Modification of the Lifshitz-Kosevich formula for anomalous quantum oscillations in inverted insulators

It is generally believed that quantum oscillations are a hallmark of a Fermi surface and the oscillations constitute the ringing of it. Recently, it was understood that in order to have well defined quantum oscillations you do not only not need well defined quasiparticles, but also the presence of a Fermi surface is unnecessary. In this paper we investigate such a situation for an inverted insulator from a analytical point of view. Even in the insulating phase clear signatures of quantum oscillations are observable and we give a fully analytical formula for the strongly modified Lifshitz-Kosevich amplitude which applies in the clean as well as the disordered case at finite temperatures.