  Recent optical second-harmonic generation experiments observed unexpected
broken spatial symmetries in the undoped spin-orbit Mott insulator
Sr$_2$IrO$_4$, leading to intensive debates on the nature of its ground state.
We propose that it is a canted antiferromagnetism with a hidden order of
circulating staggered pseudospin current. Symmetry analysis shows that a proper
$c$-axis stacking of the canted antiferromagnetism and the pseudospin current
lead to a magnetoelectric coexistence state that breaks the two-fold rotation,
inversion, and time-reversal symmetries, consistent with experimental
observations. We construct a three-dimensional Hubbard model with spin-orbit
coupling for the five localized 5$d$ Wannier orbitals centered at Ir sites, and
demonstrate the microscopic realization of the desired coexistence state in a
wide range of band parameters via a combination of self-consistent Hartree-Fock
and variational calculations.

Strongly Correlated Electrons