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

Abstract

We investigate the Josephson effcet in superconductor-normal-superconductor junction (SNS) base on the doped unbiased silicene under the perpendicular electric field and off-resonance circularly polarized light. The Andreev reflection (including the retroreflection and specular one) during the subgap transport, the free energy, and the reversal of the Josephson effect as well as the emergence of φ 0 -junction are exploited. The Andreev reflection is complete in the NS interface even for the clean interface and without the Fermi wave vector mismatch, which is opposite to the case of ferromagnet-superconductor interface. The important role played by the dynamical polarization of the degrees of freedom to the 0 − π transition and the generation of φ 0 -junction are mentioned in this paper. The scattering by the charged impurity in the substrate affects the transport properties in the bulk as well as the valley relaxation, which can be taken into consider by the macroscopic wave function. In 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 need to be taken into account as long as the spacing model is much larger than the superconducting gap. D − U) 2 / v F with U the electrostatic potential induced by the doping or gate voltage in the superconducting region, which breaks the electron-hole symmetry, and lifts the zero-model (between the lowest conduction band and the highest valence band) above the Fermi level (imaging the zero Dirac-mass here) [1]. The U has been experimentally proved to be valid in controlling the phase shift of the φ 0 -junction as well as the 0 − π transition[2] like the bias voltage. Note that the Dirac-mass here is related to the band gap by ∆ = 2m ησz τz D . Thus we can know that µ s (m ησz τz D − U) 2 and the incident angle is larger than the transmission *

Dynamical polarization and the optical response of silicene and related materials

“…For the low-energy Dirac-Hamilatonian of silicene in tight-binding model, it reads [3,4,5,6,7] H(t) = v F (ητ x P x (t) + τ y P y (t)) + ηλ SOC τ z σ z + aλ R 2 ητ z (P y σ x − P x σ y )…”

Superconductivity in silicon

“…Apart from amorphous silicon, metal-silicon alloys have also been used as a tunnel layer in Josephson junctions owing to their superior reproducibility and efficient processing [75][76][77]. Several recent reports present silicene based Josephson junctions as potential systems for future superconducting devices including quantum technology [78][79][80]. It has been investigated that induced strain is unavoidable in silicene sheet supported by underneath substrate, consequently resulting in the Dirac point shifting along with the deformed Dirac cone [81,82].…”

Electronic transport and dynamical polarization in bilayer silicene-like systems

“…The trigonal warping term breaks the valley symmetry and will leads to the single-Dirac-cone state under the light in a finite intensity which is simialr to the effect of the out-of-plane antiferromagnetic exchange field. The above matrix can also be written as [10,9,4,22,23,13,16,24,20]…”