Renormalization of the Majorana bound state decay length in a perpendicular magnetic field

Orbital effects of a magnetic field in a proximitized semiconductor nanowire are studied in the context of the spatial extent of Majorana bound states. We develop analytical model that explains the impact of concurring effects of paramagnetic coupling of the nanowire bands via the kinetic energy operator and spin-orbit interaction on the Majorana modes. We find, that the perpendicular field, so far considered as to be detrimental to the Majorana fermion formation, is in fact helpful in establishing the topological zero-energy-modes in a finite system due to significant decrease in the Majorana decay length.