Figure 1

(a) Side-view drawing of the sample geometry. (b) Overview measurement of the differential conductance $dI/d{V}_{\mathrm{SD}}$ of the nanotube quantum dot system in the few-hole region ($1\le N_h\le 2$, with $N_h=0$ and $N_h=3$ visible at the edges of the plot) as function of backgate voltage $V_g$ and bias voltage $V_{\mathrm{SD}}$ (logarithmic color scale, negative differential conductance is plotted white). In the CB regions, the number of trapped valence band holes $N_h$ is indicated.Reuse & Permissions

Figure 2

(a) Differential conductance $dI/d{V}_{\mathrm{SD}}$ in the region where the nanotube is charged with $1\le N_h\le 2$ holes, as function of gate voltage $V_g$ and bias voltage $V_{\mathrm{SD}}$ (linear color scale). (b) Detail zoom of part of the SET region with $1\le N_h\le 2$, as marked in (a), using a different color scale. In both (a) and (b), arrows point out line features corresponding to excited states (see text) [17]. (c) Excitation energies corresponding to the lines of enhanced $dI/d{V}_{\mathrm{SD}}$ in (a) and (b) with positive slope; the $x$ axis is the line number. The solid line is a linear fit, resulting in an average energy difference of $\Delta E=0.425\pm 0.004\mathrm{meV}$ per line. (d) Detail zoom of the CB region with $N_h=2$, as marked in (a) (logarithmic color scale) [17]. A white dashed line sketches the edge of the SET region. For better contrast, different color scale ranges are chosen in parts of the plot. (e) Relative excitation energies for the line features in (d), using the same parameters for position to energy conversion. A linear fit gives $\Delta E=0.810\pm 0.025\mathrm{meV}$. (f) Schematic of cotunnel-assisted sequential tunneling (COSET) (see text).Reuse & Permissions

Figure 3

Single quantum dot model reproducing the observed transport features. (a) Process and energy level scheme analogous to Fig. 2f, leftmost panel, showing the lead Fermi levels, the accessible states within the quantum dot, and tunneling and relaxation rates relevant for pumping the vibration mode into nonequilibrium [17]. For a detailed description of the panels and the rates $\Gamma$, ${\Gamma }^{\prime }$, and ${\gamma }^{\prime }$, see the text. (b) Calculated differential conductance as function of $V_g$ and $V_{\mathrm{SD}}$, for the following parameters: vibrational level spacing $\hslash \omega =810\mu \mathrm{eV}$, $kT=8.6\mu \mathrm{eV}=10\hslash {\Gamma }^{\prime }={10}^3\hslash \Gamma ={10}^4\hslash {\gamma }^{\prime }={10}^4\hslash \gamma$. The tunnel couplings were chosen smaller than in the experiment to ensure a well-behaved perturbation expansion. $V_g$ is scaled with the gate conversion factor $\alpha =C_g/C$ (see, e.g., 15, 19). Arrows indicate the enhancement of COSET at high bias.Reuse & Permissions

Figure 4

Alternative mechanism for obtaining a vibrational nonequilibrium occupation. (a) Schematic side-view drawing detailing the possible formation of a small quantum dot beneath one of the metallic contact leads. (b) Transport processes for this “double quantum dot” case: additional cotunneling processes are enabled when the small quantum dot enters the energy window given by $V_{\mathrm{SD}}$ (see text).Reuse & Permissions