Unconventional current-phase relation in Josephson junctions of twisted bilayer graphene

We study the current-phase relation in Josephson junctions of twisted bilayer graphene [1-3], computing Green’s functions with a decimation technique based on a real space description [4]. Due to the narrow bands, the critical current near the magic angle is four orders of magnitude higher than in monolayer graphene. We find a highly non-sinusoidal current-phase relation, with two maxima for certain angles, which implies that increasing the current could lead to spontaneous jumps of the phase difference across the junction. There is strong electron-hole asymmetry, which diminishes near the magic angle. We argue that the superconducting gap to bandwidth ratio is the main quantity governing the current-phase relation and the local density of states at the junction.

[1] F. K. de Vries et. al. Nature Nanotechnology pp. 1-4 (2021).

[2] D. Rodan-Legrain et. al., Nature Nanotechnology pp. 1-7 (2021).

[3] J. Diez-Merida, et. al. (2021). arXiv preprint arXiv:2110.01067.

[4] H. Sainz-Cruz, T. Cea, P. A. Pantaleon, and F. Guinea, Phys. Rev. B 104, 075144 (2021).

The authors acknowledge funding from the European Commision Graphene Flagship, Core 3, grant number 881603, and from grants NMAT2D (Comunidad de Madrid, Spain), SprQuMat and SEV-2016-0686, (Ministerio de Ciencia e Innovación, Spain).