Topological insulator: a new quantized spin Hall resistance robust to dephasing.

The dephasing effect on the quantum spin Hall effect (QSHE) is studied. Without dephasing, the longitudinal resistance in a QSHE system exhibits the quantum plateaus. We find that these quantum plateaus are robust against the normal dephasing but fragile with the spin dephasing. Thus, these quantum plateaus survive only in mesoscopic samples. Moreover, the longitudinal resistance increases linearly with the sample length but is insensitive to the sample width. These characters are in excellent agreement with the recent experimental results [Science 318, 766 (2007)10.1126/science.1148047]. In addition, we define a new spin Hall resistance that also exhibits quantum plateaus. In particular, these plateaus are robust against any type of dephasing and therefore, survive in macroscopic samples and better reflect the topological nature of QSHE.