Theory of giant diode effect in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave superconductor junctions on the surface of a topological insulator

Abstract

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 $sin\ensuremath{\varphi}$, $cos\ensuremath{\varphi}$, and $sin2\ensuremath{\varphi}$ terms with almost the same order in the Josephson current $I(\ensuremath{\varphi})$ is essential to get larger values of the $Q$ factor given by $Q=({I}_{c}^{+}\ensuremath{-}|{I}_{c}^{\ensuremath{-}}|)/({I}_{c}^{+}+|{I}_{c}^{\ensuremath{-}}|)$ with ${I}_{c}^{+}=\mathrm{max}[I(\ensuremath{\varphi})]$ and the negative one ${I}_{c}^{\ensuremath{-}}$ for the macroscopic phase difference $\ensuremath{\varphi}$ 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 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.

Topics & Concepts