  Mesoscopic point contacts between elemental metals and the topological 3D
Dirac semimetal Cd$_3$As$_2$ have been recently shown to be superconducting
with unconventional pairing while Cd$_3$As$_2$ itself does not superconduct.
Here we show that the same superconducting phase at mesoscopic interfaces on
Cd$_3$As$_2$ can be induced with a known conventional superconductor Nb where a
pronounced zero-bias conductance peak is observed which undergoes splitting in
energy under certain conditions. The observations are consistent with the
theory of the emergence of Andreev bound states (ABS) due to the presence of a
pair potential with broken time reversal symmetry. The data also indicate the
possibility of Majorana bound states as expected at the interfaces between
$s$-wave superconductors and topologically non-trivial materials with high
degree of spin-orbit coupling.
