# Multipole superconductivity in nonsymmorphic Sr$_2$IrO$_4$

## TL;DR

This paper investigates unconventional superconductivity in doped Sr$_2$IrO$_4$, revealing unique gap structures and the stabilization of FFLO states due to nonsymmorphic symmetry and magnetic multipole order.

## Contribution

It demonstrates how nonsymmorphic symmetry and magnetic multipole order lead to novel superconducting gap structures and FFLO states in Sr$_2$IrO$_4$.

## Key findings

- Unusual superconducting gap structures protected by nonsymmorphic symmetry.
- Stabilization of FFLO superconductivity in the $-+-+$ state.
- Signatures of magnetic multipole order in superconducting properties.

## Abstract

Discoveries of marked similarities to high-$T_{\text{c}}$ cuprate superconductors point to the realization of superconductivity in the doped $J_{\text{eff}} = 1 / 2$ Mott insulator Sr$_2$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 $J_{\text{eff}} = 1 / 2$ 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.