Ferromagnetic-insulators-modulated transport properties on the surface of a topological insulator

Transport properties on the surface of a topological insulator (TI) under the modulation of a two- dimensional (2D) ferromagnet/ ferromagnet junction are investigated by the method of wave function matching. The single ferromagnetic barrier modulated transmission probability is expected to be a periodic function of the polarization angle and the planar rotation angle, that decreases with the strength of the magnetic proximity exchange increasing. However, the transmission probability for the double ferromagnetic insulators modulated n- n junction and n- p junction is not a periodic function of polarization angle nor planar rotation angle, owing to the combined effects of the double ferromagnetic insulators and the barrier potential. Since the energy gap between the conduction band and the valence band is narrowed and widened respectively in ranges of 0 < theta < pi/2 and pi/2 < theta < pi, the transmission probability of the n-n junction first increases rapidly and then decreases slowly with the increase of the magnetic proximity exchange strength. While the transmission probability for the n- p junction demonstrates an opposite trend on the strength of the magnetic proximity exchange because the band gaps contrarily vary. The obtained results may lead to the possible realization of a magnetic/ electric switch based on TIs and be useful in further understanding the surface states of TIs.