# Odd-frequency superconducting pairing in one-dimensional systems

## TL;DR

This review discusses the emergence of odd-frequency superconductivity in one-dimensional systems like nanowires and topological insulators, highlighting its connection to Majorana modes and potential applications.

## Contribution

It provides a comprehensive overview of recent theoretical and experimental progress in understanding odd-frequency pairing in 1D systems and its relation to topological superconductivity.

## Key findings

- Odd-frequency pairing is linked to Majorana zero modes.
- Nanowires with Rashba spin-orbit coupling exhibit odd-frequency correlations.
- Topological insulator edges show unconventional superconducting states.

## Abstract

Odd-frequency superconductivity represents a truly unconventional ordered state which, in contrast to conventional superconductivity, exhibits pair correlations which are odd in relative time and, hence, inherently dynamical. In this review article we provide an overview of recent advances in the study of odd-frequency superconducting correlations in one-dimensional systems. In particular, we focus on recent developments in the study of nanowires with Rashba spin-orbit coupling and metallic edges of two-dimensional topological insulators in proximity to conventional superconductors. These systems have recently elicited a great deal of interest due to their potential for realizing one-dimensional topological superconductivity whose edges can host Majorana zero modes. We also provide a detailed discussion of the intimate relationship between Majorana zero modes and odd-frequency pairing. Throughout this review, we highlight the ways in which odd-frequency pairing provides a deeper understanding of the unconventional superconducting correlations present in each of these intriguing systems and how the study and control of these states holds the potential for future applications.