Negative quantum capacitance of gated carbon nanotubes

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.

Figure 1

(a) Schematic cross section of the simulated system; (b) screened electrostatic potential computed along the channel inside the CNT. A gate bias $\delta V_G=0.1\mathrm{mV}$ is applied. Different curves correspond to different carrier densities giving three different screening behaviors; (c) circuital model for the coaxially gated CNT device.

Figure 2

Total charge induced on the CNT (10,0) by the gate bias $\delta V_G=0.1\mathrm{mV}$, computed as a function of both the Fermi level and the carrier density. Dash–dotted line refers to the classical situation. Dashed line has been obtained for $C_Q=e^2{\rho }_0\left({ϵ}_F\right)L$, neglecting electron–electron interactions effects. Solid line refers to the DFT calculations.

Figure 3

(a) Computed quantum capacitance of the coaxially gated CNT (10,0) as a function of both the Fermi level and the carrier density. Solid line refers to DFT calculations. Dashed line refers $C_{Q_{\mathrm{DOS}}}=e^2{\rho }_0\left({ϵ}_F\right)L$; (b) electron–electron interaction contribution to the quantum capacitance. Solid line refers to the DFT atomistic calculation. Dash–dotted line is an analytical result for the ratio $C_{Q_{\mathrm{DOS}}}∕C_{Q_{\mathrm{HF}}}$ obtained for a parabolic-confined quantum wire matching the CNT.