Dephasing effect of quantum spin topological states in HgTe/CdTe quantum well

HgTe/CdTe quantum well is a typical two dimensional topological material which supports the helical edge states and quantum spin Hall effect that is imposing in applying of spin electronic devices. The special plateau valued with \begin{document}$0.25\;h/e^{2}$\end{document}of nonlocal resistance in H-shaped four terminal devices can be used as the fingerprint of quantum spin Hall effect. Based on the HgTe/CdTe quantum well, with the aid of nonequilibrium Green's function theory and multi-terminal Landauer-Büttiker formula, we calculate the nonlocal resistance and study the dephasing effect of spin topological states in the presence of exchange field and external magnetic field. It is found the dephasing processes play a role completely different from exchange field and external magnetic field. The latter destroy time reversal symmetry and change the width and relative position of topological gap, but do not influent the topological stability of helical edge states. In the contrary, dephasing processes don't change the width and relative position, however, they broke the topological stability. We consider two kinds of dephasing: normal dephasing and spin dephasing. In the first kind, the carriers lose only the phase memory while maintaining the spin memory. In the second kind, the carriers lose both phase and spin memories. Because of the spin locking properties, normal dephasing almost have no influence on the helical edge states. While the spin dephasing will induce spin flip backscattering and finally destroy helical edge states seriously.