Theory of quantum spin Hall effect detection by measurements of the polarization resistance

The detection of quantum spin Hall effect (QSHE) is investigated by using ferromagnetic leads as probes. A polarization resistance is introduced and it is defined as a voltage over a current, thus, can be measured with high precision like the usual resistance. The polarization resistance exhibits the quantum plateau with the plateau value h/2e(2). In particular, this quantized plateau is found to be robust against both spin- and normal-dephasing effects. Furthermore, such a robust feature of the plateau is insensitive to all experimental probing conditions and fluctuations, including type of probes, coupling strength, probing position, coupling means, fluctuation of magnetic flux. Therefore, the polarization resistance R-p can well reflect the topological nature of QSHE and it provides a direct and quantitative way to detect QSHE with high precision in an experiment.