Abstract
Twisting or sliding two-dimensional crystals with respect to each other gives rise to moiré patterns determined by the difference in their periodicities. Such lattice mismatches can exist for several reasons: differences between the intrinsic lattice constants of the two layers, as is the case for graphene on BN1; rotations between the two lattices, as is the case for twisted bilayer graphene2; and strains between two identical layers in a bilayer3. Moiré patterns are responsible for a number of new electronic phenomena observed in recent years in van der Waals heterostructures, including the observation of superlattice Dirac points for graphene on BN1, collective electronic phases in twisted bilayers and twisted double bilayers4,5,6,7,8, and trapping of excitons in the moiré potential9,10,11,12. An open question is whether we can use moiré potentials to achieve strong trapping potentials for electrons. Here, we report a technique to achieve deep, deterministic trapping potentials via strain-based moiré engineering in van der Waals materials. We use strain engineering to create on-demand soliton networks in transition metal dichalcogenides. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of this network occur in bound pairs with different interlayer stacking arrangements. One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Soliton networks thus provide a path to engineer deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials.
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Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was supported by the National Science Foundation (NSF) via grant no. DMR-1610110 (to D.E.) and by the NSF MRSEC programme through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634; to H.O. and A.N.P.). Support for STM measurements was provided by the Air Force Office of Scientific Research (grant no. FA9550-16-1-0601). The computational work was supported primarily by contract W911NF-16-1-0447 from the Army Research Office (to V.B.S.) and by grant no. CMMI-1727717 (to H.K.) from the NSF.
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D.E. performed STM experiments under the guidance of A.N.P. H.K. performed density functional theory and molecular dynamics simulations under the guidance of V.S. H.O. performed analytical calculations. D.E., H.O. and A.N.P. wrote the manuscript with assistance from H.K. and V.S.
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Supplementary Table 1, Figs. 1–6 and Discussion.
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Source data for Fig. 2b,c.
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Source data for Fig. 4a,b(plus inset),f.
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Edelberg, D., Kumar, H., Shenoy, V. et al. Tunable strain soliton networks confine electrons in van der Waals materials. Nat. Phys. 16, 1097–1102 (2020). https://doi.org/10.1038/s41567-020-0953-2
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DOI: https://doi.org/10.1038/s41567-020-0953-2
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