Néel-Vector Control of the Josephson Diode Effect in $\mathcal{PT}$-symmetric Antiferromagnets
The interplay of superconductivity and magnetism gives rise to rich phenomena in Josephson junctions. In this Letter, we study Josephson junctions formed by conventional $s$-wave superconductors and a $\PT$-symmetric collinear antiferromagnet modeled on CuMnAs. Using microscopic modeling and symmetry analysis, we show that these junctions exhibit both the Josephson diode effect and $φ_{0}$-junction states. Remarkably, both effects are controlled by the Néel vector: rotating it by $90^{\circ}$ switches off both, while reversing it switches the diode polarity. To reveal the microscopic mechanism, we develop a channel-resolved scattering theory that accurately captures the anomalous phases and establishes the exact condition for the diode effect. The interplay of the channel current-phase relations yields a sizable diode efficiency, tunable by both the magnitude and direction of the exchange field. Furthermore, a Green-function reduction identifies a single renormalized $\PT$-degenerate band as the transport carrier and precisely reproduces the full current amplitudes. Our work establishes $\PT$-symmetric antiferromagnets as versatile platforms for field-free, highly tunable Josephson diodes and $φ_{0}$ junctions.