Fig. 3: Energetically stabilization of flattened NbSe₂ nanotube.

a Calculated forming energy of varied NbSe₂ configurations (energy per atom) as a function of the number of NbSe₂ units in their cross-section. The formation of single- or double-layer configurations roughly satisfies the 1/n dependence, while flat and circular tubes obey the 1/n² rule. b Forming energy of NbSe₂ tubular structures as a function of their equivalent diameter, in which circular and flat tubes are in red and purple, respectively. The purple-shaded region represents where their energy favors the isolation of flat tubes, as derived from a. The inset shows that NbSe₂ diameters for different circular tubes depend on their cross-sectional unit number measured by the relaxed atomic model, following a linear relationship. c Average Nb-Se bond lengths of inner and outer layers of “Se-Nb-Se” sandwich structures of NbSe₂ circular tubes at different n. The upper limit of the error bars is the maximum of all Nb-Se bond lengths in the optimized NbSe₂ circular tube model, the lower limit is the minimum bond length, and the red dot is the average bond length. The inset shows a typical circular tube model with arrows indicating the inner and outer Nb-Se bonds. d Bond length distribution of short and long Nb-Se bonds in the flat tube along the clockwise direction of Nb atoms shown in the inset at n = 20.