The three-dimensional (3D) topological insulator (TI) p-n junction under magnetic fields presents an interesting transport property which is investigated both theoretically and numerically in this paper. Transport in this device can be tuned by the axial magnetic field. Specifically, the scattering coefficients between incoming and outgoing modes oscillate with axial magnetic flux at the harmonic form. In the condition of horizontal mirror symmetry, the initial phase of the harmonic oscillation is dependent on the parities of incoming and outgoing modes. This symmetry is broken when a vertical bias is applied which leads to a kinetic phase shift added to the initial phase. On the other hand, the amplitude of oscillation is suppressed by the surface disorder while it has no influence on the phase of oscillation. Furthermore, with the help of the vertical bias, a special $(1,-2)$ 3D TI p-n junction can be achieved, leading to an unusual spin precession phenomenon.

• Received 29 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.085422