Anomalous Josephson effect in d-wave superconductor junctions on TI surface

TL;DR

This paper investigates the Josephson effect in d-wave superconductor junctions on topological insulator surfaces, revealing anomalous current-phase relations and enhanced currents due to zero energy states, with implications for probing pairing symmetries.

Contribution

It demonstrates the existence of anomalous Josephson current-phase relations and enhanced Josephson currents in d-wave superconductor junctions on TI surfaces, including effects of s-wave components.

Findings

Anomalous current-phase relation $I()=-I(-+ p)$ observed.

Josephson current can be proportional to $ ext{cos} $ without magnetization.

Zero energy states enhance the Josephson current.

Abstract

We study Josephson effect of $d$-wave superconductor (DS)/ferromagnet insulator(FI)/DS junctions on a surface of topological insulator (TI). We calculate Josephson current $I\left(\varphi \right) $ for various orientations of the junctions where $\varphi $ is the macroscopic phase difference between two DSs. In certain configurations, we find anomalous current-phase relation $I(\varphi)=-I\left( -\varphi +\pi \right)$ with $2\pi$ periodicity. In the case where the first order Josephson coupling is absent without magnetization in FI, $I(\varphi)$ can be proportional to $\cos \varphi$. The magnitude of the obtained Josephson current is enhanced due to the zero energy states on the edge of DS on TI. Even if we introduce an $s$-wave component of pair potential in DS, we can still expect the anomalous current-phase relation in asymmetric DS junctions with $I\left( \varphi =0\right) \neq 0$. This can be used to probe the induced $d$-wave component of pair potential on TI surface in high-$T_{c}$ cuperate/TI hybrid structures.