Abstract
Atomistic density functional theory (DFT) calculations of the capacitance between a metallic cylindric gate and a carbon nanotube (CNT) are reported. We find that the quantum capacitance of the CNT becomes negative as the CNT carrier density is reduced. This corresponds to an unconventionally high charge accumulation on the CNT, which in turn overscreens the external gate field. The relationship between this behavior and the predominance of the attractive exchange energy contribution is pointed out.