Domain wall engineering in graphene-based Josephson junctions

Recent progress has enabled the controlled fabrication of domain walls (DWs) in graphene, which host topological kink states. Meanwhile, reliable techniques for constructing graphene-based Josephson junctions have been established. While the experimental prerequisites for combining DWs with Josephson junctions are now available, this direction remains largely unexplored. In this work, we theoretically investigate transport properties in graphene-based Josephson junctions mediated by topological kink states and propose three DW engineering strategies. (i) DW number engineering uncovers a continuous evolution of critical current interference pattern from Aharonov-Bohm oscillation to Fraunhofer diffraction with increasing DW number, reproducing experimental observations [J. Barrier et al., Nature (London) 628, 741 (2024)] and suggesting enhanced sensitivity for magnetometry applications. (ii) DW symmetry engineering demonstrates that an asymmetric configuration of DWs under magnetic field yields an ideal Josephson diode characterized by pronounced nonreciprocal transport. (iii) DW geometry engineering reveals that intersecting DWs enable controllable supercurrent splitting with ratios among leads tunable through the intersection angle, magnetic field, and superconducting phase difference. Our findings elucidate the rich physics of DW-based Josephson junctions and establish a versatile platform for next-generation quantum devices.