  We report the stability and electronic structures of the boron nitride
nanotubes (BNNTs) with diameters below 4 A by semi-empirical quantum mechanical
molecular dynamics simulations and ab initio calculations. Among them (3,0),
(3,1), (2,2), (4,0), (4,1) and (3,2) BNNTs can be stable well over room
temperature. These small BNNTs become globally stable when encapsulated in a
larger BNNT. It is found that the energy gaps and work functions of these small
BNNTs are strongly dependent on their chirality and diameters. The small zigzag
BNNTs become desirable semiconductors and have peculiar distribution of nearly
free electron states due to strong hybridization effect. When such a small BNNT
is inserted in a larger one, the energy gap of the formed double-walled BNNT
can even be much reduced due to the coupled effect of wall buckling difference
and NFE-pi hybridization.
