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Register a new userPhonon Renormalization in Reconstructed MoS$_2$ Moire Superlattices
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In moire 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 moire 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 moire pattern. We develop a new low-energy continuum model for phonons that overcomes the outstanding challenge of calculating properties of large moire supercells and successfully captures essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moire crystals with nanometer-size supercells. The newly developed theory promotes a comprehensive and unified understanding of structural, optical, and electronic properties of moire superlattices.
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Moire superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moire flat bands and strong, long-range Coulomb interactions1-5. However, microscopic knowledge of the atomically-reconstructed moire superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moire phenomena. Here we quantitatively study the moire flat bands in three-dimensional (3D) reconstructed WSe2/WS2 moire superlattices by comparing scanning tunneling spectroscopy (STS) of high quality exfoliated TMD heterostructure devices with ab initio simulations of TMD moire superlattices. A strong 3D buckling reconstruction accompanied by large in-plane strain redistribution is identified in our WSe2/WS2 moire heterostructures. STS imaging demonstrates that this results in a remarkably narrow and highly localized K-point moire flat band at the valence band edge of the heterostructure. A series of moire flat bands are observed at different energies that exhibit varying degrees of localization. Our observations contradict previous simplified theoretical models but agree quantitatively with ab initio simulations that fully capture the 3D structural reconstruction. Here the strain redistribution and 3D buckling dominate the effective moire potential and result in moire flat bands at the Brillouin zone K points.
The quasiparticle band-gap renormalization induced by the doped carriers is an important and well-known feature in two-dimensional semiconductors, including transition-metal dichalcogenides (TMDs), and it is of both theoretical and practical interest. To get a quantitative understanding of this effect, here we calculate the quasiparticle band-gap renormalization of the electron-doped monolayer MoS$_2$, a prototypical member of TMDs. The many-body electron-electron interaction induced renormalization of the self-energy is found within the random phase approximation and to account for the quasi-2D character of the Coulomb interaction in this system a Keldysh-type interaction with a nonlocal dielectric constant is used. Considering the renormalization of both the valence and the conduction bands, our calculations reveal a large and nonlinear band-gap renormalization upon adding free carriers to the conduction band. We find a 410 meV reduction of the band gap for the monolayer MoS$_2$ on SiO$_2$ substrate at the free carrier density $n=4.9times 10^{12} rm{cm^{-2}}$ which is in excellent agreement with available experimental results. We also discuss the role of exchange and correlation parts of the self-energy on the overall band-gap renormalization of the system. The strong dependence of the band-gap renormalization on the surrounding dielectric environment is also demonstrated in this work, and a much larger shrinkage of the band gap is predicted for the freestanding monolayer MoS$_2$.
Moire superlattices in van der Waals (vdW) heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. A lack of a simple way to characterize moire superlattices has impeded progress in the field. In this work we outline a simple, room-temperature, ambient method to visualize real-space moire superlattices with sub-5 nm spatial resolution in a variety of twisted vdW heterostructures including but not limited to conducting graphene, insulating boron nitride and semiconducting transition metal dichalcogenides. Our method utilizes piezoresponse force microscopy, an atomic force microscope modality which locally measures electromechanical surface deformation. We find that all moire superlattices, regardless of whether the constituent layers have inversion symmetry, exhibit a mechanical response to out-of-plane electric fields. This response is closely tied to flexoelectricity wherein electric polarization and electromechanical response is induced through strain gradients present within moire superlattices. Moire superlattices of 2D materials thus represent an interlinked network of polarized domain walls in a non-polar background matrix.
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 theoretically demonstrate that moire phonons at the lowest-energy bands can become chiral. A general symmetry analysis reveals that they originate from stacking configurations leading to an asymmetric interlayer binding energy that breaks the $C_{2z}$ symmetry on the moire length scale. Within elastic theory, we provide a complete classification of van der Waals heterostructures in respect to hosting moire chiral phonons and discuss their emergence in twisted bilayer MoS$_2$ as an example. The formation of the chiral phonons can be qualitatively understood using an effective model, which emphasizes their origin in the energy difference between stacking domains. Since moire chiral phonons are highly tunable, with excitation energies in only a few meV, and moire scale wavelengths, they might find potential applications in phononic twistronic devices.
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