Topological superconductivity by phase tuning

Topological superconductivity in one dimension requires time-reversal symmetry breaking, but at the same time, it is hindered by the necessity for large external magnetic fields. We introduce a scheme in which a systematic manipulation of the phases of three superconducting pads tunes the system into a topological state. This scheme requires a tiny field that could be even less than a microtesla or current bias of the phases of the superconductors. The scheme is operational for several platforms and materials, including wires with strong spin-orbit coupling, planar 2D, certain transition metal dichalcogenides, and two layers of 2D systems. Our platform relies on two key ingredients: the three parallel superconductors form two SNS junctions with phase winding, and the Fermi velocities for the two spin branches transverse to the junction must be different from one another. The two phase differences between the three superconductors define a parameter plane that includes large topological regions. We analytically derive the critical curves where the topological phase transitions occur and corroborate the results with a numerical calculation based on a tight-binding model. We further propose material platforms with unequal Fermi velocities, establishing the experimental feasibility of our approach