Role of the Electron–Phonon Interaction in the Superconductivity of the 2-Dimensional Sn/Si(111) Interface

In order to elucidate the mechanism creating superconductivity in the 2-dimensional layer of a p-doped Sn/Si(111) surface, we have analyzed the many-body effects associated with the electron-phonon (e-ph) coupling and the electron–electron interaction. First, we have calculated the DFT surface band of the system and the coupling associated with the different interactions. In our calculations we find a mean field (DFT) electron bandwidth of 0.54 eV, an attractive coupling <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>U</mi><mrow><mi>n</mi><mi>e</mi><mi>g</mi></mrow></msup><mo>=</mo><mn>0.32</mn></mrow></semantics></math></inline-formula> eV associated with the e-ph coupling and an effective electron–electron Hubbard repulsion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mo>=</mo><mn>0.83</mn></mrow></semantics></math></inline-formula> eV. Then, we analyze the Hubbard Hamiltonian, neglecting in this step the e-ph coupling that is much smaller than the Hubbard coupling, by considering a p-doping in this Hamiltonian of 10%; by means of a Dynamical Mean Field (DMF) approach combined with an interpolative calculation for the self-energy, we deduce the local density of states (DOS) and show that the quasi-particle DOS induced by the doping is not large enough to induce magnetism in the Sn-monolayer. This leads us to analyze the possibility of having superconductivity by considering the attractive interaction induced by the e-ph coupling within an appropriate BCS-Hamiltonian. Our calculations show that the quasiparticle metallic system has a superconductivity critical temperature of ≈7–9 K, in good agreement with experiments.