  Indium antimonide (InSb) nanowires are used as building blocks for quantum
devices because of their unique properties, i.e., strong spin-orbit interaction
and large Land\'e g-factor. Integrating InSb nanowires with other materials
could potentially unfold novel devices with distinctive functionality. A
prominent example is the combination of InSb nanowires with superconductors for
the emerging topological particles research. Here, we combine the II-VI cadmium
telluride (CdTe) with the III-V InSb in the form of core-shell (InSb-CdTe)
nanowires and explore potential applications based on the electronic structure
of the InSb-CdTe interface and the epitaxy of CdTe on the InSb nanowires. We
determine the electronic structure of the InSb-CdTe interface using density
functional theory and extract a type-I band alignment with a small conduction
band offset ($\leq$ 0.3 eV). These results indicate the potential application
of these shells for surface passivation or as tunnel barriers in combination
with superconductors. In terms of the structural quality of these shells, we
demonstrate that the lattice-matched CdTe can be grown epitaxially on the InSb
nanowires without interfacial strain or defects. These epitaxial shells do not
introduce disorder to the InSb nanowires as indicated by the comparable
field-effect mobility we measure for both uncapped and CdTe-capped nanowires.
