Electrostatics of straight and bent single-walled carbon nanotubes

Response of a single-walled carbon nanotube to external electric field, F, is calculated analytically within the classical electrostatics. Field-induced charge density distribution is approximately linear along the axis of a metallic nanotube and depends rather weakly, as ln(h/ r), on the nanotube length, h (here r is the nanotube radius). In a semiconducting nanotube with a gap, Eg, charge separation occurs as F exceeds the threshold value Fth=Eg /eh. For F>Fth, positively and negatively charged regions at the ends of nanotube are separated by a neutral strip in the middle. Properties of this neutral strip, length and induced charge distribution near the ends, are studied in detail. We also consider a bent nanotube and demonstrate that the number of neutral strips can be one or two depending on the direction of F.