  We demonstrate that partially overlapping Majorana bound states (MBSs)
represent a generic low-energy feature that emerges in non-homogeneous
semiconductor nanowires coupled to superconductors in the presence of a Zeeman
field. The emergence of these low-energy modes is not correlated with any
topological quantum phase transition that the system may undergo as the Zeeman
field and other control parameters are varied. Increasing the characteristic
length scale of the variations in the potential leads to a continuous evolution
from strongly overlapping MBSs, which can be viewed as "regular" Andreev bound
states (ABSs) that cross zero energy, to well separated weakly overlapping
MBSs, which have nearly zero energy in a significant range of parameters and
generate signatures similar to the non-degenerate zero-energy Majorana zero
modes (MZMs) that emerge in the topological superconducting phase. We show that
using charge (or spin) transport measurements it is virtually impossible to
distinguish MZMs from weakly overlapping MBSs emerging in the
topologically-trivial regime.
