  In this work we investigate novel spherical core-shell nanoparticles with
band inversion. The core and the embedding medium are normal semiconductors
while the shell material is assumed to be a topological insulator. The envelope
functions are found to satisfy a Dirac-like equation that can be solved in a
closed form. The core-shell nanoparticle supports midgap bound states located
at both interfaces due to band inversion. These states are robust since they
are topologically protected. The energy spectrum presents mirror symmetry due
to the chiral symmetry of the Dirac-like Hamiltonian. As a major result, we
show that the thickness of the shell acts as an additional parameter for the
fine tuning of the energy levels, which paves the way for electronics and
optoelectronics applications.
