The search for low-dimensional topological superconductivity is fueled by the promise of new and exotic physics, such as chiral superconductivity and non-Abelian anyons. However, the need to break time-reversal symmetry, usually by applying a relatively large external magnetic field, has hindered the realization of these novel phases of matter due to the deterioration effects of the field on the superconductor. We propose to break the time-reversal symmetry by controlling and tuning the superconductors' phases only to a regime where topological superconductivity emerges without needing an external exchange field. Our platforms rely on commonly available semiconductor-superconductor heterostructures, where spin-orbit coupling plays a central role. The main advantages of our approach over the existing ones are its tunability, suitability to a wide range of materials, and lack of magnetic field-induced impurity states. We present one- and two-dimensional schemes, and complement simplified models by analyzing disorder effects and transport simulations.
 O. Lesser, K. Flensberg, F. von Oppen, and Y. Oreg, PRB 103, 121116 (2021).
 O. Lesser, A. Saydjari, M. Wesson, A. Yacoby, and Y. Oreg, PNAS 118 (27) e2107377118 (2021).
 O. Lesser and Y. Oreg, J. Phys. D 55, 164001 (2022).
 O. Lesser, Y. Oreg, and A. Stern, PRB 106, L241405 (2022).
 O. Lesser, A. Stern, and Y. Oreg, manuscript in preparation.