A Field Guide to non-Onsager Quantum Oscillations in Metals

Quantum oscillation (QO) measurements constitute a powerful method to measure the Fermi surface (FS) properties of metals. The observation of QOs at specific frequencies is usually taken as strong evidence for the existence of extremal cross-sectional areas of the FS that directly correspond to the measured frequency value according to the famous Onsager relation. Here, we review mechanisms that generate QO frequencies that defy the Onsager relation and discuss material candidates. These include magnetic breakdown, magnetic interaction, chemical potential oscillations, and Stark quantum interference, most of which lead to signals occurring at combinations of "parent" Onsager frequencies. A special emphasis is put on the recently discovered mechanism of quasi-particle lifetime oscillations (QPLOs). We aim to provide a field guide that allows, on the one hand, to distinguish such non-Onsager QOs from conventional QOs arising from extremal cross sections and, on the other hand, to distinguish the various non-Onsager mechanisms from each other. We give a practical classification of non-Onsager QOs in terms of the prerequisites for their occurrence and their characteristics. We show that, in particular, the recently discovered QPLOs may pose significant challenges for the interpretation of QO spectra, as they may occur quite generically as frequency differences in multi-orbit systems, without the necessity of visible "parent" frequencies in the spectrum, owing to a strongly suppressed temperature dephasing of QPLOs. We present an extensive list of material candidates where QPLOs may represent an alternative explanation for the observation of unexpected QO frequencies.