Long-range spin-triplet supercurrents in antiferromagnetic Josephson junctions

We theoretically study the supercurrent in antiferromagnet/superconductor (AF/S) Josephson junctions. The AF can become spin-polarized when the parity-time symmetry is broken. In $\mathrm{S}/{\mathrm{AF}}_{1}/{\mathrm{AF}}_{2}/\mathrm{S}$ junctions, the supercurrent, carried by spin-singlet Cooper pairs, is highly sensitive to the electrostatic potential ${U}_{2}$ in the ${\mathrm{AF}}_{2}$ layer. At high ${U}_{2}$, the supercurrent undergoes a $0\ensuremath{-}\ensuremath{\pi}$ transition, similar to the behavior seen in S/F/S junctions. In contrast, at low ${U}_{2}$, the supercurrent in the thick fully spin-polarized ${\mathrm{AF}}_{2}$ layer vanishes, suggesting that a third AF layer (${\mathrm{AF}}_{3}$) is required to sustain long-range spin-triplet supercurrents. In AF trilayer junctions, the orientations of the N\'eel vectors in the ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{3}$ layers are crucial for determining the supercurrent behavior. Noncollinear configurations of the N\'eel vectors promote the emergence of long-range spin-triplet supercurrents. At low ${U}_{2}$, the current-phase relation (CPR) follows a sinusoidal form, with the $0\ensuremath{-}\ensuremath{\pi}$ transition modulated by the N\'eel vector orientations. Notably, anomalous Josephson current arises when the N\'eel vectors in the ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{3}$ layers lie in the $x\ensuremath{-}y$ plane. At higher ${U}_{2}$, the second harmonic dominates the CPR, leading to a more complex CPR. Furthermore, we propose a simplified physical mechanism to explain the propagation of Cooper pairs, which helps clarify the observed supercurrent behavior.