True Josephson supercurrent in a Scanning Tunneling Microscope (STM) with a niobium tip and sample

We have measured I-V characteristics of Josephson junctions formed between a Nb tip and a Nb surface in a 50 mK scanning tunneling microscope (STM). Depending on the distance between the tip and sample, which sets the normal state tunneling resistance R$_n$, the I-V characteristics are either in the phase-diffusion, underdamped or overdamped regime. For R$_n$ = 500 k$\Omega$ the I-V curves show a quasiparticle current rise of 2 nA when biased at V = 2$\Delta$/e, but the junction is in the phase-diffusion regime and no supercurrent is visible at V = 0. For R$_n$ between 5 k$\Omega$ and 50 k$\Omega$, the IV curves show a hysteretic switching response, as expected for an underdamped junction, and a true Josephson supercurrent at V = 0. For example, at R$_n$ = 5.95 k$\Omega$, the junction shows a quasiparticle current of 200 nA and a suppressed but true switching critical current of 15 nA. For R$_n$ $<$ 1 k$\Omega$, the tunneling characteristics are those of an overdamped junction suggesting that the tip may be in physical contact with the surface, producing a weak link. In this regime at R$_n$ = 272 $\Omega$, the critical current is about 3 $\mu$A and is non-hysteretic. We extract and discuss key tunneling parameters (gap, capacitance and loss) in the different regimes.