Low-frequency Quantum Oscillations in Bilayers and Quasi-two-dimensional Systems

In a quasi-two-dimensional (Q2D) system, the weak coupling of two dimensional layers produces a Fermi surface with cross-sectional area that modulates along the direction of stacking. In agreement with the predictions of standard Lifshitz-Kosevich theory, quantum oscillation studies on this sort of system see clear oscillations at two frequencies corresponding to the extremal areas of the Fermi surface cross section. However, recent experimental studies have found additional slow oscillations at the frequency corresponding to the difference of these high frequencies, which suggests effects beyond Lifshitz-Kosevich theory. Here we explore the causes of such low frequency oscillations. We first examine a simple bilayer model then extend the analysis to infinite-layer Q2D systems, finding that a sufficient ingredient to produce this phenomenon in both cases is to fix the total particle number in the system rather than the chemical potential, as is standard theoretical practice. We also examine the role of interlayer interactions.