Electric Field and Light Field Modulated Josephson Effect in Silicene-Based SNS Josephson Junction: Andreev Reflection and Free Energy

We investigate the Josephson effect in superconductor-normal-superconductor junction (SNS) base on an unbiased silicene under the perpendicular electric field and off-resonance circularly polarized light both analytically and numerically. The Andreev reflection (during the subgap transport), free energy, Josephson current, and the reversal of the Josephson effect are explored. The Andreev reflection is complete (for tunnel limit) in the NS interface even for the clean sample and without the Fermi wave vector mismatch, which is opposite to the case of ferromagnet-superconductor interface. The dynamical polarization of the related degrees of freedom is also related to the 0 − π transition and the generation of ϕ0-junction. In the short junction limit, the approximated results about the Andreev level and free energy are also discussed. Beside the low-energy limit of the tight-binding model, the finite-size effect is needed to be taken into account. The effect of the time-dependent drive and the Green’s function method also represented in the end of this paper.