Fig. 1: Physics of atomic layers stacking probed by moiré metrology in vdW twisted bilayers—experiment and theory.

a Illustration of ___domain formations in a relaxed twisted bilayer structure. Center: atomic positioning after relaxation (see Supplementary Information S1 for more details). Atoms are colored to highlight stacking configurations. The energy imbalance leads to curved single ___domain walls (SDWs), with radius of curvature indicated by κ⁻¹, and in some cases with formation of double ___domain walls (DDWs). Two systems with energy imbalance are considered: TDBG (top) and T-H-MoSe₂/WSe₂ (bottom). b STS map of TDBG with θ = 0.07°, revealing rhombohedral (ABCA—dark) and Bernal (ABAB—bright) domains with minimal external strain. The rhombohedral phase bends inward (dashed turquoise line) revealing an energy imbalance between the two phases as discussed in the text. c Mid-IR (940 cm⁻¹) nearfield phase imaging of TDBG resolves ABCA (dark) and ABAB (bright) phases and DDW formations. d STM map of T-H-MoSe₂/WSe₂ resolving MM’ (bright) and MX’ (dark) stacking configurations as well as DDW formation in various strain conditions. e–g Stacking energy density from full relaxation calculations of the experimental cases of (b-d), respectively (see “Methods”, Supplementary Information S1–2 and text for more details). The color-map is shared for (e, f). Magnified regions in f (and arrows in c) highlight a DDW formation and a moiré dislocation (see Discussion in Supplementary Information S3). Calculated region of (f) is marked by dashed shape in (c).