Quantum oscillations with topological phases in the kagome metal CsTi3Bi5

Quantum oscillations provide a valuable tool for probing the Fermi surfaces and their topology in solids, offering critical insights into transport and electronic properties. Notably, Onsager's relation establishes a direct relation between the oscillation frequency and the Fermi surface area. However, estimating the oscillation phase accumulated along quantum orbits in the computation is still challenging due to multiple contributions from the Berry phase, orbital, and spin magnetic moments. Particularly, the wave function's gauge freedom, which allows a unitary rotation among degenerate states, must be carefully treated. In this work, we develop a gauge-independent Wilson loop scheme to evaluate all oscillation phase contributions and apply it to the new kagome metal CsTi3Bi5. We find that the spin-orbit coupling dramatically alters the oscillation phases compared to the spinless case. Additionally, the oscillation phases of representative quantum orbits exhibit a distinct three-dimensional signature despite the cylinderlike Fermi surface geometry. Our work unveils the Fermi surface topology of CsTi3Bi5 and paves the way for theoretical investigations of quantum oscillations in practical materials.