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

TL;DR

This paper theoretically investigates the superconducting diode effect in a Josephson junction on a topological insulator surface, revealing how tuning crystal axes and magnetization enhances diode efficiency and relates to Majorana states.

Contribution

It introduces a theoretical model showing how simultaneous sine and cosine terms in Josephson current lead to a large diode effect in d-wave superconductor junctions on topological insulators.

Findings

Large diode effect with a factor of 2 difference in critical currents.

Tuning crystal axes and magnetization enhances diode efficiency.

Relation between zero energy Majorana states and diode effect.

Abstract

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.