Germanene nanotubes

In this chapter, the various electronic properties of germanium nanotubes (GeNTs) were investigated by the density functional theory. The cooperative and competitive relationships between the chiral angle, periodic boundary conditions, and multi-orbital hybridizations create unusual narrow gaps and quasi-flat bands in the ultra-small armchair and zigzag tubes, respectively. The features varied dramatically with tube radii. Armchair GeNTs (aGeNTs) have an indirect-to-direct band gap transition as their radius is increased to a particular value, while zigzag GeNTs (zGeNTs) present a metalsemiconductor transition. The projected density of states was used to elucidate the critical transitions, and the evolution of p and s orbital mixing states during the process are discussed in detail. The information presented here provides a better understanding of the essential properties of GeNTs.