  The anomalous proximity effect in dirty superconducting junctions is one of
most striking phenomena highlighting the profound nature of Majorana bound
states and odd-frequency Cooper pairs in topological superconductors. Motivated
by the recent experimental realization of planar topological Josephson
junctions, we describe the anomalous proximity effect in a
superconductor/semiconductor hybrid, where an additional dirty normal-metal
segment is extended from a topological Josephson junction. The topological
phase transition in the topological Josephson junction is accompanied by a
drastic change in the low-energy transport properties of the attached dirty
normal-metal. The quantization of the zero-bias differential conductance, which
appears only in the topologically nontrivial phase, is caused by the
penetration of the Majorana bound states and odd-frequency Cooper pairs into a
dirty normal-metal segment. As a consequence, we propose a practical experiment
for observing the anomalous proximity effect.
