Topological phase diagram of a three-terminal Josephson junction: From the conventional to the Majorana regime

We study the evolution of averaged transconductances in three-terminal Josephson junctions when the superconducting leads are led throughout a topological phase transition from an \(s\)-wave to a \(p\)-wave (Majorana) phase by an in-plane magnetic field \(B_x\). We provide a complete description of this transition as a function of \(B_x\) and a magnetic flux \(\Phi\) threading the junction. For that we use a spinful model within a formalism that allows to treat on equal footing the contribution to the transconductance from both the Andreev subgap levels and the continuum spectrum. We unveil a fractionalization in the quantization of the transconductance due to the presence of Majorana quasiparticles, reflecting the effective pumping of half a Cooper pair charge in the \(p\)-wave regime.