Phase control of zero energy modes in topological Josephson junctions*

Recent works have realized Majorana zero modes in planar Josephson junctions consisting of a semiconductor with strong spin-orbit coupling proximitized by two superconducting leads. Such systems offer the tantalizing possibility of using the phase difference Φ across the two superconductors as a new experimental knob to tune into and out of the topological regime, possibly at ultra-fast timescales, apart from having advantages such as reduced sensitivity to chemical potential tuning and appearance of Majorana bound states at zero magnetic field. Here, we demonstrate strong phase control of Andreev bound states that emerge from the gap at Φ~0 and coalesce at zero energy at Φ~π. The zero energy modes at Φ~π appear at in-plane magnetic fields as low as ~220 mT and persist robustly with variations of in-plane Zeeman field and gate voltages in a wide range. At larger in-plane magnetic fields, the zero energy modes become phase independent and stick for all values of Φ. We also study the behavior of the zero energy states with respect to large out-of-plane magnetic fields that can tune the phase texture within the Josephson junction, and possibly result in motion of Majorana zero modes.