Signatures of Interactions in the Andreev Spectrum of Nanowire Josephson Junctions

We performed microwave spectroscopy of an InAs nanowire between superconducting contacts implementing a finite-length, multichannel Josephson weak link. Certain features in the spectra, such as the splitting by spin-orbit interactions of the transition lines among Andreev states, have been already understood in terms of noninteracting models. However, we identify here additional transitions, which evidence the presence of Coulomb interactions. By combining experimental measurements and model calculations, we reach a qualitative understanding of these very rich Andreev spectra.

Figure 1

(a) Andreev spectrum of a typical finite-length weak link with spin orbit interaction. Colored arrows highlight the possible microwave absorption lines depicted in (b). Transition lines are classified into pair (red) and mixed pair (blue) transitions and intermanifold (solid green) and intramanifold (dashed green) single particle transitions. (c) Optical image of the measured device, with a phase-biased nanowire (NW) weak link [close view in SEM image (d), with underlying local back gate] placed close to the shorted end of a microwave readout resonator (full view in [18]). Left port connected to the gate is devoted to tune the properties of the NW with a dc voltage $V_g$ and to drive microwave transitions with a tone at frequency $f_1$.

Figure 2

Experimental results showing microwave two-tone spectra as a function of phase difference ($\delta$) for a sequence of decreasing gate voltages $V_g=5.563\mathrm{V}+\delta V_g$. The colored lines on the right half of the spectra are guides to the eye indicating what we identify as single quasiparticle (green), pair (red), and mixed pair (blue) transition lines. Note that a second group of SQPT is visible around 20 GHz; it likely corresponds to single quasiparticle transitions from the first to the third Andreev doublet (not highlighted here).

Figure 3

Transition lines within the four-site model without (a) and with (b) the effect of Coulomb interactions. Within this model effective singlet and triplet pairing, characterized by parameters ${\mathrm{\Gamma }}_s$ and ${\mathrm{\Gamma }}_t$, arise by assuming $\mathrm{\Delta }\to \infty$ in the leads.

Figure 4

Evolution with the weak link effective charging energy $E_c^{\mathrm{eff}}$ of the spectral lines as a function of phase difference as obtained from the extended TB model with 31 sites in the $x$ direction (11 in the normal region) and three transverse chains, describing a junction with length $\sim 550\mathrm{nm}$ and width $\sim 200\mathrm{nm}$ [detailed parameters in [18] ]. Full lines correspond to the main inter-SQPT (green), lowest PT (red), and mixed PTs (blue). The faint lines correspond to secondary transitions (i.e., from the first to the third or from the second to the third manifolds, intramanifold, and higher PTs). Excitations up to $N_{\mathrm{pr}}=12$ are included in the effective interacting Hamiltonians. Rightmost panel is the data of the central panel of Fig. 2.