Berry phase of non-ideal Dirac fermions in topological insulators

A distinguishing feature of Dirac fermions is the Berry phase of $\pi$ associated with their cyclotron motions. Since this Berry phase can be experimentally assessed by analyzing the Landau-level fan diagram of the Shubnikov-de Haas (SdH) oscillations, such an analysis is widely employed in recent transport studies of topological insulators to elucidate the Dirac nature of the surface states. However, the reported results have usually been unconvincing. Here we show a general scheme for describing the phase factor of the SdH oscillations in realistic surface states of topological insulators, and demonstrate how one could elucidate the Dirac nature in the real experimental data.