Durability of the superconducting gap in Majorana nanowires under orbital effects of a magnetic field

We analyze the superconducting gap in semiconductor/superconductor nanowires under orbital effects of a magnetic field in the weak- and strong-hybridization regime using a universal procedure which guarantees the stationarity of the system, i.e., vanishing of the supercurrent induced by a spatially varying vector potential. We perform minimization of the free energy with respect to the vector potential which allows for taking into account the orbital effects even for systems with intrinsically broken spatial symmetry. For the experimentally relevant scenario of a strongly coupled semiconductor/superconductor system, where the wave function of the charge carriers hybridizes between the two materials, we find that the gap closes due to the orbital effects in a sizable magnetic field in correspondence with the recent experiment [S. M. Albrecht et al., Nature (London) 531, 206 (2016)].