This file contains six sections, Supplementary Figs. 1–5, Tables 1 and 2, and references. The Supplementary Information contains five figures: Supplementary Fig. 1 Schematic of twisted WSe 2 /MoSe 2 in reciprocal space. a, For general twist angle, all possible first-order moiré satellites are shown. Contributions from WSe 2 are shown in red, and those from MoSe 2 are shown in blue. Arrows indicate the atomic-scale basis vectors q 0 and q 1 . The region of interest at (2, −1) is highlighted, in which the UED data presented in the main text are collected. b, Definitions of the moiré scale reciprocal lattice vectors. c, Schematic of twisted WSe 2 /MoSe 2 , showing only those satellites with significant intensity when the system is in equilibrium due to strain waves caused by atomic relaxation. d,e, Torsional PLDs have a significant effect on the highlighted peaks, related to the (2, −1) region of interest by rotation. f,g, Radial PLDs have a significant effect on the highlighted peaks, related to the (2, −1) experimental region of interest by rotation. h, The highlighted peaks in the (2, −1) experimental region of interest are sensitive to torsional PLDs. i, The highlighted peaks in the (2, −1) experimental region of interest are sensitive to radial PLDs. j, The highlighted peaks in the (2, −1) region are summed in computing the satellite peak intensities shown in Supplementary Figs. 4 and 5. Supplementary Fig. 2 Illustration of phase interference. Interference due to prefactors in Supplementary equations (29)–(34). a, Chalcogenide (yellow) and metal (red) imperfectly destructively interfere at diffraction order (0, 1). b, Chalcogenide and metal atoms perfectly constructively interfere at (2, −1). c, Chalcogenide and metal atoms imperfectly constructively interfere at (0, 2). Supplementary Fig. 3 Graphical derivation of moiré superlattice vectors. See supplementary equations (41)–(43). In the small-angle approximation, a rotation is a motion orthogonal to the vector joining the displaced atom to the axis of rotation. The moiré supercell can be defined by the repetition of metal-on-metal stacking (\({{\rm{R}}}_{M}^{M}\)). A metal-on-metal stacking repeats at a distance such that the rotation has displaced an atom by one atomic lattice vector (the shortest path between adjacent atoms). Hence, the vector joining adjacent \({{\rm{R}}}_{M}^{M}\) sites is orthogonal to an atomic lattice vector, and the moiré superlattice is rotated 90° relative to the atomic lattice. Supplementary Fig. 4 Fields spanning all possible threefold symmetric moiré PLD in 2° twisted WSe 2 /MoSe 2 . a,d,g,j, In-plane visualization of the displacement fields. b,e,h,k, Changes in diffraction intensity with PLD amplitude, added to the static PLD. The WSe 2 Bragg peak in the region of interest (ROI) is highlighted in red in Supplementary Fig. 1a. The MoSe 2 Bragg peak is highlighted in blue, and the sum of satellite features is highlighted in black in Supplementary Fig. 1j. The WSe 2 layer moves antiparallel to MoSe 2 . c,f,i,l, Repeating the same calculations except the WSe 2 layer moves parallel to MoSe 2 . Supplementary Fig. 5 Fields spanning all possible threefold symmetric moiré PLD in 57° twisted WSe 2 /MoSe 2 . a,d,g,j, In-plane visualization of the displacement fields. b,e,h,k, Changes in diffraction intensity with PLD amplitude, added to the static PLD. The WSe 2 Bragg peak in the region of interest (ROI) is highlighted in red in Supplementary Fig. 1a. The MoSe 2 Bragg peak is highlighted in blue, and the sum of satellite features is highlighted in black in Supplementary Fig. 1j. The WSe 2 layer moves antiparallel to MoSe 2 . c,f,i,l, Repeating the same calculations except the WSe 2 layer moves parallel to MoSe 2 . The Supplementary Information contains two tables. Supplementary Table 1 Ab initio numerically calculated electron–phonon coupling for 0° WSe 2 / MoSe 2 . The first column labels the phonon mode, the second column shows coupling to the conduction band at the K point, and the final column shows coupling to the valence band at the K point. Optical intralayer modes \({{A}^{^{\prime} }}_{1},{E}^{^{\prime} }\) carry subscripts indicating the layer affected. Supplementary Table 2 Reproduction of main-text Table 1.