  The observation of quantum oscillations in topological Kondo insulators SmB6
and YbB12 is a recent puzzling experimental discovery. Quantum oscillations
observed in the resistivity and the magnetization are usually explained by the
existence of the Fermi surface. However, Kondo insulators do not have a Fermi
surface and thus should not show quantum oscillations. By performing dynamical
mean-field calculations for topologically nontrivial Kondo insulators in a
magnetic field, we analyze the effect of correlations on the emergence of
quantum oscillations in narrow-gap topological Kondo insulators and demonstrate
that the interplay between correlations and nonlocal hybridization,
ubiquitously occurring in topological Kondo insulators, can lead to observable
quantum oscillations without the necessity of a Fermi surface. Particularly, we
show that correlations make it easier to observe quantum oscillations in the
magnetization and the resistivity of the bulk material. The fundamental
mechanism for these quantum oscillations is a combination of correlation
effects and Landau levels coming very close to the Fermi energy. We furthermore
demonstrate that quantum oscillations in a three-dimensional system can be
understood by analyzing the physics on the two-dimensional planes in the
momentum space for which the hybridization in direction of the magnetic field
vanishes. We believe that this scenario is relevant to understanding the
observation of quantum oscillations in the magnetic torque for SmB6 as well as
oscillations in the resistivity and the magnetic torque of YbB12.
