Hi Marco, at first glance it's just one more research paper trying to impress with jargon... Condolences...
I could imagine a "vector" electron transfer as:
1) The nanotube imposes a dispersion relation between E and the vector k, and even, these are restricted to discrete values. The other medium (vacuum?) imposes a different dispersion relation. To pass from one medium to the other, the electron needs some movement properties (like light needs some angle to exit a glass fibre), and in the new medium, its E and vector k are altered, just like light refraction, or like an electron passing through a heterojunction. If a photon helps the transfer, the relation between possible E and vector K before and after the transfer must include this photon too.
2) More remote possibility: the electron passes only with the help of a mediator, a "vector" etymologically, like insects are vectors of diseases.