Magnetic field resistant quantum interferences in Josephson junctions based on bismuth nanowires

We investigate proximity-induced superconductivity in micrometer-long bismuth nanowires connected to superconducting electrodes with a high critical field. At low temperature we measure a supercurrent that persists in magnetic fields as high as the critical field of the electrodes (above 11 T). The critical current is also strongly modulated by the magnetic field. In certain samples we find regular, rapid SQUID-like periodic oscillations occurring up to high fields. Other samples exhibit less periodic but full modulations of the critical current on Tesla field scales, with field-caused extinctions of the supercurrent. These findings indicate the existence of low dimensionality, phase coherent, interfering conducting regions through the samples, with a subtle interplay between orbital and spin contributions. We relate these surprising results to the electronic properties of the surface states of bismuth, strong Rashba spin-orbit coupling, large effective $g$ factors, and their effect on the induced pair correlations. In particular, we emphasize the possible contribution of topological edge states of specific facets of the nanowires.

Figure 1

Magnetic-field dependence of the supercurrent of ${\mathrm{Bi}}_1$ (a) and ${\mathrm{Bi}}_3$ (b–d), in a perpendicular field. Fast, squid-like oscillations with periods of 800 and 150 G for ${\mathrm{Bi}}_1$ and ${\mathrm{Bi}}_3$, respectively, are noticeable, up to unusually high fields (at least 6 T for ${\mathrm{Bi}}_1$, 10 T for ${\mathrm{Bi}}_3)$. ${\mathrm{Bi}}_3$ displays an additional periodic modulation with a 2300 G period, and an irregular modulation of ${\mathrm{Bi}}_1$'s critical current occurs on the Tesla scale. (e) Sketch of two edge states interfering to produce SQUID-like oscillations up to high field. Inset: Scanning electron micrograph of ${\mathrm{Bi}}_1$ and its superconducting contacts.

Figure 2

(a) Color-coded differential resistance of ${\mathrm{Bi}}_2$, as a function of dc current and magnetic field, with selected differential resistance curves on the right. (b and c) Field dependence of $I_c$ and zero bias differential resistance extracted from panel (a). Note the oscillatory behavior on the Tesla scale, and the increase of maximal critical current with field.

Figure 3

Color-coded differential resistance as a function of current and field, and extracted curves, for three field orientations, on sample ${\mathrm{Bi}}_3^{*}$ (that corresponds to sample ${\mathrm{Bi}}_3$ after thermal cycling and aging). (a) Field along the nanowire axis; (b, c) two field orientations perpendicular to the wire axis.