Extended Data Fig. 6: The invariance of the total twist rate in the radial growth of a pinned structure.

a, STEM image of a cross-sectional sample prepared from a twisted structure pinned on a substrate. This twist structure was formed by non-uniform radial growth on a twisted nanowire (similar to the structure shown in Fig. 4a), showing varying radial sizes for different portions of the structure. To verify the invariance of the total twist rate in the radial growth of a pinned structure, we used electron diffraction to measure the twist rates of different portions with varying radial sizes in the structure. b, Magnified STEM image of a thin portion highlighted by the dashed red box in a. c, CBED patterns for the [210] and [100] zone axes collected at locations marked by arrows in b. This suggests that the thin portion has a twist of 23° over a length of 970 nm, amounting to a twist rate of 0.4 rad mm⁻¹. d, Magnified TEM image showing a thick portion highlighted by the dashed blue box in a. e, SAED patterns for the [010], [110] and [100] zone axes collected at locations marked by arrows in d. This suggests that the thick portion has a twist of 90° over a length of 4 μm, giving rise to a twist rate of 0.4 rad mm⁻¹ as well. This electron diffraction analysis shows that twist rates at different portions with varying radial sizes in the structure are almost same, despite the significant difference in their radial size. Note that the thick portion has a radial size (about 450 nm) two times larger than that of the thin portion (about 150 nm). This result suggests that the overall twist rate of the structure is determined by the twist rate of the nanowire upon substrate pinning, and further radial growth does not result in untwisting that decreases the twist rate. The high twist rate of the initial nanowire with Eshelby twist is therefore preserved during radial growth.