Research Paper: Transport Through Potential and Magnetic Barriers on Topological Insulator Surfaces with Hexagonal Warping Effects

The transport properties of the Dirac fermions through the electric and magnetic barriers on the surface of a 3D topological insulator with a hexagonal warping effect have been investigated using the transfer matrix method. It was found that the transmission probability and the electric conductance are strongly modulated by the gate voltage, incident energy, number of barriers, and the exchange field strength. It was remarkable that the Dirac fermion is not perfectly transmitted at the normal incidence, confirming the role of the proximity effect in the suppression of transmission for normal incident electrons. The magnetic field can open up a band gap in the conductance spectrum at the Dirac point, depending on the magnetization orientation. The time-reversal symmetry remains broken as long as the magnetization orientations in modulated regions are not entirely parallel to the surface of a topological insulator. The resonant states and the position of resonant peaks are dependent on the gate voltage and incident energy values. It is shown that the number of tunneling resonances increases with increasing the number of barriers. The hexagonal warping effect can increase electronic transport at high energies. The results found here are consistent with those obtained previously.