Hybridization energy oscillations of Majorana and Andreev bound states in semiconductor-superconductor nanowire heterostructures

The recent experimental observations of decaying energy oscillations with increasing magnetic field in semiconductor-superconductor Majorana nanowires is in contrast with the theoretical expectations based on the presence of Majorana zero modes localized at the ends of the system. These observations have been recently theoretically justified by considering a position-dependent spin-orbit coupling that can emerge due to a tunnel gate. Here, we show that the window in parameter space where this phenomenology occurs is vanishingly small when compared to the parameter region where Majorana oscillations should increase in amplitude with the applied magnetic field. Further, including a position-dependent effective potential that is also induced due to a tunnel gate practically removes this small window. Using extensive numerical calculations, we show that, as expected, increasing amplitude oscillations of the hybridization energy represent a generic property of topological Majorana zero modes, while decreasing amplitude oscillations are a generic property of low-energy trivial Andreev bound states, recently called partially separated Andreev bound states. By averaging over several realistic parameter configurations, we identify robust features of the hybridization energy that can be observed in a typical differential conductance experiment without fine-tuning the control parameters.