The dielectric response of semiconducting carbon nanotubes is studied within a tight-binding theory. We focus on “zigzag” tubes, finding that the induced charge exhibits large oscillations within the unit cell. The spatial extent of the response function is roughly equal to the nanotube radius, for any radius. We point out that the dielectric constant of undoped tubes (or any low-dimensional semiconductor) is 1. Our results are confirmed by direct numerical calculations.

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