We show that a planar Josephson junction having $d$-wave superconducting regions, with a skyrmion crystal placed underneath, produces a robust gate-tunable superconducting diode effect. The spatially varying exchange field of the skyrmion crystal breaks both inversion and time-reversal symmetries, leading to an asymmetric current-phase relation with an anomalous phase shift. Our theoretical calculations, obtained using resistively and capacitively shunted junction model combined with the Bogoliubov–de Gennes method, reveal that the diode efficiency is largely tunable by controlling external gate voltage and skyrmion radius. Incorporation of a $d$-wave superconductor such as a high-$T_c$ cuprate enables the diode to function at higher operating temperatures. Planar Josephson junctions coupled with higher-order skyrmion crystals also generate a finite diode efficiency. Our results establish a unique and practically realizable mechanism for devising tunable superconducting diodes that operate without an external magnetic field, based on magnetic texture-superconductor hybrid platforms.

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• Josephson effect
• Superconductivity
• Josephson junctions
• Bogoliubov-de Gennes equations