Mirage Andreev Spectra Generated by Mesoscopic Leads in Nanowire Quantum Dots

We study transport mediated by Andreev bound states formed in InSb nanowire quantum dots. Two kinds of superconducting source and drain contacts are used: epitaxial Al/InSb devices exhibit a doubling of tunneling resonances, while, in $\mathrm{NbTiN}/\mathrm{InSb}$ devices, Andreev spectra of the dot appear to be replicated multiple times at increasing source-drain bias voltages. In both devices, a mirage of a crowded spectrum is created. To describe the observations a model is developed that combines the effects of a soft induced gap and of additional Andreev bound states both in the quantum dot and in the finite regions of the nanowire adjacent to the quantum dot. Understanding of Andreev spectroscopy is important for the correct interpretation of Majorana experiments done on the same structures.

Figure 1

(a) Scanning electron micrograph of a representative $\mathrm{Al}/\mathrm{InSb}$ device. The shaded blue regions show the Al thin shell with a break in the middle. (b) Illustrative energy diagrams of a soft gap probe, a hard-gapped lead and an ABS in the dot (solid lines) for two different source drain biases $V\approx \mathrm{\Delta }$ (left) and $V\approx 2\mathrm{\Delta }$ (right). (c) and (d) Magnetic field evolution of the two-terminal transport. The field is applied parallel to the nanowire axis.

Figure 2

(a) Scanning electron micrograph of the $\mathrm{NbTiN}/\mathrm{InSb}$ device. The green dot marks the quantum dot, the white line is a conceptual confining potential set by gates $t$, $p$, and $s$. (b) Tunneling conductance through the dot as a function of bias and $V_p$. Arrows point to four apparent replicas of the lowest loop-like resonance. Data obtained at zero magnetic field (see Supplemental Material [25] for field dependence). (c) Illustrative energy diagram with the soft gap probe, two ABS on the dot (${\mathrm{QD}}_1$ and ${\mathrm{QD}}_2$) and two ABS in the hard gap lead (${\mathrm{LEAD}}_1$ and ${\mathrm{LEAD}}_2$). (d) Theoretical model results as a function of dot on site energy ${\epsilon }_{\mathrm{dot}}$, with ${\mathrm{QD}}_{1,2}$ energies ${\epsilon }_1^D={\epsilon }_{\mathrm{dot}}$ and ${\epsilon }_2^D={\epsilon }_{\mathrm{dot}}-1.7\mathrm{meV}$, ${\mathrm{LEAD}}_{1,2}$ energies ${\epsilon }_1^L=0.5\mathrm{meV}$ and ${\epsilon }_2^L=1.5\mathrm{meV}$, induced pairing ${\mathrm{\Gamma }}_S=0.27\mathrm{meV}$, parent gap ${\mathrm{\Delta }}_p=2.7\mathrm{meV}$, and Coulomb energy $U=6.8\mathrm{meV}$ (see Supplemental Material [25] for model details).

Figure 3

Tunneling differential conductance at zero field across a quantum dot between a soft-gap superconducting electrode and a proximitized nanowire lead with a hard gap. The quantum dot has one (a) or two (b)–(d) spinful levels, while the nanowire has zero (a) and (b), one (c), or two (d) subgap Andreev bound states. Magnetic field is zero in all panels, simulation parameters similar to those in Fig. 2. See Fig. S1 in the Supplemental Material [25] for details on the corresponding energy spectra.

Figure 4

(a) Data in the regime similar to Fig. 2. (b) Illustrative energy diagram with a peak in the density of states in the left probe that aligns with ABS, and produces NDC in the loop-like structure within the superconducting gap.