Anomalous Quantum Oscillations in Metals and Insulators

Quantum oscillation phenomena describe the periodic variation of thermodynamic and transport properties of materials as a function of magnetic field. Since their discovery in 1930, their observation is commonly assumed to be a definite sign for the presence of a Fermi surface (FS) in a metal. Indeed, the effect forms the basis of a well-established experimental procedure for accurately measuring FS topology and geometry of metallic systems. In this talk I will discuss recent developments which challenge the canonical description of quantum oscillations. I will first review our work on quantum oscillations in insulators. Next, I will discuss the possibility of sharp quantum oscillation frequencies in metals which do not correspond to Fermi surface orbits and the effect of strong electron interactions as weak as well as electron-phonon scattering. Finally, I will present experimental results confirming our theoretical predictions and discuss the broader implications of anomalous quantum oscillations.