Theoretical explanation of electric field‐induced superconductive critical temperature shifts in Indium thin films

Herein, ab initio density functional theory computations and the self-consistent solution of one-band s-wave generalized Eliashberg equations with proximity effect are combined to explain 60 years old experimental data on how a static electric field can affect the superconductive critical temperature of indium thin films. Although electronic densities of states, Fermi energy shifts, and Eliashberg spectral functions can be computed ab initio, the only parameter in the theory that cannot be determined a priori is the thickness of the surface layer affected by the electric field. However, it is shown that in the weak electrostatic field limit, Thomas–Fermi approximation is valid and, therefore, no free parameters are left, as this perturbed layer is known to have a thickness of the order of the Thomas– Fermi screening length. Moreover, it is shown that the theoretical model can reproduce experimental data, even when the magnitudes of the induced charge densities are so small to be usually neglected.