Quantum ground state control in superconductor-silicene structures: $0$-$\pi$ transitions, $\varphi_0$-junctions, and Majorana bound states

We demonstrate theoretically that proximity-induced superconductivity in silicene offers the possibility to exert strong quantum ground state control. We show that electrically controlled $0$-$\pi$ transitions occur in Josephson junctions in the presence of an exchange field due to the buckling of the silicene lattice. We also discover that zigzag-oriented interfaces, featuring intervalley scattering, cause a $\varphi_0$ state with an applied electric field. Finally, we demonstrate that Majorana bound states along the silicene edge are tunable via the edge orientation, electric, and in-plane spin exchange fields.