# Superconducting Diode Effect in Topological Hybrid Structures

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Nonlinear Usadel Equations

#### 2.2. Linear Usadel Equations

#### Single-Mode Approximation

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SDE | Superconducting diode effect |

SOC | Spin–orbit coupling |

S | Superconductor |

F | Ferromagnetic material |

TI | Topological insulator |

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**Figure 1.**Schematic representation of the superconducting diode, where a two-dimensional (2D) S/F structure is placed on the surface of a three-dimensional (3D) topological insulator.

**Figure 2.**The total supercurrent I as a function of the Cooper pair momentum q calculated self−consistently via linear and nonlinear methods. The parameters of the calculation: ${d}_{s}=1.2\xi ,$ ${d}_{f}=\xi ,\gamma =0.5,\xi h/\alpha =0.3$.

**Figure 3.**The total supercurrent I as a function of the Cooper pair momentum q, calculated self−consistently via linear single-mode approximation and the self-consistent nonlinear method. The amplitude of the single-mode solution $\delta =0.05\pi {T}_{cs}$. The vertical dotted line corresponds to the critical temperature calculated by the single-mode approximation. The parameters of the calculation were: ${d}_{s}=1.2\xi ,{d}_{f}=\xi ,\gamma =0.5,\xi h/\alpha =0.3$.

**Figure 4.**$\Delta I$ as a function of temperature. The parameters of the calculation were: ${d}_{s}=1.2\xi ,$ ${d}_{f}=\xi ,$ $\xi h/\alpha =0.2$.

**Figure 5.**SDE quality factor $\eta $ as a function of exchange field h. The parameters of the calculation were: ${d}_{s}=1.2\xi ,{d}_{f}=\xi ,\gamma =0.5$.

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## Share and Cite

**MDPI and ACS Style**

Karabassov, T.; Amirov, E.S.; Bobkova, I.V.; Golubov, A.A.; Kazakova, E.A.; Vasenko, A.S.
Superconducting Diode Effect in Topological Hybrid Structures. *Condens. Matter* **2023**, *8*, 36.
https://doi.org/10.3390/condmat8020036

**AMA Style**

Karabassov T, Amirov ES, Bobkova IV, Golubov AA, Kazakova EA, Vasenko AS.
Superconducting Diode Effect in Topological Hybrid Structures. *Condensed Matter*. 2023; 8(2):36.
https://doi.org/10.3390/condmat8020036

**Chicago/Turabian Style**

Karabassov, Tairzhan, Emir S. Amirov, Irina V. Bobkova, Alexander A. Golubov, Elena A. Kazakova, and Andrey S. Vasenko.
2023. "Superconducting Diode Effect in Topological Hybrid Structures" *Condensed Matter* 8, no. 2: 36.
https://doi.org/10.3390/condmat8020036