  Nonreciprocal responses of noncentrosymmetric quantum materials attract
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 rectification effect is highly desired to
guide the design of 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 $\sin\varphi$, $\cos\varphi$ and $\sin 2\varphi$ terms with almost
the same order in Josephson current $I(\varphi)$ is essential to get larger
values of $Q$ factor given by $Q=(I_{c}^{+} - \mid I_{c}^{-} \mid)/ (I_{c}^{+}
+ \mid I_{c}^{-} \mid)$ with $I_{c}^{+}={\rm max}(I(\varphi))$ and the negative
one $I_{c}^{-}$ for macroscopic phase difference $\varphi$ 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 $I_{c}$'s between the
positive and negative directions can be about factor 2, where the current-phase
relation is modified largely from the conventional one. The relevance of the
zero energy Majorana bound states at the interface is also revealed. This
result can pave a way to realize an efficient superconducting diode with low
energy cost.
