Possible pairing symmetries in SrPtAs with a local lack of inversion center

We discuss possible pairing symmetries in the hexagonal pnictide superconductor SrPtAs. The local lack of inversion symmetry of the two distinct conducting layers in the unit cell results in a special spin-orbit coupling with a staggered structure. We classify the pairing symmetry by the global crystal point group $D_{3d}$, and suggest some candidates for the stable state using a tight-binding model with an in-plane, density-density type pairing interaction. We may have some unconventional states such as $s+f$ wave and a mixture of chiral $d$ wave and chiral $p$ wave. The spin-orbit coupling is larger than the interlayer hopping, and the mixing between spin-singlet and spin-triplet states can be seen in spite of the fact that the system has a global inversion center.

Figure 1

Fermi surfaces at (a) $k_z=0$ and (b) $k_z=\pi /c$. Inner blue, middle red, and outer green lines show the Fermi surfaces for band 1, band 2, and band 3, respectively. Note that there are two branches in each band as suggested in Eq. (3), but one of the branches in band 3 does not cross the Fermi level at $k_z=0$.

Figure 2

The phase diagram of the stable pairing states in the coupling constant space $(g_{\mathrm{on}},g_{\mathrm{nn}})$. The tight-binding parameters suggested by LDA calculation (Refs. 9 and 10) is used. The sequences of dots show equal $T_c$ lines at $T_c/t_1^{\left(2\right)}={10}^{-5},{10}^{-4},{10}^{-3}$ from bottom to top.

Figure 3

The phase diagram of the stable paring state in the coupling constant space $(g_{\mathrm{on}},g_{\mathrm{nn}})$ in the DOS enhanced situation, where the Fermi level is located at the vHS point of band 3. The sequences of dots show equal $T_c$ lines at $T_c/t_1^{\left(2\right)}={10}^{-5},{10}^{-4},{10}^{-3}$ from bottom to top.