Field-free Josephson diode and tunable $\phi_0$-junction in chiral kagome antiferromagnets

The recent realization of superconducting proximity effect in chiral antiferromagnets (cAFMs) opens a new route to nonreciprocal superconducting transport of fundamental interest and practical importance. Using microscopic modeling and symmetry analysis, we show that Josephson junctions formed by conventional $s$-wave superconductors (SCs) and cAFMs on the kagome lattice exhibit Josephson diode effects and anomalous phase shifts ($\phi_0$-junction state) when space inversion $\mathcal{I}$, time-reversal $\mathcal{T}$, and combined mirror-time-reversal $\mathcal{TM}_z$ symmetries are simultaneously broken. We propose two setups to realize these phenomena and achieve high diode efficiency. (i) An SC/cAFM/SC junction with spin-orbit coupling, which enables a field-free diode effect with a robust tunable $\phi_0$-junction state. (ii) An SC/cAFM/cAFM$^\prime$/SC junction, where two cAFM layers with different in-plane order orientations, under an out-of-plane Zeeman exchange field, produces significant diode effect and anomalous phase shifts. These results establish a direct link between $\mathcal{TM}_z$ symmetry breaking and nonreciprocal superconductivity, suggesting cAFMs as versatile platforms for symmetry-engineered Josephson diodes and tunable $\phi_0$-junctions.