Theory of the persistent superconducting diode effect in twisted high-T_c cuprates

C-axis Josephson junctions fabricated from Bi₂Sr₂CaCu₂O_8+δ flakes twisted near 45° exhibit superconducting diode effect with a well-defined polarity which persists even after the sample has been cycled through the normal phase by raising its temperature or by exceeding its critical current. This observation suggests that time-reversal symmetry in these twisted flakes is broken not only below T_c, as suggested by existing theoretical work which predicts a chiral d+id' phase, but also in the normal state. We present here a symmetry-based phenomenological framework that explains the observed properties of such junctions with a minimal number of assumptions. Our model postulates an extra Ising order parameter that is linearly coupled to the superconducting chirality and remains ordered in the normal state -- thus providing the mechanism for the memory effect that underlies the fixed diode polarity. We show that, remarkably, this coupling is only symmetry-allowed in twisted junctions; at zero twist it vanishes in accord with the large body of experimental data indicating that untwisted optimally doped cuprates are non-magnetic.