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

${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ has been suggested as a Mott insulator from a single $J_{\mathrm{eff}}=1/2$ 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 $J_{\mathrm{eff}}=1/2$ (pseudospin-$1/2$) space, we propose that the low energy electronic structure of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ 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 an external magnetic field (a $g$ tensor with a staggered antisymmetric component). This perspective naturally explains the magnetic properties of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. 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 ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. In particular, we propose that (electron-)doping ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ can potentially realize high-temperature superconductivity.

Figure 1

Schematic picture of one ${\mathrm{IrO}}_2$ layer. Large filled or open circles indicate the Ir atoms on two sublattices. Small open circles are oxygens. Small $x$, $y$ are the global axis, while capital $X$, $Y$ indicate local cubic axis (sublattices dependent).