Study of the superconducting phase in silicene under biaxial tensile strain

The electron-doped silicene under the influence of the biaxial tensile strain is predicted to be the phonon-mediated superconductor. By using the Eliashberg formalism, we investigate the thermodynamic properties of the superconducting silicene in the case when the tension is $5\%$ and the electron doping equals $3.5\times10^{14}~{\rm cm^{-2}}$. Under such conditions, silicene monolayer is expected to exhibit the highest superconducting transition temperature ($T_C$). In particular, based on the electron-phonon spectral function and assuming wide range of the Coulomb pseudopotential values ($\mu^{\star}\in\left\langle0.1,0.3\right\rangle$) it is stated that the superconducting transition temperature decreases from $18.7$ K to $11.6$ K. Similar behavior is observed in the case of the zeroth temperature superconducting energy gap at the Fermi level: $2\Delta(0)\in\left\langle6.68, 3.88\right\rangle$ meV. Other thermodynamic parameters differ from the predictions of the Bardeen-Cooper-Schrieffer theory. In particular, the ratio of the energy gap to the critical temperature changes in the range from $4.14$ to $3.87$. The ratio of the specific heat jump to the specific heat in the normal state takes the values from $2.19$ to $2.05$, and the ratio of the critical temperature and specific heat in the normal state to the thermodynamic critical field increases from $0.143$ to $0.155$. It is also determined that the maximum value of the electron effective mass equals $2.11$ of the electron band mass.