Quantum Oscillations in the Magnetisation and Density of States of Insulators

The observation of $1/B$-periodic behavior in Kondo insulators SmB$_6$ and YbB$_{12}$ challenges the conventional wisdom that quantum oscillations (QO) necessarily arise from Fermi surfaces in metals. We revisit recently proposed theories for this phenomena, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast with metals where all observables exhibit oscillations at the same frequency. The magnetization oscillations are shown to arise from all occupied Landau levels and exhibit the same frequency as the unhybridized case. The LE-DOS oscillations arise from gap-edge states in a disorder-free system and exhibit a beat pattern between two distinct frequencies at low temperature. Disorder induced in-gap states lead to an additional contribution to the DOS at the unhybridized frequency. The temperature dependence of the magnetization and DOS oscillations are qualitatively different and both show marked deviations from the Lifshitz-Kosevich form. We also compute transport to ensure that we are probing a regime with insulating upturns in the dc resistivity.