Josephson junction of minimally twisted bilayer graphene

TL;DR

This paper theoretically explores the transport properties of Josephson junctions made from minimally twisted bilayer graphene, revealing distinct modes with unique Josephson effects influenced by electric fields and edge states.

Contribution

It introduces a theoretical model for Josephson junctions in minimally twisted bilayer graphene, highlighting the emergence of zig-zag and pseudo-Landau level modes with novel transport phenomena.

Findings

Zig-zag modes show linear dispersion of Andreev bound states and $4\\pi$-periodic Josephson current.

Pseudo-Landau level modes have flat Andreev bound states and no bulk Josephson current.

Edge states can induce $4\\pi$-periodic Josephson response even in pseudo-Landau level regime.

Abstract

We theoretically investigate the transport properties of Josephson junctions composed of superconductor/minimally twisted bilayer graphene/superconductor structures. In the presence of an out-of-plane electric field, the low energy physics is best described by a network of chiral domain-wall states. Depending on system parameters, they lead to the emergence of zig-zag or pseudo-Landau level modes with distinct transport characteristics. Specifically, we find zig-zag modes feature linear dispersion of Andreev bound states, resulting in a $4\pi$-periodic Josephson current. In contrast, pseudo-Landau level modes exhibit flat Andreev bound states and, consequently, a vanishing bulk Josephson current. Interestingly, edge states can give rise to $4\pi$-periodic Josephson response in the pseudo-Landau level regime. We also discuss experimental signatures of such responses.