  The recent experimental observations of decaying energy oscillations in
semiconductor-superconductor Majorana nanowires is in contrast with the typical
expectations based on the presence of Majorana zero modes localized at the ends
of the system, when the amplitude of the hybridization energy oscillations is
predicted to increase with the applied magnetic field. These observations have
been theoretically justified recently by considering a position-dependent,
step-like spin-orbit coupling near end of the nanowire, which could arise due
to the presence of tunnel gates in a standard tunneling conductance experiment.
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 increase in amplitude with the applied field. Further,
including a position-dependent effective potential, which is also induced
naturally near the end of the wire by, e.g., tunnel gates, practically removes
the small window associated with decaying oscillations. 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 that typically
emerge in non-homogeneous systems. 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.
