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Using density functional theory, the electronic structures of single walledmolybdenum disulfide nanotubes (MoS$_2$ NTs) were investigated as a function ofdiameter. Our calculations show that the electronic structure near the band gapis sensitive to the NT diameter: armchair MoS$_2$ NTs act as indirect gapsemiconductors for diameters up to approximately 5.0 nm, while armchair MoS$_2$NTs with larger diameters act as direct gap semiconductors with band edgeslocated in the vicinity of $k = 2\pi/3$. This finding implies that MoS$_2$ NTswith large diameters should exhibit similar photoluminescence to 2D monolayerMoS$_2$ sheets. This indirect-to-direct band gap crossover is ascribed to theupward shift of the valence band peak at the $\Gamma$ point in small diameterNTs, which is caused by the tensile strain resulting from their tubularstructures.

Indirect-to-direct band gap crossover of single walled MoS$_2$ nanotubes