Nanotubes in circularly polarized laser fields

Let us recall, first, the full symmetry of CNTs, the identification of which has been completed recently by Damnjanovic et al. [23]. The non-symmorphic rod-group [23] describing achiral CNTs with index n can be decomposed in the following manner, 

Adding the time-dependent laser field, the single-electron Floquet Hamiltonian is given, without loss of generality, by 

The vector potential A(r, t) for the incident circularly polarized plane-wave, propagating along z-axis, is given hy 

once the circularly polarized field is applied all symmetry operations which involve the reflection of p and/or z collapse to the same GTRS, 

The unitary DSs for a general nanotube involve, therefore, the translation Tj and screw axis symmetries only. 

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