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

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