  Magnetic oscillations in strongly correlated insulating systems have garnered
interest due to oscillations seemingly originating from the bulk, despite an
anticipated gapped spectrum. We use the large-$N$ mean-field theory to study
the behavior of normal and topological Kondo insulators under a magnetic field.
In both cases spinons acquire a charge and hybridize with electrons, producing
magnetic oscillations that resemble two-band noninteracting systems. We show
that in such band insulators magnetic oscillations are exponentially suppressed
at weak magnetic fields. A self-consistent mean-field calculation for the Kondo
insulators reveals that the temperature dependence of the oscillations departs
from the noninteracting case due to the temperature and magnetic-field
dependence of the hybridization, even though mean-field parameters remain
homogeneous at low fields. Larger magnetic fields result in the Kondo
breakdown, where the magnetic oscillation is solely due to the decoupled
conduction electrons. These findings offer new insights into the magnetic
properties of Kondo insulators, with implications for interpreting experimental
results in heavy fermion materials like SmB$_6$.
