Quantum oscillations in the magnetization and density of states of insulators

The Fermi surface, the defining characteristic of metals, leads to oscillatory behavior of various observables as a function of the inverse of magnetic field. It was thus a great surprise when such oscillations were seen in insulators without any Fermi surface, like in Kondo insulators and semiconductor quantum wells. I will discuss a general theory [1] of quantum oscillations in insulators, focusing on a minimal model of an insulator with a hybridization gap. I will show that, in striking contrast to metals, the oscillation frequency for magnetization differs from observables like the resistivity, which depend on the low-energy density of states of electronic excitations. To complement our detailed analysis of their frequency, phase, and temperature-dependent amplitude, I will present a simple physical picture for understanding why quantum oscillations occur in insulators and why they differ in significant ways from the well-understood metallic case.

[1] A. Panda, S. Banerjee, M. Randeria. PNAS, 119, e2208373119 (2022).