Transport properties of Cu-doped bismuth selenide single crystals at high magnetic fields up to 60 Tesla: Shubnikov-de Haas oscillations and π-Berry phase

We report Shubnikov-de Haas (SdH) and Hall oscillations in Cu-doped high quality bismuth selenide single crystals. To increase the accuracy of Berry phase determination by means of the of the SdH oscillations phase analysis we present a study of n-type samples with bulk carrier density n∼1019−1020cm−3 at high magnetic field up to 60 Tesla. In particular, Landau level fan diagram starting from the value of the Landau index N=4 was plotted. Thus, from our data we found π-Berry phase that directly indicates the Dirac nature of the carriers in three-dimensional topological insulator (3D TI) based on Cu-doped bismuth selenide. We argued that in our samples the magnetotransport is determined by a general group of carriers that exhibit quasi-two-dimensional (2D) behaviour and are characterized by topological π-Berry phase. Along with the main contribution to the conductivity the presence of a small group of bulk carriers was registered. For 3D-pocket Berry phase was identified as zero, which is a characteristic of trivial metallic states.