Josephson tunneling across a planar junction generally depends on the relative twist angle, θ, between the two layers. However, if under a discrete rotation, the order parameter in one layer is odd and the other is even (as, e.g., for a s-wave to \({d}_{{x}^{2}-{y}^{2}}\)-wave junction under a π/2 rotation) then the bulk Josephson current vanishes for all θ. Even in this case, we show that for a finite junction, the Josephson current, J, has a nonzero edge contribution that depends on θ and the orientation of the junction edges in ways that can serve as an unambiguous probe of the order parameter symmetry of any time-reversal preserving system (including multiband systems and those in which spin-orbit coupling is significant). We also analyze the microscopic considerations that determine the magnitude of J.

穿过平面结的 Josephson 隧穿通常取决于两层之间的相对扭曲角 θ。然而，如果在离散旋转下，一层中的阶次参数是奇数，另一层是偶数（例如，在 π/2 旋转下，对于 \（{d}_{{x}^{2}-{y}^{2}}\） 波结的 s 波），那么本体约瑟夫森电流对于所有 θ 都消失了。即使在这种情况下，我们也表明，对于有限结点，约瑟夫森电流 J 具有非零边贡献，该贡献取决于 θ 和结边的方向，其方式可以作为任何时间反转守恒系统（包括多频带系统和自旋轨道耦合很重要的系统）的阶次参数对称性的明确探针。我们还分析了决定 J 大小的微观因素。