Zang X, Singh N, Schwingenschlögl U. Topological characterization of carbon nanotubes.
JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018;
30:335301. [PMID:
30033939 DOI:
10.1088/1361-648x/aad21f]
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Abstract
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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