Twisted Hubbard Model for Sr$_2$IrO$_4$: Magnetism and Possible High Temperature Superconductivity

Sr$_2$IrO$_4$ has been suggested as a Mott insulator from a single $J_{eff}=1/2$ band, similar to the cuprates. However this picture is complicated by the measured large magnetic anisotropy and ferromagnetism. Based on a careful mapping to the $J_{eff}=1/2$ (pseudospin-1/2) space, we propose that the low energy electronic structure of Sr$_2$IrO$_4$ can indeed be described by a SU(2) invariant pseudospin-1/2 Hubbard model very similar to that of the cuprates, but with a ``twisted'' coupling to external magnetic field (a g-tensor with a staggered antisymmetric component). This perspective naturally explains the magnetic properties of Sr$_2$IrO$_4$. We also derive several simple facts based on this mapping and the known results about the Hubbard model and the cuprates, which may be tested in future experiments on Sr$_2$IrO$_4$. In particular we propose that (electron-)doping Sr$_2$IrO$_4$ can potentially realize high-temperature superconductivity.