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What Influences Long-Wavelength Moiré Superlattice Morphology?

Moiré superlattices are lattice interference effects that make the crystal lattice highly sensitive to intrinsic atomic reconstructions and extrinsic mechanical perturbations. In an article published in the journal Nano Letters, researchers used scanning tunneling spectroscopy (STS) and scanning tunneling microscopy (STM) to observe the long-wavelength tungsten sulfide (WS2) superlattice structure.

What Influences Long-Wavelength Moiré Superlattice Morphology?

Study: Morphology Deformation and Giant Electronic Band Modulation in Long-Wavelength WS2 Moiré Superlattices. Image Credit: MZinchenko/

The results revealed that the long-wavelength WS2 superlattices were rebuilt into different moiré morphologies and confirmed that the exchange between the intrinsic atomic reconstruction and extrinsic nonuniform heterostrain resulted in moiré superlattices. Additionally, this interchange introduces a localized inhomogeneous intralayer strain within the moiré superlattices.

Comapred to the interlayer hybridization-induced electronic modulation at the valence band edge, the localized intralayer strain induced a strong K point modulation of the conduction band that reached up to 300 millielectronvolts in heavily deformed moiré superlattices. The STM observations provided information on the transition metal dichalcogenides (TMDs) moiré superlattices.

Effect of Moiré Superlattices on Physical Properties

Moiré superlattices in van der Waals heterostructures have given rise to several emergent electronic phenomena due to the interplay between atomic structure and electron correlations. A lack of a simple way to characterize the local structure of moiré superlattices has impeded progress in the field.

In the long-wavelength moiré superlattices of stacked TMDs, structural reconstruction occurs ubiquitously, which significantly impacts their electronic properties. However, complete microscopic understandings of the interplay between the lattice reconstruction and alteration of electronic properties and their further response to external perturbations in the reconstructed TMDs moiré superlattice are still lacking.

Layered TMDs with moiré superlattices paved a new path to explore novel electronic and excitonic quantum phenomena that arise from the unusual arrangement in moiré superlattices which consequently introduced a wide range of electronic band-edge states. The moiré superlattices emerge from the crystal interface’s interference effect, where its geometry deforms severely on subjecting to atomic scale perturbations.

The atomic scale perturbations include mechanical deformations like extrinsic perturbations and lattice reconstruction like intrinsic perturbations that instantly rearranges the moiré superlattices structure into stacking domains of larger size. Although the reconstruction of the intrinsic lattice was previously reported to affect the structure of moiré superlattices and their electronic states, their interplay with extrinsic perturbations remains unexplored. This interplay inspired the current work to explore complete microscopic information on the morphology deformations in moiré superlattices and their corresponding modulations in the electronic band in TMD moiré superlattices.

Long-wavelength WS2 Moiré Superlattices

In the present study, the STS and STM measurements were combined with first-principles calculations to reveal the structural deformation leading to moiré superlattices in long-wavelength WS2, consequently modulating its electronic band at the atomic scale. To this end, various moiré morphologies were observed, with their geometry varying between a regular hexagon and their deformed counterparts with substantial structural deformation.

Here, the intrinsic lattice reconstruction and extrinsic heterostrain significantly contributed to the evolution in morphology in long-wavelength WS2 moiré superlattices. Moreover, the distinguished interchange between the intrinsic and extrinsic factors introduced a strong and localized strain among the layers in the crystal lattice. This local strain was nonuniform across the unit cells in moiré superlattices which strongly modulated the K-point energy position in the conduction band.

The regularly hexagonal moiré’s theoretical and experimental results revealed that the lattice deformation induced due to the strain greatly influenced the location of the KC point in the conduction band. Further STS measurements on the deformed moiré region confirmed the dependence of conduction band modulation on the local deformation in the crystal lattice.

The STM image of an intensely deformed moiré superlattice revealed that the one-dimensional domain walls (DW1) showed a length of 45 nanometers and a width of 18 nanometers. Furthermore, an intersection angle of 11 degrees was observed between DW1 and the zigzag direction and analyzing the DW1 through STM images showed a distinct compressive deformation in the lattice in the armchair direction.

Moreover, in heavily deformed moiré superlattices, the K-point energy position reached 300 millielectronvolts. While the valence band edge modulation with interlayer origin relied on the interlayer hybridization, the conduction band modulation with intralayer origin depended on intralayer atomic orbital overlaps.


To summarize, the evolution in the morphology and its consequent modulation in the electronic band was studied in long-wavelength WS2 moiré superlattice under the combined effects of extrinsic heterostrain and intrinsic lattice reconstruction. The nonuniform and localized intralayer strain induced by the interchange between these intrinsic and extrinsic factors modulated the K-point energy position at the conduction band, which reached up to 300 millielectronvolts in the deformed moiré superlattice. The results provided an understanding of the TMD moiré superlattice’s fascinating physics.


Li, K., Xiao, F., Guan, W., Xiao, Y., Xu, C., Zhang, J., Lin, C. (2022). Morphology Deformation and Giant Electronic Band Modulation in Long-Wavelength WS2 Moiré Superlattices. Nano Letters

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Bhavna Kaveti

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Bhavna Kaveti

Bhavna Kaveti is a science writer based in Hyderabad, India. She has a Masters in Pharmaceutical Chemistry from Vellore Institute of Technology, India, and a Ph.D. in Organic and Medicinal Chemistry from Universidad de Guanajuato, Mexico. Her research work involved designing and synthesizing heterocycle-based bioactive molecules, where she had exposure to both multistep and multicomponent synthesis. During her doctoral studies, she worked on synthesizing various linked and fused heterocycle-based peptidomimetic molecules that are anticipated to have a bioactive potential for further functionalization. While working on her thesis and research papers, she explored her passion for scientific writing and communications.


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