Fig. 4: Effect of circumferential tensile strain on the band-edge levels of MoSe₂ nanotubes.

a DFT-computed circumferential tensile strain as a function of tube diameter D. The reference for the strain calculation at each tube diameter is the circumference of a corresponding unrelaxed tube rolled from a monolayer. The circumference of a tube is measured from the transition-metal atoms. As illustrated, after structural relaxation D > D₀, where D₀ is the original tube diameter. b Evolution of the electronic band structure of a MoSe₂ monolayer as a function of uniaxial tensile strain. The strain varies from zero to 10% at a step of 2%. c Plot of the band-edge energy levels of MoSe₂ monolayer as a function of uniaxial tensile strain. The green, red, and blue lines represent the data for CBM at K, VBM at K, and VBM at Γ, respectively. d Change in the VBM orbital character as the diameter of zigzag nanotube is decreased. The top and bottom panels show the electronic band structures near the VBM of zigzag MoSe₂ tubes with a diameter of 41 Å and 21 Å, respectively. The insets illustrate the electron density isosurface of the corresponding VBM state at Γ. e Diameter dependence of the valence-band (VB) orbital energy, for the topmost in-plane and out-of-plane orbitals. The filled circles are from DFT calculations, whereas the open circles are from our model that takes into account both the flexoelectric and circumferential tensile strain effects. f Comparison of the DFT-computed CBM and VBM energies of MoSe₂ zigzag nanotubes (filled circles) with those from our model (open squares).