Pressure and magnetic field effects on metal-insulator transitions of bulk and domain wall states in pyrochlore iridates

We have explored the critical metal-insulator phenomena for pyrochlore-type $R_2$Ir$_2$O$_7$, in which electron correlation strength and magnetic configuration are systematically controlled by varying the average rare-earth ionic radius ($R$=Nd$_{1-x}$Pr$_{x}$ and Sm$_{y}$Nd$_{1-y}$), external pressure, and magnetic field. Metal-insulator transitions in bulk are caused by increasing $x$ or tuning external pressure, indicating that the effective electron correlation is responsible for the transition. The metallic state intervenes between the paramagnetic insulating and antiferromagnetically ordered insulating phases for \SNIO ($y$=0.7-0.9), reminiscent of the first-order Mott transition. Furthermore, the metal-to-insulator crossover is observed (around $y$=0.7) for the charge transport on magnetic domain walls in the insulating bulk. An application of magnetic field also drives metal-insulator transitions for \NPIO in which a variety of exotic topological quantum states are potentially realized.