Multipole Superconductivity in Nonsymmorphic ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

Discoveries of marked similarities to high-$T_{\mathrm{c}}$ cuprate superconductors point to the realization of superconductivity in the doped $J_{\mathrm{eff}}=1/2$ Mott insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. Contrary to the mother compound of cuprate superconductors, several stacking patterns of in-plane canted antiferromagnetic moments have been reported, which are distinguished by the ferromagnetic components as $-++-$, $++++$, and $-+-+$. In this paper, we clarify unconventional features of the superconductivity coexisting with $-++-$ and $-+-+$ structures. Combining the group theoretical analysis and numerical calculations for an effective $J_{\mathrm{eff}}=1/2$ model, we show unusual superconducting gap structures in the $-++-$ state protected by nonsymmorphic magnetic space group symmetry. Furthermore, our calculation shows that the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity is inevitably stabilized in the $-+-+$ state since the odd-parity magnetic $-+-+$ order makes the band structure asymmetric by cooperating with spin-orbit coupling. These unusual superconducting properties are signatures of magnetic multipole order in nonsymmorphic crystal.

Figure 1

Crystal and magnetic symmetries of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ in the 4 ${\mathrm{IrO}}_2$ planes: (a) $z=\frac{1}{8}$, (b) $z=\frac{3}{8}$, (c) $z=\frac{5}{8}$, and (d) $z=\frac{7}{8}$ [16]. The two magnetic patterns of interest, $-++-$ (black arrows) and $-+-+$ (red arrows), are shown. They differ by the ferromagnetic in-plane component along the $b$ axis. Iridium atoms (yellow circles) are labeled as $a_{-},\dots ,d_{-},a_{+},\dots ,d_{+}$.

Figure 2

The contour plot of quasiparticle energy dispersion $E$ in the $s$-wave superconducting state normalized by the order parameter ${\mathrm{\Delta }}_0$ on (a) $k_z=0$, (b) $k_z=\pm \pi /c$, (c) $k_x=0$, and (d) $k_x=\pm \pi /a$. The insets in (a), (b), (c), and (d) show the dispersion $E/{\mathrm{\Delta }}_0$ along the respective blue line. Line nodes (black lines) appear on the ZF, $k_z=\pm \pi /c$ and $k_x=\pm \pi /a$.

Figure 3

The contour plot of quasiparticle energy dispersion $E/{\mathrm{\Delta }}_0$ for the $d_{xy}$-wave order parameter on (a) $k_z=0$, (b) $k_z=\pm \pi /c$, (c) $k_x=0$, and (d) $k_x=\pm \pi /a$. The insets show $E/{\mathrm{\Delta }}_0$ along the respective blue line. Line nodes (black lines) appear on the ZF $k_z=\pm \pi /c$ and the BP $k_x=0$.

Figure 4

The largest eigenvalue ${\chi }_{\max }^{(0)}$ in (a) the normal state ($h=0$), (b) the small moment $-+-+$ state ($h=0.2$), and (c) the large moment $-+-+$ state ($h=0.8$). We fix the temperature $T=0.01\sim T_{\mathrm{c}}$. For $h=0$, 0.2, and 0.8, the $s$-wave on-site interaction $U$ is respectively assumed to be 0.26, 0.47, and 1.45 in the absence of the ASOC, while it is 0.31, 0.55, and 1.60 in the presence of the ASOC.