Transport properties of defect-controlled Bi₂Te₃ single crystals: fingerprint of surface Dirac electrons

We show that in three-dimensional (3D) topological insulator Bi₂Te₃, the surface nature is revealed as a quantization of motion in Dirac fermions due to their confinement at the surface. The consequence of this z-quantization is the oscillation in magnetoresistance (MR) with periodicity proportional to the magnetic field. We demonstrate that based on single Dirac theory at the surface, where disorder is properly taken into account, the thickness of the surface state or a fundamental length scale of topologically nontrivial state is extracted from the oscillating part of MR data. The same theoretical framework also explains the nonoscillating part of MR and Hall resistance at the low field region, showing that topological contribution is important.