Silicene-based π and φ0 Josephson junctions

We investigate the supercurrent in a silicene-based Josephson junction under external-field modulations spatially. Employing the qualitative analysis and solving the Dirac-Bogoliubov-de Gennes equation, it is found that, for the bulk states, a pi junction is generated from the valley polarization by combining an antiferromagnetic exchange magnetization and spin-orbit coupling. In contrast, for the topologically protected edge states, a pi as well as a phi(0) junction can be obtained by adjusting ferromagnetic exchange field or antiferromagnetic exchange magnetization to shift the edge states in wave vector space; or alternatively by modulating electric and light fields to modify the Fermi velocity of the edge states. It is proposed that a direct current superconducting quantum interference devices can be used to observe these pi and phi(0) junctions in experiment.