Title: Evidence for $π$-shifted Cooper quartets in PbTe nanowire three-terminal Josephson junctions

Abstract: Josephson junctions are typically characterized by a single phase difference across two superconductors. This conventional two-terminal Josephson junction can be generalized to a multi-terminal device where the Josephson energy contains terms that result from entanglement of multiple independent phase variables. It was recently proposed that such multi-terminal couplings should result in a $\pi$-shifted quartet supercurrent. We show for the first time experimental signature of this $\pi$-shifted supercurrent, by using a three-terminal Josephson junction based on selective-area-grown PbTe nanowires. We further observe conductance steps at zero magnetic field co-existent with supercurrent in both two- and three-terminal devices, indicating ballistic superconductivity in the few quantum modes regime. Superconducting transport in the few-modes regime is a necessary condition for realizing topologically protected bound states such as Majorana zero modes in one-dimensional nanowires and Weyl nodes in multi-terminal Josephson junctions.