Theory of quantum transport in Josephson junctions with a ferromagnetic insulator

We investigate the Josephson transport through ferromagnetic insulators (FIs) by taking into account the band structure of FIs explicitly. Using the recursive Green's function method, we found the formation of a pi-junction in such systems. Moreover the atomic-scale 0-pi oscillation is induced by increasing the thickness of FI and its oscillation period is universal, i.e., just single atomic layer. Based on these results, we show that stable pi-state can be realized in junctions based on high-Tc superconductors with La$_2$BaCuO$_5$ barrier. Such FI-based Josephson junctions may become an element in the architecture of future quantum computers.