Zero-Bias Anomaly in a Nanowire Quantum Dot Coupled to Superconductors

We studied the low-energy states of spin-$1/2$ quantum dots defined in $\mathrm{InAs}/\mathrm{InP}$ nanowires and coupled to aluminum superconducting leads. By varying the superconducting gap $\Delta$ with a magnetic field $B$ we investigated the transition from strong coupling $\Delta \ll T_K$ to weak-coupling $\Delta \gg T_K$, where $T_K$ is the Kondo temperature. Below the critical field, we observe a persisting zero-bias Kondo resonance that vanishes only for low $B$ or higher temperatures, leaving the room to more robust subgap structures at bias voltages between $\Delta$ and $2\Delta$. For strong and approximately symmetric tunnel couplings, a Josephson supercurrent is observed in addition to the Kondo peak. We ascribe the coexistence of a Kondo resonance and a superconducting gap to a significant density of intragap quasiparticle states, and the finite-bias subgap structures to tunneling through Shiba states. Our results, supported by numerical calculations, own relevance also in relation to tunnel-spectroscopy experiments aiming at the observation of Majorana fermions in hybrid nanostructures.

Figure 1

(a) Left panel: Color plot of $dI/dV$ vs ($B^{\perp }$, $V_{\mathrm{SD}}$) measured at the center of diamond $\alpha$. The dashed lines highlight the emergence of finite-bias peaks related to the opening of a superconducting gap. The superimposed line trace shows the $B^{\perp }$ dependence of the linear conductance. Right panel: $dI/dV(V_{\mathrm{SD}})$ traces taken at different $B^{\perp }$ values. The inset shows a scanning electron micrograph of a typical device (scale bar: 200 nm). (b) $dI/dV(V_{\mathrm{SD}})$ traces measured in an even diamond revealing the Dynes-like DOS of leads. (c) Numerical calculations. The smaller solid dots denote the position of the $\Delta$ and $2\Delta$ peaks, whereas the open dots highlight the position of the Shiba bound state peaks. (d) Linear conductance ($G_0$) normalized to the normal-state value ($G_0^N$) and plotted as a function of $\Delta /k_B{T}_K$ for diamonds $\alpha$ (red dots) and $\beta$ (black squares).

Figure 2

(a) $B^{\perp }$ dependence measured in diamond $\beta$. (b) $dI/dV$ line profiles taken at different $B$. The inset is a voltage-current measurement carried out at $B=0$, which reveals transport of a dissipationless supercurrent in the device.

Figure 3

(a) Schematics of the formation of Yu-Shiba-Rusinov bound states resulting from the interaction of the QD with the strongly coupled lead. (b) $B^{\parallel }$ dependence of $dI/dV$ measured in diamond $\gamma$. (c) The solid line depicts the $dI/dV$ taken at $B=0$. Two pairs of peaks are observed at $|e{V}_{\mathrm{sd}}|=\Delta +E_B$, $E_B$. The dashed line shows the equivalent $dI/dV$ taken in an even diamond, for comparison. (d) Numerical calculation of the $dI/dV$ for $B=0$. (e) Position of the intragap peaks as a function of $B$. The inset shows the data before performing the rescaling in units of $\Delta$. The dashed line displays the field dependence of $\Delta$.