Role of strong spin-orbit coupling in the superconductivity of the hexagonal pnictide SrPtAs

In clean inversion symmetric materials, spin-orbit coupling is not thought to have a pronounced effect on spin-singlet superconductivity. Here we show that, for the recently discovered pnictide superconductor SrPtAs, this is not the case. In particular, for spin-singlet superconductivity in SrPtAs, strong spin-orbit coupling leads to a significant enhancement of both the spin susceptibility and the paramagnetic limiting field with respect to that usually expected for spin-singlet superconductors. The underlying reason for this is that, while SrPtAs has a center of inversion symmetry, it contains weakly coupled As-Pt layers that do not have inversion symmetry. This local inversion-symmetry breaking allows for a form of spin-orbit coupling that dramatically effects superconductivity. These results indicate that caution should be used when interpreting measurements of the spin susceptibility and the paramagnetic limiting field if superconductivity resides in regions of locally broken inversion symmetry.

Figure 1

(a) Structure and (b) Brillouin zone in SrPtAs. Red, blue, and gray spheres denote Pt, As, and Sr atoms, respectively.

Figure 2

Energy bands of SrPtAs (a) without and (b) with SOC. Zero energy represents the Fermi level. Indices $a$, $b$, and $c$ in (a) represent the three bands crossing the Fermi level.

Figure 3

Cross sections of the Fermi surface of SrPtAs with and without SOC. (a) [(b)] is for $k_z=\pi /c$ and no SOC (with SOC), while (c) [(d)] is for $k_z=0$ and no SOC (with SOC). Indices $a$, $b$, and $c$ in (a) represent the three bands crossing the Fermi level.

Figure 4

Spin susceptibility at $T=0$ in the superconducting state normalized with respect to the normal state susceptibility for the three bands crossing the Fermi surface as a function of ${\alpha }^{\nu }/t_c^{\nu }$. The black squares denote approximate values for these three bands. The tight-binding parameters used are ($t_1$, $t_c$, $t_{c2}$, $\mu$): Band $a$ ($1.25,0.1,0.05,0.5$); band $b$ ($1,0.1,0.05,2.5)$; and band $c$ ($-0.48,0.075,-0.03,0.6$).