  Recent tunneling conductance measurements on semiconductor-superconductor
nanowires find zero-bias peaks to be ubiquitous across wide ranges of chemical
potential and Zeeman energy. Motivated by this, we demonstrate that
topologically-trivial Andreev abound states (ABSs) pinned near zero energy are
produced rather generically in inhomogeneous systems with multi-band occupancy
in the presence of inter-band coupling. We first investigate the inter-band
coupling mechanism responsible for the pinning within a multi-band 1D toy
model, then we confirm the findings using a 3D Schr\"{o}dinger-Poisson approach
that incorporates the geometric and electrostatic details of the actual device.
Our analysis shows that level-repulsion generated by inter-band coupling can
lead to a rather spectacular pinning of the lowest-energy mode near zero energy
in systems (or regions) characterized by very-short length scales
($\sim100~$nm).We show that level repulsion between the lowest energy levels
can mimic the gap opening feature (simultaneous with the emergence of a
near-zero energy mode) predicted to occur in Majorana hybrid systems. We also
demonstrate that nearly-zero bias differential conductance features exhibiting
particle-hole asymmetry are due to the presence of (topologically-trivial) ABSs
pinned near zero-energy by level repulsion, not to Majorana zero modes,
quasi-Majoranas, or any other low-energy mode that involves (partially)
separated Majorana bound states. Our findings demonstrate the importance of
understanding in detail multi-band physics and electrostatic effects in the
context of the ongoing search for Majorana modes in
semiconductor-superconductor heterostructures.
