Is it possible to determine unambiguously the Berry phase solely from quantum oscillations?

The Berry phase, a fundamental geometric phase in quantum systems, has become a crucial tool for probing the topological properties of materials. Quantum oscillations, such as Shubnikov-de Haas (SdH) oscillations, are widely used to extract this phase, but its unambiguous determination remains challenging. This work highlights the inherent ambiguities in interpreting the oscillation phase solely from SdH data, primarily due to the influence of the spin factor R_S, which depends on the Landé g-factor and effective mass. While the Lifshitz-Kosevich (LK) theory provides a framework for analyzing oscillations, the unknown g-factor introduces significant uncertainty. For instance, a zero oscillation phase could arise either from a nontrivial Berry phase or a negative R_S. We demonstrate that neglecting R_S in modern studies, especially for topological materials with strong spin-orbit coupling, can lead to doubtful conclusions. Through theoretical analysis and numerical examples, we show how the interplay between the Berry phase and Zeeman effect complicates phase determination. Additionally, we also discuss another underappreciated mechanism - the magnetic field dependence of the Fermi level. Our discussion underscores the need for complementary experimental techniques to resolve these ambiguities and calls for further research to refine the interpretation of quantum oscillations in topological systems.