Recently, gate-defined Josephson junctions in magic angle twisted bilayer graphene (MATBG) were studied experimentally and highly unconventional Fraunhofer patterns were observed. In this work, we show that an interaction-driven valley-polarized state connecting two superconducting regions of MATBG would give rise to a long-sought-after purely electric controlled φ0-junction in which the two superconductors acquire a finite phase difference φ0 in the ground state. We point out that the emergence of the φ0-junction stems from the valley-polarized state which breaks time-reversal symmetry and trigonal warping effects which break the intravalley inversion symmetry. Importantly, a spatially non-uniform valley polarization order parameter at the junction can explain the highly unconventional Fraunhofer patterns observed in the experiment. Our work explores the novel transport properties of the valley-polarized state and suggests that gate-defined MATBG Josephson junctions could realize the first purely electric controlled φ0-junctions with applications in superconducting devices.
@article{arxiv.2202.05663,
title = {$\varphi_0$-Josephson junction in twisted bilayer graphene induced by a valley-polarized state},
author = {Ying-Ming Xie and Dmitri K. Efetov and K. T. Law},
journal= {arXiv preprint arXiv:2202.05663},
year = {2023}
}