Nonreciprocal charge transport, including superconducting diode effect (SDE), has been investigated for the bilayer-structure BST/FST composed of topological insulator BST=(Bi,Sb)₂Te₃ and FST=Fe(Se,Te) superconductor thin films (2-10nm thick) which realizes the two-dimensional superconductivity with the vertical polarity. A conspicuous nonreciprocal charge transport under a transverse small magnetic field, termed electrical magneto-polar anisotropy (eMPA), is observed at temperatures immediately above the BKT transition temperature (~8K) with variations of sign change and magnitude of eMPA. This bilayer structure also shows the SDE characteristic for the 2D superconducting system with broken spatial symmetry.

Such a nonreciprocal charge transport has also been explored in the bulky single crystals of (La, Nd, Sr)₂CuO₄ with the stripe instability that leads to the superconducing transition analogous to the BKT transition. Conspicuous nonreciprocal transport phenomena, not only eMPS but also electrical magneto-chiral anisotropy (eMChA), are observed as a token of broken inversion symmetries in the high-Tc superconducting states with coexisting stripe orders. Possible mechanisms for such a gigantic nonreciprocal effect as observed in high-Tc cuprates are discussed.