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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). The authors thank Dr Sen Lin and Prof Zhi Song for helpful discussions.