Quantum oscillations in strong magnetic fields, berry phase, and superconductivity in three-dimensional topological Bi2–x Cu x Se3 insulators

Two-dimensional (2D) Shubnikov–de Haas oscillations and 2D Hall oscillations are observed in 3D copper-doped Bi2Se3 single crystals in magnetic fields up to 19.5 T at temperatures down to 0.3 K. Three samples with a high bulk carrier concentration (n ≈ 1019–1020 cm–3) are studied. The rotation of the samples in a magnetic field shows that these oscillations are related to numerous parallel 2D conducting channels 1–5 nm thick. Their basic kinetic parameters are found. Quantized Hall resistance Rxy is detected in 1-nm-thick 2D conducting channels at high fields. The distance Δ(1/Rxy) between the steps in the field dependence of 1/Rxy is found to be constant for different Landau levels, 1.3e2/h per 1-nm-thick layer. The constructed fan diagrams of 2D Landau levels for various angles of sample inclination with respect to the magnetic field direction allowed us to conclude that the Berry phase in the 2D conducting channels is γ ≈ π and independent of the magnetic field direction. When studying the angular dependence of upper resistive critical magnetic field Hc2 in one of the superconducting samples, we showed that it can be considered as a bulk superconductor consisting of superconducting layers with an effective thickness of about 50 nm.