Universality of moiré physics in collapsed chiral carbon nanotubes

8 pags., 8 figs., 1 tab.
We report the existence of moir\'e patterns and magic angle physics in all families of chiral collapsed carbon nanotubes. A detailed study of the electronic structure of all types of chiral nanotubes, previously collapsed via molecular dynamics, has been performed. We find that each family possesses a unique geometry and moir\'e disposition, as well as a characteristic number of flat bands. Remarkably, all kinds of nanotubes behave the same with respect to magic angle tuning, showing a monotonic behavior that gives rise to magic angles in full agreement with those of twisted bilayer graphene. Therefore, magic angle behavior is universally found in chiral collapsed nanotubes with a small chiral angle, giving rise to moir\'e patterns. Our approach comprises first-principles and semi-empirical calculations of the band structure, density of states and spatial distribution of the localized states signaled by flat bands.
We thank the Centro de Supercomputación de Galicia, CESGA, (www.cesga.es, Santiago de Compostela, Spain) for providing access to their supercomputing facilities. This work was supported by grant PID2019-106820RB-C21 funded by MCIN/AEI/ 10.13039/501100011033/ and by “ERDF A way of making Europe”, by grant TED2021-129457B-I0 funded by MCIN/AEI/10.13039/501100011033/ and by the “European Union NextGenerationEU/PRTR” and by grant PRE2019-088874 funded by MCIN/AEI/10.13039/501100011033 and by “ESF Investing in your future”. ESM acknowledges financial support from FONDECYT Regular, Chile 1221301, and LC gratefully acknowledges the support from Comunidad de Madrid (Spain) under the Multiannual Agreement with Universidad Complutense de Madrid, Program of Excellence of University Professors, in the context of the V Plan Regional de Investigación Científica e Innovación Tecnológica (PRICIT).