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WS₂ layers show nonlinear phase changes in electron ptychography

Researchers compared monolayer, bilayer and trilayer regions of WS₂ in one specimen using electron ptychography. The measured phase of tungsten columns rose about 13.2% from one to two layers, but only 4.7% from two to three.

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The phase reconstructed from diffraction patterns recorded as an electron probe scans a sample can reveal atomic-scale electrostatic potential. Its interpretation is affected by specimen thickness, multiple scattering and overlap between projected atomic columns. The team used different thickness regions in a twisted trilayer WS₂ specimen as an internal reference within the same field of view.

Mean tungsten-column phase rose about 13.2% from the monolayer region to the bilayer, but only 4.7% from the bilayer to the trilayer. Short-range projected W-W overlap added roughly 8–9%, while W-S overlap had little effect. The measurements show that phase does not simply rise linearly with layer count and provide a benchmark for interpreting phase-based potential maps.

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Approximate increase in mean W-column phase from monolayer to bilayer13.2Approximate relative change measured under the same acquisition and reconstruction conditions in one specimen; it is not a linear increase with layer count.
Increase in mean W-column phase from bilayer to trilayer4.7Relative increase measured in the same specimen under the same conditions; short-range projected W-W overlap can also affect phase.
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Quantity and scope are taken from the methods and results of the first arXiv version dated 9 October 2026; they should not be generalized beyond the study.

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