Quantum oscillations (QOs) describe the periodic variation of physical observables as a function of inverse magnetic field in metals. The Onsager relation connects the basic QO frequencies with the extremal areas of closed Fermi surface pockets, and the theory of magnetic breakdown explains the observation of sums of QO frequencies at high magnetic fields. Here we develop a quantitative theory of difference-frequency QOs in two- and three-dimensional metals with multiple Fermi pockets with parabolic or linearly dispersing excitations. We show that a nonlinear interband coupling, e.g., in the form of interband impurity scattering, can give rise to otherwise forbidden QO frequencies which can persist to much higher temperatures compared to the basis frequencies. We discuss the experimental implications of our findings for various material candidates, for example multifold fermion systems, like CoSi, and the relation to magneto-intersubband oscillations known for coupled two-dimensional electron gases.

• Received 15 March 2022
• Revised 19 June 2023
• Accepted 25 July 2023

DOI:https://doi.org/10.1103/PhysRevB.108.054202