Spintronic interactions between topological edge states in chiral carbon nanotubes: a natural helical symmetry approach

Single-wall carbon nanotubes (CNTs) possess topological edge states depending on the chiral indices and edge geometries. We apply the natural helical crystal lattice (NHCL) model to analyze the topological features of chiral nanotubes in a most systematic and intuitive manner. Based on the symmetry of the topological features, NHCL allows one to determine the smallest possible unit cell in which each band corresponds to a complete and closed segment of the petal patterns in the Hamiltonian parameter space that defines the Berry phase of the wavefunction. The winding number of a CNT of an arbitrary chirality with a certain edge morphology is derived and summarized. Our study demonstrates a systematic strategy of topological classification covering a broad range of CNT chiralities and morphologies, which allows for fundamental exploration as well as device inspiration for carbon nanoelectronics.