# Fractional Josephson effect in nonuniformly strained graphene

## TL;DR

This paper predicts a fractional Josephson effect in strained graphene with induced superconductivity, where pseudo-Landau level inversion leads to gapless modes and 4π-periodic tunneling, revealing novel topological phenomena.

## Contribution

It introduces a mechanism for realizing the fractional Josephson effect in strained graphene via pseudo-Landau level inversion and gapless mode formation.

## Key findings

- Prediction of 4π-periodic fractional Josephson effect.
- Identification of gapless modes along the junction.
- Demonstration of pseudo-Landau level inversion effects.

## Abstract

Nonuniform strain distributions in a graphene lattice can give rise to uniform pseudomagnetic fields and associated pseudo-Landau levels without breaking time-reversal symmetry. We demonstrate that by inducing superconductivity in a nonuniformly strained graphene sheet, the lowest pseudo-Landau levels split by a pairing gap can be inverted by changing the sign of the pairing potential. As a consequence of this inversion, we predict that a Josephson $\pi$ junction deposited on top of a strained graphene sheet exhibits one-dimensional gapless modes propagating along the junction. These gapless modes mediate single electron tunneling across the junction, giving rise to the $4\pi$-periodic fractional Josephson effect.