Josephson effect for superconductors lacking time-reversal and inversion symmetries

Because of the absence of a center of inversion in some superconducting compounds, a p-wave admixture to the dominant d-wave (or s) order parameter must exist. If time reversal is also violated, an allowed invariant is the product of the d wave (or s wave), p wave, and an appropriately directed current. We show that this leads to a new and remarkable property of the Josephson current for tunneling into a s-wave superconductor along the direction parallel to the axis of the p-wave component. These ideas are applied to the heavy-fermion compounds which lack center of inversion due to crystalline symmetry, as well as time-reversal symmetry, such as CePt(3)Si. They also apply to the superconducting state of the cuprates in the pseudogap region of the phase diagram where in the normal phase some experiments have detected a time-reversal and inversion symmetry broken phase.