LAUSR

Significance The Fermi surface, the defining characteristic of metals, leads to oscillatory behavior as a function of the magnetic field in various experiments. It was thus a great surprise when such oscillations were recently seen in insulators without any Fermi surface. Here we develop a general theory of quantum oscillations in insulators. We find 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, we 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.