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Nanotube bundles and tube-tube orientation: A van der Waals Density Functional Study

We study the binding energy, intertube distance and electronic structure of bundles consisting of single walled carbon nanotubes of the same chirality. We model various nanotube structures (chiralities) and orientations with van der Waals density functional theory. The orientation of the tubes in the bundle strongly influences the properties of the bundles if the chirality of the tubes shares symmetry with the trigonal bundle structure, meaning chiralities which have a $60^\circ$-rotational symmetry (C$_6$-axis), e.g. ($12,0$) bundles. The bundle structure breaks the symmetry depending on the arrangement of the neighboring tubes. Pseudogaps open in the electronic density of states and intertube distances ($\pm5$-10%) vary in dependence of the relative orientation of the tubes in the bundle. Bundles of C$_6$-axis armchair tubes have metallic configurations. A $15^\circ$ rotation off the high symmetry configuration (AA-stacked) of a ($6,6$) bundle shows metallic behavior and has higher binding energy than the high symmetry configuration. We find binding energies between $19 meV/atom$ and $35 meV/atom$, depending on the chirality of the tubes. The intertube distances are between $3.2 Å$ and $3.4 Å$ but independent of orientation for non C$_6$-axis tubes.