  Mesoscopic superconducting islands hosting Majorana zero modes (MZMs), or
Majorana islands in short, offer a prototype of topological qubits. In this
work we investigate theoretically the model of a generic Majorana island
tunneling-coupled to a single-piece metallic substrate, hence an
\textit{embedded Majorana island}. We show the crucial consequences of an
interplay between the topological ground states nonlocally addressed by the
MZMs and the metallic bath with coherent electron propagation: on the one hand,
the topological degeneracy on the Majorana island can be preserved, by virtue
of the particle-hole symmetry, despite the apparent bath-induced coupling
between MZMs; on the other hand, the electronic interference in the metallic
bath may lead to profound alterations to the renormalization group behavior of
the hybrid system towards low energy/temperature compared with conventional
Kondo physics. This work serves to establish the model of embedded Majorana
islands as an experimentally relevant and theoretically intriguing problem
particularly in the direction of topological quantum computation.
