Spontaneous spin polarization at the edge of the chiral superconducting state in the BHZ metal

The chiral superconducting state with non-zero Chern number support the chiral edge state. The edge state has a degeneracy with respect to spin except for the spinless pairing case. It has been pointed out in the model of the chiral d-wave pairing in honeycomb pnictide superconductor SrPtAs that the degeneracy is lifted due to the spin-orbit coupling and we have the spontaneous magnetization around the sample surface [1]. We would emphasize that that the normal state of SrPtAs shows the spin Hall effect. To investigate the phenomena in a simpler situation, we consider the spin polarization in a model of the chiral p-wave state with Sz=0 in the BHZ [2] metal, which is the doped quantum spin Hall insulator and shows the spin Hall effect.
[1] J. Goryo, Y. Imai, W.B. Rui, A. P. Schnyder, and M. Sigrist, Phys. Rev. B, 96, 140502 (2017). [2] B. A. Bernevig, T. L. Hughes, and S. -C. Zhang, Science, 314, 1757 (2006).
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