We address velocity-modulation control of electron wave propagation in a normal/ferromagnetic/normal silicene junc- tion with local variation of Fermi velocity, where the properties of charge, valley, and spin transport through the junction are investigated. By matching the wavefunctions at the normal-ferromagnetic interfaces, it is demonstrated that the variation of Fermi velocity in a small range can largely enhance the total conductance while keeping the current nearly fully valley- and spin-polarized. Further, the variation of Fermi velocity in ferromagnetic silicene has significant influence on the valley and spin polarization, especially in the low-energy regime. It may drastically reduce the high polarizations, which can be realized by adjusting the local application of a gate voltage and exchange field on the junction.
We study the electronic structure and spin polarization of the surface states of a three-dimensional topological insulator thin film modulated by an electrical potential well. By routinely solving the low-energy surface Dirac equation for the system, we demonstrate that confined surface states exist, in which the electron density is almost localized inside the well and exponentially decayed outside in real space, and that their subband dispersions are quasilinear with respect to the propagating wavevector. Interestingly, the top and bottom surface confined states with the same density distribution have opposite spin polarizations due to the hybridization between the two surfaces. Along with the mathematical analysis, we provide an intuitive, topological understanding of the effect.
We study the local density of states （LDOS） for electrons scattering off the line edge of an atomic step defect on the surface of a three-dimensional （3D） topological insulator （TI） and the line edge of a finite 3D TI, where the front surface and side surface meet with different Fermi velocities, respectively. By using a S-function potential to model the edges, we find that the bound states existed along the step line edge significantly contribute to the LDOS near the edge, but do not modify the exponential behavior away from it. In addition, the power-law decaying behavior for LDOS oscillation away from the step is understood from the spin rotation for surface states scattering off the step defect with magnitude depending on the strength of the potential. Furthermore, the electron refraction and total reflection analogous to optics occurred at the line edge where two surfaces meet with different Fermi velocities, which leads to the LDOS decaying behavior in the greater Fermi velocity side similar to that for a step line edge. However, in the smaller velocity side the LDOS shows a different decaying behavior as x-1/2, and the wavevector of LDOS oscillation is no longer equal to the diameter of the constant energy contour of surface band, but is sensitively dependent on the ratio of the two Fermi velocities. These effects may be verified by STM measurement with high precision.
