Evolution of possible Weyl semimetal states across the Mott transition in pyrochlore iridates induced by hole doping

We study possible Weyl semimetals of strongly correlated electrons by investigating magnetotransport properties in pyrochlore ${R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ ($R$ denotes rare-earth ions), choosing three types of $R$ ions to design the exchange coupling scheme between $R\phantom{\rule{4pt}{0ex}}4f$ and Ir $5d$ moments: nonmagnetic Eu $(4{f}^{6})$, isotropic Gd $(4{f}^{7})$, and anisotropic Tb $(4{f}^{8})$. In the doping-induced semimetallic state, distinctive features of magnetoresistance and the Hall effect are observed in $R=\mathrm{Gd}$ and Tb compounds due to the effects of the exchange-enhanced isotropic and anisotropic Zeeman fields, respectively, exemplifying the double-Weyl semimetal and the two-in two-out line-node semimetal as predicted by theories. In particular, the Hall angle of an $R=\mathrm{Gd}$ compound is strongly enhanced to 1.5% just above the critical doping for the Mott transition. Furthermore, an unconventional Hall contribution is discerned for a lower doping regime of the $R=\mathrm{Gd}$ compound, which can be ascribed to the emergence of Weyl points with the field-distorted all-in all-out order state. These findings indicate that the hole-doping-induced Mott transition as well as the characteristic $f\text{\ensuremath{-}}d$ exchange interaction stabilizes versatile topological semimetal states in a wide range of material parameter space.