Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al-MoTe2-Al junctions

Abstract: When a normal metal $N$ is sandwiched between two superconductors, the energy gaps in the latter act as walls that confine electrons in $N$ in a square-well potential. If the voltage $V$ across $N$ is finite, an electron injected into the well undergoes multiple Andreev reflections (MAR) until it gains enough energy to overcome the energy barrier. Because each reflection converts an electron to a hole (or vice versa), while creating (or destroying) a Cooper pair, the MAR process shuttles a stream of pairs across the junction. An interesting question is, given a finite $V$, what percentage of the shuttled pairs end up as a Josephson supercurrent? This fraction does not seem to have been measured. Here we show that, in high-transparency junctions based on the type II Dirac semimetal MoTe$2$, the MAR leads to a stair-case profile in the current-voltage ($I$-$V$) response, corresponding to pairs shuttled incoherently by the $n^{th}$-order process. By varying the phase $\varphi$ across the junction, we demonstrate that a Josephson supercurrent ${\bf J}{\rm s}\sim \sin\varphi$ co-exists with the MAR steps, even at large $V$. The observed linear increase in the amplitude of ${\bf J}{\rm s}$ with $n$ (for small $n$) implies that ${\bf J}{\rm s}$ originates from the population of pairs that are coherently shuttled. We infer that the MAR steps and the supercurrent are complementary aspects of the Andreev process. The experiment yields the percentage of shuttled pairs that form the supercurrent. At large $V$, the coherent fraction is initially linear in $n$. However, as $V\to 0$ ($n\gg 1$), almost all the pairs end up as the observed Josephson supercurrent.