Proposal for Majorana modes without a magnetic field in phase-biased Joesphson tri-junction*

We present a proposal for a phase-biased Josephson-junction-based Majorana system without an applied magnetic field. Such applied magnetic fields tend to degrade topological superconducting devices by suppressing superconductivity. Our proposal is similar to promising work that has already been demonstrated in phase-biased Josephson junctions in HgTe quantum wells. We show that in such a system, it is possible to eliminate the external magnetic field by introducing a third superconductor on the other side of the quantum well. We will discuss how this configuration hosts Majorana zero modes at the ends of the well following a similar mechanism to that in topological insulators as proposed by Fu and Kane. We demonstrate this idea by simulation with realistic experimental parameters and picking HgTe as the candidate junction material.