Tuning commensurability in twisted van der Waals bilayers

• Published in: Nature (London) Vol. 625; no. 7995; pp. 494 - 499
• Main Authors: Li, Yanxing, Zhang, Fan, Ha, Viet-Anh, Lin, Yu-Chuan, Dong, Chengye, Gao, Qiang, Liu, Zhida, Liu, Xiaohui, Ryu, Sae Hee, Kim, Hyunsue, Jozwiak, Chris, Bostwick, Aaron, Watanabe, Kenji, Taniguchi, Takashi, Kousa, Bishoy, Li, Xiaoqin, Rotenberg, Eli, Khalaf, Eslam, Robinson, Joshua A, Giustino, Feliciano, Shih, Chih-Kang
• Format: Journal Article
• Language: English
• Published: England Nature Publishing Group 18.01.2024
• Subjects: Crystals; Electrons; Fourier transforms; Graphene; MATERIALS SCIENCE; Moire patterns; Quasicrystals; Spectroscopy; Spectrum analysis; Superlattices; Symmetry; Translation; Tungsten; Valence band; Valleys
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/s41586-023-06904-w

Moiré superlattices based on van der Waals bilayers created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θ ), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θ  = 30° and the commensurate moiré crystals at θ  = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the K valley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.