Eightfold Shell Filling in a Double-Wall Carbon Nanotube Quantum Dot

We fabricated a quantum-dot device consisting of an individual double-wall carbon nanotube and studied its electrical transport properties at low temperatures. In the negative bias region, the gate modulation curve exhibited quasiperiodic current oscillations, attributed to the Coulomb blockade of single-electron tunneling. We observed both four- and eightfold shell filling in the Coulomb diamond structures. The observation implies an eightfold degeneracy in the single-particle energy levels, which is higher than the fourfold degeneracy of a single-wall carbon nanotube. We show that the observed eightfold shell filling is a unique characteristic of a double-wall carbon nanotube quantum-dot device.

Figure 1

(a) An atomic force microscopy image of a carbon nanotube. (b) Topography maps along the lines $A$ and $B$ in (a). (c) A scanning electron microscopy image of a typical device. (d) A gate modulation curve of the sample at 2 K with a source-drain bias of 1 mV.

Figure 2

(a) Density plot of the differential conductance ($dI/dV$) as a function of the gate voltage $V_g$ and source-drain bias voltage $V_{\mathrm{sd}}$. The gate voltage range spans consecutive several fourfold shell-filling patterns and one eightfold pattern. The dashed lines indicate small jumps in the gate voltage. The small and large dots are a guide for eyes. (b) and (c) are highlighted images of the borders of the Coulomb diamond and the high-order energy levels. Dark lines denote mirror-symmetric ones while gray lines show asymmetric ones.

Figure 3

A schematic of the conductance peaks pattern. Right after the eightfold shell-filling, the peak-to-peak spacing between two neighboring fourfold patterns will be given by $U+\delta$, which is much less than $U+\Delta$. The corresponding boundary Coulomb diamond thus becomes only slightly larger than those within a shell.