g-factor as the heterobilayer near 60deg. This is consistent with the Umklapp recombination of interlayer excitons near the commensurate 21.8{deg} twist angle. The emitters exhibit strong circular polarization, which implies the preservation of three-fold rotation symmetry by the trapping potential. Together with the power and excitation energy dependence, all evidence points to their origin as interlayer excitons trapped in a smooth moire potential with inherited valley-contrasting physics.
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