Theory of giant diode effect in d-wave superconductor junctions on the surface of a topological insulator

Nonreciprocal responses of noncentrosymmetric quantum materials attracted recent intensive interests, which is essential for the rectification function in diodes. A recent breakthrough is the discovery of superconducting diode effect. The principle to enlarge the rectification effect is highly desired to guide the design of the superconducting diode. Here, we study theoretically the Josephson junction S/FI/S (S: d-wave superconductor, FI: ferromagnetic insulator) on the surface of a topological insulator (TI). The simultaneous existence of sin phi, cos phi, and sin 2 phi terms with almost the same order in the Josephson current I(phi) is essential to get larger values of the Q factor given by Q = (Ic+ - |Ic- |)/(Ic+ + |Ic-|) with Ic+ = max[I(phi )] and the negative one Ic- for the macroscopic phase difference phi of two superconductors on TI. We find that it can show a very large diode effect by tuning the crystal axes of d-wave superconductors and the magnetization of FI. The difference of the maximum Josephson currents Ic's between the positive and negative directions can be about a factor of 2, where the current-phase relation is modified largely from the conventional one. The relevance of the zero-energy Andreev bound states as Majorana bound states at the interface is also revealed. This result can pave the way to realize an efficient superconducting diode with low-energy cost.