Resonant and Inelastic Andreev Tunneling Observed on a Carbon Nanotube Quantum Dot

We report the observation of two fundamental subgap transport processes through a quantum dot (QD) with a superconducting contact. The device consists of a carbon nanotube contacted by a Nb superconducting and a normal metal contact. First, we find a single resonance with position, shape, and amplitude consistent with the theoretically predicted resonant Andreev tunneling (AT) through a single QD level. Second, we observe a series of discrete replicas of resonant AT at a separation of $\sim 145\mu \mathrm{eV}$, with a gate, bias, and temperature dependence characteristic for boson-assisted, inelastic AT, in which energy is exchanged between a bosonic bath and the electrons. The magnetic field dependence of the replica’s amplitudes and energies suggest that two different bosons couple to the tunnel process.

Figure 1

(a) Schematic of resonant AT. Two electrons tunnel through the QD into $\mathsf{S}$ for ${\mu }_{\mathrm{QD}}={\mu }_{\mathsf{S}}$ and ${\mu }_{\mathsf{N}}>{\mu }_{\mathrm{QD}}$. (b) Schematic of inelastic AT. Two electrons tunnel through the QD into $\mathsf{S}$ at ${\mu }_{\mathrm{QD}}={\mu }_{\mathsf{S}}+(n/2)\hslash {\omega }_{\mathsf{b}}$ for ${\mu }_{\mathsf{N}}>{\mu }_{\mathrm{QD}}$ by emitting multiples of the energy $\hslash {\omega }_{\mathsf{b}}$ to the environment. (c) SEM image of a representative device and schematic of the measurement setup. (d) Differential conductance of QD1 as function of $V_{\mathrm{SD}}$ and $V_{\mathrm{BG}}$. (e) Detailed conductance map of the region indicated in (d). The resonant and inelastic AT lines are labeled $\mathsf{R}$ and IE, respectively. The dotted lines point out the Coulomb blockade diamond edges and ABS an Andreev bound state.

Figure 2

Resonance line shapes: $G$ as function of $V_{\mathrm{BG}}$ (points) at zero bias (a) in the normal state at $B=5\mathrm{T}$ and (b) at zero field in the superconducting state. The blue, red, and dotted green lines are best fits to the data using the expressions for a Breit-Wigner (BW), resonant AT, and a thermally broadened QD resonance, respectively.

Figure 3

Temperature dependence of resonant and inelastic AT. Differential conductance $G$ as function of $V_{\mathrm{BG}}$ at (a) $V_{\mathrm{SD}}=0$ and (b) $V_{\mathrm{SD}}=-0.5\mathrm{mV}$ for the three indicated temperatures. The black arrow points out the resonant AT line, the red arrows the boson-absorbing and the blue arrows the boson-emitting resonances [21]. The inset in Fig. (a) shows the peak amplitudes of the features indicated in the main figure.

Figure 4

Magnetic field dependence of resonant and inelastic AT. (a) $G$ as a function of the bias $V_{\mathrm{SD}}$ and the external magnetic field $B$ at a fixed back gate voltage where the resonance $\mathsf{R}$ crosses $V_{\mathrm{SD}}=0$. (b) Tunnel coupling $\mathrm{\Gamma }={\mathrm{\Gamma }}_1+{\mathrm{\Gamma }}_2$ of resonance $\mathsf{R}$ extracted from the resonant AT and the Breit-Wigner expressions as a function of $B$. The fits are obtained from color scale images at the same relative position [21]. (c) Energy and (d) amplitude of the inelastic AT peaks (IE) as a function of $B$. The resonances are labeled in (c) for increasing energy.