Topological phases in R2Ir2O7

We construct and analyze a theoretical model for the pyrochlore iridates R$_2$Ir$_2$O$_7$ with R (= Pr, Nd, Sm, Gd, Tb, Dy, Ho, Yb) magnetic. The electrons on trivalent rare earth ions R$^{3+}$ form local Ising doublets due to the local crystal field. Based on a space group symmetry analysis, we write down the generic Kondo coupling between the Ising spin at R sites and the effective spin at Ir sites. Besides this interaction, we also include direct electron tunneling between Ir sites and indirect electron tunneling via intermediate oxygens for Ir-Ir coupling. This simple minimal model gives a rich phase diagram with broad regions of topological semi-metal and axion insulator phases. Based on these findings, we propose R$_2$Ir$_2$O$_7$ to be one of the most promising candidates to realize the topological semi-metal and axion insulator phases. Implications for existing and future experiments are discussed.