Electron Transport in Single-Wall Carbon Nanotube Weak Links in the Fabry-Perot Regime

We fabricated reproducible high transparency superconducting contacts consisting of superconducting $\mathrm{Ti}/\mathrm{Al}/\mathrm{Ti}$ trilayers to gated single-wall carbon nanotubes. The reported semiconducting single-wall carbon nanotubes have normal state differential conductance up to $3e^2/h$ and exhibit clear Fabry-Perot interference patterns in the bias spectroscopy plot. We observed subharmonic gap structure in the differential conductance and a distinct peak in the conductance at zero bias, which is interpreted as a manifestation of the supercurrent. The gate dependence of this supercurrent as well as the excess current are examined and compared to the coherent theory of superconducting quantum point contacts with good agreement.

Figure 1

Current and conductance for the S-SWCNT-S Josephson junction as a function of voltage applied to the back gate with 1 mV source-drain voltage. The high conductance regime with Fabry-Perot oscillations is reached at large negative gate voltages ($<-6\mathrm{V}$). Coulomb blockade peaks are seen at lower gate voltages.

Figure 2

(a) Bias spectroscopy plot in the high transparency gate region, with a small magnetic field ($B=100\mathrm{mT}$) to suppress the superconducting state of the electrodes. (b) Analogous to (a) but without magnetic field, i.e., with superconducting electrodes. (c) Close-up on two of the resonances from which the excess current and supercurrent of Fig. 4 are extracted. Arrows are pointing to the gate voltages where the graphs in Figs. 3a, 3b are measured.

Figure 3

Differential conductance versus source-drain voltage measured with a lock-in amplifier ($5\mu \mathrm{V}$ excitation) at different gate voltages as indicated in Fig. 2c. The upper curve (black) is for the superconducting electrodes, and the lower curve (red) is with the magnetic field of 100 mT to suppress the superconductivity of the electrodes. (a) is measured at a resonance of the Fabry-Perot pattern, while (b) is measured at an antiresonance. Blue arrows point to the supercurrent peak.

Figure 4

Comparison between measured and theoretical data. (a) Measured (dots) and fitted (line) excess current as a function of conductance ($G=g{e}^2/h$). The fitted line is calculated from Eq. (1) using $\tilde{\Delta }$ as a fitting parameter. (b) Measured (dots) and fitted (lines) supercurrent. The fits are to $a(I_c{)}^{3/2}$ (solid line) and $a{I}_c$ (dashed line), using $a$ as a fitting parameter; see text for discussion. (c) Measured conductance in the Fabry-Perot regime as a function of gate voltage. (d) Measured (dots) and calculated (crosses) excess current. (e) The zero-bias anomaly area measured (dots) and calculated (crosses). The theoretical points (crosses) in (d) and (e) are calculated using the measured conductance in (c) and Eqs. (1, 2), respectively.