<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>φ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>-Josephson junction in twisted bilayer graphene induced by a valley-polarized state
Ying-Ming Xie, Dmitri K. Efetov, K. T. Law
Abstract
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 ${\ensuremath{\varphi}}_{0}$-junction in which the two superconductors acquire a finite phase difference ${\ensuremath{\varphi}}_{0}$ in the ground state. We point out that the emergence of the ${\ensuremath{\varphi}}_{0}$-junction stems from the valley-polarized state which breaks time-reversal symmetry, and trigonal warping effects which break intravalley inversion symmetry. Importantly, a spatially nonuniform valley-polarization order parameter at the junction can explain the key features of the observed unconventional Fraunhofer patterns. Our work explores the novel transport properties of the valley-polarized state, and we suggest that gate-defined MATBG Josephson junctions could realize the first purely electric controlled ${\ensuremath{\varphi}}_{0}$-junctions.