  Trivial Andreev bound states arising from chemical potential variations could
lead to zero-bias tunneling conductance peaks at finite magnetic fields in
class $D$ nanowires, precisely mimicking the predicted zero-bias conductance
peaks arising from the topological Majorana bound states. This finding raises a
serious question on the efficacy of using zero-bias tunneling conductance
peaks, by themselves, as evidence supporting the existence of topological
Majorana bound states in nanowires. In the current work, we provide specific
experimental protocols for tunneling spectroscopy measure- ments to distinguish
between Andreev and Majorana bound states without invoking more demand- ing
nonlocal measurements which have not yet been successfully performed in
nanowire systems. In particular, we discuss three distinct experimental schemes
involving response of the zero-bias peak to local perturbations of the tunnel
barrier, overlap of bound states from the wire ends, and most compellingly,
introducing a sharp localized potential in the wire itself to perturb the
zero-bias tun- neling peaks. We provide extensive numerical simulations
clarifying and supporting our theoretical predictions.
