Quantum oscillations in small-gap insulators

In recent years it has become understood that quantum oscillations of the magnetization as a function of magnetic field, long recognized as a phenomenon intrinsic to metals, can also manifest in insulating systems. Theory has shown that in certain narrow-gap band insulators, quantum oscillations can appear with a frequency set by the area traced out by the minimum gap in momentum space. I shall provide an overview of the theories of quantum oscillations in simple band insulators of this type, and discuss the relevance of these theories to experimental measurements on novel materials. In particular, I shall focus on situations where the insulating gap is generated by electron-electron interactions.