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Quantum oscillations can be used to determine properties of the Fermi surfaceof metals by varying the magnitude and orientation of an external magneticfield. Topological insulator surface states are an unusual mix of normal andDirac fermions. Unlike in graphene and simple metals, Berry's geometric phasein topological insulator surface states is not necessarily quantised. We showthat reliably extracting this geometric phase from the phase offset associatedwith the quantum oscillations is subtle. This is especially so in the presenceof a Dirac gap such as that associated with the Zeeman splitting or interlayertunneling. We develop a semi-classical theory for general mixed normal-Diracsystems in the presence of a gap, and in doing so clarify the role of topologyand broken particle-hole symmetry. We propose a systematic procedure of fittingLandau level index plots at large filling factors to reliably extract the phaseoffset associated with Berry's phase.

Quantum oscillations and Berry's phase in topological insulator surface states with broken particle-hole symmetry