Spatial modulation of the order parameter for the ground state of superconductors in polar systems

Based on the experimental observation that the recently discovered T* phases in ceramic superconductors are polar, this paper shows that polarity implies that the ground state has a spatial modulation of the phase of the order parameter, provided this polar direction also breaks time reversal symmetry. This gives rise to experimentally testable predictions for the T* phase including an oscillatory dependence of the thickness of the insulating layer for the AC and DC Josephson effect in contrast to the monotonic dependence for classical superconductors