Quantum Oscillations in the Magnetization and Density of States of Insulators

The observation of quantum oscillations in Kondo insulators SmB₆ and YbB₁₂ challenge the conventional wisdom that these must arise from Fermi surfaces in metals. We revisit recently proposed theories, focusing on a minimal model with two opposite-parity hybridized bands, one light mass and one heavy mass in an inverted band structure, along with disorder induced in-gap states. We present a detailed comparison of the frequency, phase and amplitude of the 1/B-periodic oscillations in the magnetization (dHvA) and the low energy density of states (LEDOS, a proxy for SdH). While the LEDOS probes thermal excitations near the chemical potential, the magnetization takes into account all occupied Landau levels. We find that at the lowest non-zero temperature the two observables have distinctly different frequencies, but above a certain crossover both oscillations have the same frequency as the unhybridized case. The temperature dependence of the amplitudes in the two observables are qualitatively different with none having a Lifshitz-Kosevich form. Our conclusions are based on a combination of numerical calculations and analytical results based on the semiclassical approximation. We also compute transport to ensure that we are in a regime with insulating upturns in the dc resistivity.