Topological characterization of carbon nanotubes
Xiaoning Zang1, Nirpendra Singh1, Udo Schwingenschlögl1
1Physical Sciences and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia.
None:
We show that the tight-binding Hamiltonian of any carbon nanotube with C N symmetry can be represented by N decoupled tight-binding Hamiltonians of molecular chains, for which a general pseudospin formulation, characterized by specific paths in a two-dimensional auxiliary space, is developed. The quantum phases therefore are given by a set of N winding numbers of the paths. The paths degenerate to lines and circles for armchair and zigzag carbon nanotubes, respectively. They rotate in the auxiliary space when a magnetic field of varying strength is applied along the carbon nanotube, which gives rise to quantum phase transitions.
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