Josephson diode effect in junctions of superconductors with band asymmetric metals

At interfaces connecting two superconductors (SCs) separated by a metallic layer, an electric current is induced when there is a disparity in the phases of the two superconductors. We elucidate this phenomenon based on the weights of the Andreev bound states associated with the states carrying currents in forward and reverse directions. Typically, current phase relation (CPR) in Josephson junctions is an odd function. When time reversal and inversion symmetries are broken at the junction, CPR ceases to be an odd function and the system may exhibit Josephson diode effect. This phenomenon has been studied in spin orbit coupled systems under an external Zeeman field wherein the magnetochiral anisotropy is responsible for the Josephson diode effect. Recently introduced the band asymmetric metal (BAM) model presents a novel avenue, featuring an asymmetric band structure. We investigate DC Josephson effect in SC-BAM-SC junctions and find that band asymmetry can lead to Josephson diode effect and anomalous Josephson effect. We explain the mechanism behind these effects based on interference of plane wave modes within the Bogoliubov de-Genne formalism. We calculate diode effect coefficient for different values of the parameters.