Molecular states in carbon nanotube double quantum dots

We report electrical transport measurements through a semiconducting single-walled carbon nanotube with three additional top gates. At low temperatures the system acts as a double quantum dot with large interdot tunnel coupling allowing for the observation of tunnel-coupled molecular states extending over the whole double-dot system. We precisely extract the tunnel coupling and identify the molecular states by the sequential-tunneling line shape of the resonances in differential conductance.

Figure 1

(Color online) (a) Schematic of the fabricated device, with three top gates as labeled in (b). (b) SEM picture of a device. Dashed circles denote the regions affected by gates 1 and 2. (c) $G$ at $T=300\mathrm{K}$ versus top-gate voltage. Gates not swept are connected to the ground. Differences at $0\mathrm{V}$ arise from slightly hysteretic gate responses. Inset: Colorscale (grayscale) plot of $G$ versus gate 1 and gate 2 for fixed $V_C=-1\mathrm{V}$ at $2.2\mathrm{K}$. Bright corresponds to $0.4e^2∕\mathrm{h}$, dark to $0e^2∕\mathrm{h}$.

Figure 2

(Color online) (a) Colorscale (grayscale) plot of $dI∕d{V}_{sd}$ versus voltage applied on gate 1 $\left(V_{G1}\right)$ and gate 2 $\left(V_{G2}\right)$ at $T=290\mathrm{mK}$ and $V_{sd}=-128\mu \mathrm{V}$. The resulting honeycomb pattern represents the charge stability diagram of coupled double quantum dots. Two triple points are marked by blue/gray dots. Dashed lines are guides to the eye. (b) Closeup of a single honeycomb cell. (c) Vicinity of the triple points at $V_{sd}=391\mu \mathrm{V}$. (d) and (e) Capacitive and molecular model of a double quantum dot.

Figure 3

(Color online) (a) Colorscale (grayscale) plot of $dI∕d{V}_{sd}$ ($V_{sd}=20\mu \mathrm{V}$, $T=290\mathrm{mK}$) in the vicinity of two triple points. Dashed lines are guides to the eye. (b) Spacing $E_{\Delta }$ [see Eq. (2)] of the two high-conductance wings with respect to the $\Delta$ direction versus detuning $ϵ$. Inset: Schematics of sequential-tunnel processes allowed at the triple points (blue/dark gray dot) and at the honeycomb edges (red/gray circle) via molecular states.

Figure 4

(Color online) Colorscale (grayscale) plot of $dI∕d{V}_{sd}$ in the same region as in Fig. 3 for three different bias voltages: $V_{sd}=20$, 391, $-647\mu \mathrm{V}$ [(a), (b), and (c)]. Dark corresponds to $0e^2∕\mathrm{h}$ and bright to $0.1e^2∕\mathrm{h}$. On the right side, open circles denote traces of $dI∕d{V}_{sd}$ taken at the position of the dashed line. Solid lines represent fits to the line shape given by Eq. (3). Left-hand vertical scale: $V_{G1}$. Right-hand vertical scale: $V_{G1}$ converted into energy.