Figure 1

(a) Differential conductance of a $750\text{−}\mathrm{nm}$-long nanotube as a function of $V_{\mathit{\text{gate}}}$ measured at the temperature of $1.2\mathrm{K}$. Inset: schematics of the band structure in a metallic nanotube. (b) Differential conductance of a $600\text{−}\mathrm{nm}$-long nanotube as a function of $V_{\mathit{\text{gate}}}$ measured at the temperature of $0.3\mathrm{K}$.Reuse & Permissions

Figure 2

(Color online) (a) Addition energies (spacings between the neighboring conductance peaks multiplied by $\alpha$) as a function of $V_{\mathit{\text{gate}}}$, measured on the same sample as in Fig. 1a. (b) Same in a narrower range of $V_{\mathit{\text{gate}}}$. Blue squares: addition energies corresponding to a complete shell filling $\left(E_0^{\mathit{\text{add}}}\right)$. Green circles: addition energy corresponding to a half-filled shell $\left(E_2^{\mathit{\text{add}}}\right)$. Red diamonds: addition energies of the first and third electrons in a shell ($E_1^{\mathit{\text{add}}}$, $E_3^{\mathit{\text{add}}}$). $E_0^{\mathit{\text{add}}}$ points are noticeably higher than the base line. (c) Histogram of the addition energies.Reuse & Permissions

Figure 3

(Color online) (a) The nanotube conductance as a function of $V_{\mathit{\text{gate}}}$ and $B_{\perp }$ measured on a $600\text{−}\mathrm{nm}$-long nanotube. The conductance is color coded (bright colors correspond to a higher conductance; dark colors correspond to a lower conductance). The inferred spin sequence is indicated by numbers overlaying the image. For cluster II, the two middle traces exhibit a kink, indicating a singlet-triplet transition. (b) Addition energies for the four electrons in a shell [similar to shell I in Fig. 3a] measured as a function of $B_{\perp }$ on a different $600\text{−}\mathrm{nm}$-long nanotube. $E_1^{\mathit{\text{add}}}$ and $E_3^{\mathit{\text{add}}}$ stay remarkably constant in magnetic field, indicating that two electrons in a row (first and second, third and fourth) are added with the same spin projections. The addition energy $E_2^{\mathit{\text{add}}}$ corresponding to a half-filled shell grows in $B_{\perp }$ with a slope close to $2{\mu }_0$ (dashed line). Inset: conductance plot from which the addition energies were extracted. The symbols correspond to those in the main panel.Reuse & Permissions

Figure 4

(Color online) (a) Differential conductance map as a function of $V_{\mathit{\text{gate}}}$ (horizontal axis) and the source-drain bias (vertical axis). Each fourth Coulomb diamond is clearly larger than its neighbors. (b) Zoomed-in view of the $4N$- and $(4N-1)$-electron diamonds. A low-lying excitation of the $4N$-electron state is shown by the dashed line. Its energy $\delta E$ is clearly smaller than the shell spacing $\Delta$. White horizontal bars indicate the cotunneling thresholds.Reuse & Permissions