Pseudo Klein tunneling induced by zero Chern numbers in multiple-topological barriers silicene junction

We study spin-valley transport property in silicene-based N/TB1/TB2/TB3/N junction where N and TB i(i=1,2,3) are normal regions and topological barriers, respectively. The phase transitions in the TB regions may be controlled by applying perpendicular electric fields, the staggered exchange fields, and the circularly polarized light. When the Fermi level lies inside the gap, the topological phases in the barriers occur and may be classified by spin-valley Chern numbers. We find that the condition to give rise to spin-valley filtering effect satisfies zero values of sum of Chern numbers over all topological barrier regions. Electron with specific spin and valley is allowed to transport when the summation of its spin-valley Chern numbers of all barriers is zero. Despite the system being massive fermions, tunneling without back reflection at zero angle of incidence is found only in the asymmetric junction, predicted at the condition of the zero Chern number. Interestingly, tunneling without back reflection for all angle of incidences, like perfect Klein tunneling, is found in the case of symmetric junction. This anomalous behavior may be called "pseudo Klein tunneling" because it is generated from massive fermions unlike actual Klein tunneling which is generated from massless fermions. The conductance of filtered electron in the symmetric junction cannot be tuned, while in case of asymmetric junction, it is still controllable by external forces. Our investigation reveals the effect of multiple-topological barriers on control of spin-valley filter which may be applicable for spin-valley based electronic devices.