# BPU11 CONGRESS

August 28, 2022 to September 1, 2022
Serbian Academy of Sciences and Arts – SASA

## Anomalous Josephson effect in $d_{x^2-y^2 }/F/I/F/d_{xy}$ junctions

S06-CMPSP-103
Aug 30, 2022, 2:45 PM
15m
Main Hall (Serbian Academy of Sciences and Arts)

### Main Hall

#### Serbian Academy of Sciences and Arts

Board: S06-CMPSP-103
Oral presentation S06 Condensed Matter Physics and Statistical Physics

### Speaker

Stevan Djurdjević (University of Montenegro, Faculty of Science and Mathematics)

### Description

We study a quasi two-dimensional Josephson junction of d-wave superconductors through two ferromagnetic layers in between. Ferromagnets are separated by isolator barrier. In the frame of Bogoliubov – de Gennes formalism we solve scattering problem to find current-phase relations in the case of $d_{x^2-y^2}$/ferromagnetic barrier/$d_{xy}$-wave superconductor junctions. We find that current-phase relation is anomalous, $I(\varphi=0)≠0$, with $I(\varphi)=-I(-\varphi+\pi)$, and has $2\pi$ periodicity. Also the net Josephson current can be separated in two series which are proportional to $\sin⁡(2n\varphi)$, and $\cos⁡((2n-1)\varphi)$, for $n≥1$. These two components of Josephson current exhibit phase transition from coegsistence of $0$ and $\pi$ states to $\pi/2$ state of junction and vice versa with increasing of ferromagnetic layer thickness but for different values of thicknesses. We observed nonmonotonous temperature dependence of critical current through this junction with finite interface transparency between ferromagnets. This result gave a possibility of junction phase transition with changing a temperature. Influence of $\cos$ part of Josephson current is significant on higher temperatures.

References:
1. Stevan Djurdjević and Zorica Popović, Prog. Theor. Exp. Phys. 2021, 083I02 (2021).
2. B. Lu, K. Yada, A. A. Golubov, and Y. Tanaka, Phys. Rev. B 92, 100503(R) (2015).

### Primary author

Stevan Djurdjević (University of Montenegro, Faculty of Science and Mathematics)

### Co-author

Zorica Popović (University of Belgrade, Faculty of Physics)