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The effect of flexoelectric voltage on the electronic and optical properties of single- and double-wall carbon nanotubes is evaluated by the first-principles calculations. The voltage between the inner channel of curved sp2 carbon nanostructures and their surroundings scales linearly with nanotube wall curvature and can be boosted/reversed by appropriate outer wall functionalization. We predict and verify computationally that in double-wall nanotubes, flexoelectricity causes a straddling to staggered band gap transition. Accurate band s
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