Shot-Noise Detection in a Carbon Nanotube Quantum Dot

An on-chip detection scheme for high frequency signals is used to detect noise generated by a quantum dot formed in a single wall carbon nanotube. The noise detection is based on photon assisted tunneling in a superconductor-insulator-superconductor junction. Measurements of shot noise over a full Coulomb diamond are reported with excited states and inelastic cotunneling clearly resolved. Super-Poissonian noise is detected in the case of inelastic cotunneling.

Figure 1

Schematic drawing of the circuit (a) and a scanning electron microscope (SEM) picture of the sample (b). The SIS detector is coupled, using two on-chip capacitances $C_C$ (blue part), to the CNT-QD (the curly white lines are the custom made contacts) and is cooled to 20 mK. Four contact lines (red) are used for both the CNT and the detector. An additional contact on the CNT side is used as a side gate [see inset in (c)]. All lines incorporate an on-chip impedance $R$ to prevent the high frequency signal from leaking via parasitic capacitances in the leads. These are thin Pt wires ($25\times 0.1\times 0.02\mu \mathrm{m}$) with a resistance between 2 and $2.25\mathrm{k}\Omega$, measured at 4 K. (c) Carbon nanotube $d{I}_{\mathrm{nt}}/d{V}_{\mathrm{nt}}$ density plot shows standard Coulomb diamonds. Inset: SEM picture of the CNT with contacts and a side gate. (d) $I\mathrm{\text{−}}V$ characteristic of the detector SIS junction in the absence of noise. Current is zero in the superconducting gap region and is determined by the normal state resistance $R_N=11.3\mathrm{k}\Omega$ for $V_{\det }>2\Delta /e$. Inset: SEM picture of the detector with two SIS junctions. This SQUID geometry allows us to suppress the supercurrent by means of an external magnetic field.

Figure 2

(a) Detector signal $I_{\det }$ as a function of detector bias $V_{\det }$ for several CNT current bias values $I_{\mathrm{nt}}$. The maximum current bias $I_{\mathrm{nt}}=40\mathrm{nA}$ corresponds to a voltage $V_{\mathrm{nt}}=11\mathrm{mV}$. Inset: Same detector curves normalized to CNT current. (b) Averages of normalized detector curves for the calibrating SIS-SIS, respectively, SIS-CNT sample. Inset: Integrated detector signal $\int I_{\det }d{V}_{\det }$ (for $140\mu \mathrm{V}\le V_{\det }\le 370\mu \mathrm{V}$) versus CNT current $I_{\mathrm{nt}}$.

Figure 3

Density plots for dc [(a) and (b)] and noise measurements [(c) and (d)] as a function of nanotube bias $V_{\mathrm{nt}}$ and gate voltage $V_g$. Standard dc measurement of current $I_{\mathrm{nt}}$ and conductance $d{I}_{\mathrm{nt}}/d{V}_{\mathrm{nt}}$ are presented in (a) and (b) for two adjacent Coulomb diamonds. The diamonds correspond to a fixed number of electrons ($N$, respectively $N+1$) on the quantum dot. Noise power $S_I$ obtained according to Eq. (3), together with its derivative $d{S}_I/d{V}_{\mathrm{nt}}$, are presented in (c), respectively (d). Both are normalized to the electron charge such that we can use the same color scale for dc and noise measurements.

Figure 4

(a) Fano factor density plots corresponding to the two parts of the Coulomb diamond indicated in Fig. 3b. (b) Individual Fano factor curves determined for gate voltages indicated in the inset density plot. The red curve was measured in a different Coulomb diamond. $F>1$ indicates super-Poissonian noise corresponding to inelastic cotunneling. For CNT currents $I_{\mathrm{nt}}<150\mathrm{pA}$ (the dashed part of the curves), no excess noise can be measured, with the sensitivity of our detection scheme.