Berry phase in quantum oscillations of topological materials

Quantum oscillation is an important phenomenon in low temperature transport studies of topological materials. In three-dimensional topological insulators, Dirac semimetals, Weyl semimetals, and other topological nontrivial materials, the topologically nontrivial band structure will add a phase correction to the quantum oscillation patterns, which is known as the nontrivial Berry phase. Berry phase analysis via quantum oscillation is a powerful method to investigate the nontrivial band topology of topological materials. In this review, we introduce the concepts of the Berry phase and quantum oscillations, and provide some classification of topological materials. We then employ some important studies on each type of topological material to discuss the nontrivial Berry phase. We conclude by pointing out the importance of quantum transport studies on topological materials, as well as drawing attention to the exploration of the nontrivial Berry phase in a new material system that could shed more light on the topology-based electronics.