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

Nonreciprocal responses of noncentrosymmetric quantum materials attract\nrecent intensive interests, which is essential for the rectification function\nin diodes. A recent breakthrough is the discovery of superconducting diode\neffect. The principle to enlarge rectification effect is highly desired to\nguide the design of superconducting diode. Here, we study theoretically the\nJosephson junction S/FI/S (S: $d$-wave superconductor, FI: ferromagnetic\ninsulator) on the surface of a topological insulator (TI). The simultaneous\nexistence of $\\sin\\varphi$, $\\cos\\varphi$ and $\\sin 2\\varphi$ terms with almost\nthe same order in Josephson current $I(\\varphi)$ is essential to get larger\nvalues of $Q$ factor given by $Q=(I_{c}^{+} - \\mid I_{c}^{-} \\mid)/ (I_{c}^{+}\n+ \\mid I_{c}^{-} \\mid)$ with $I_{c}^{+}={\\rm max}(I(\\varphi))$ and the negative\none $I_{c}^{-}$ for macroscopic phase difference $\\varphi$ of two\nsuperconductors on TI. We find that it can show a very large diode effect by\ntuning the crystal axes of $d$-wave superconductors and the magnetization of\nFI. The difference of the maximum Josephson currents $I_{c}$'s between the\npositive and negative directions can be about factor 2, where the current-phase\nrelation is modified largely from the conventional one. The relevance of the\nzero energy Majorana bound states at the interface is also revealed. This\nresult can pave a way to realize an efficient superconducting diode with low\nenergy cost.\n