Electron-phonon coupling and superconductivity in the (4/3)-monolayer of Pb on Si(111): Role of spin-orbit interaction

Abstract

The effect of spin-orbit coupling on the electron-phonon interaction in a (4/3)-monolayer of Pb on Si (111) is investigated within the density-functional theory and linear-response approach in the mixed-basis pseudopotential representation. We show that the spin-orbit interaction produces a large weakening of the electron-phonon coupling strength, which appears to be strongly overestimated in the scalar relativistic calculations. The effect of spin-orbit interaction is largely determined by the induced modification of Pb electronic bands and a stiffening of the low-energy part of phonon spectrum, which favor a weakening of the electron-phonon coupling strength. The state-dependent strength of the electron-phonon interaction in occupied Pb electronic bands varies depending on binding energy rather than electronic momentum. It is markedly larger than the value averaged over electron momentum because substrate electronic bands make a small contribution to the phonon-mediated scattering and agrees well with the experimental data.

Electron–Phonon Interaction in the 4/3-Monolayer of Pb on Si(111): Theory Versus He-Atom Scattering Experiments

“…However, the most important fact is that the L branch of 4/3 ML Pb/Si(111) is clearly observed with HAS, which gives an explicit indication of a relatively strong contribution to the total electron–phonon interaction. The calculated contribution of the longitudinal optical modes to the e–ph (Eliashberg) spectral function can be clearly seen in Figure 3­(d,f) of ref as a doubled peak between 8 and 10 meV and a separate peak at the highest frequency of 12 meV. The contribution of these phonons to the strength of e–ph interaction, defined as the spectral function weighted by 1/ω, where ω is the phonon frequency, is about 20%.…”

“…In Figure , the phonon dispersion curves of the 4/3 ML Pb film on Si(111), calculated including spin–orbit interaction and detailed in ref , are superimposed on the calculated phonon dispersion curves of Si(111) in the ideal 1 × 1 structure (light broken lines) on the same wavevector scale to allow a detailed comparison with the actual HAS experimental data. To obtain a more reliable description of the modes, the substrate thickness was increased up to 60 layers by inserting bulk-like layers with force constants taken from an ab initio calculation of bulk Si.…”

“…The presence of superconductivity in lead nanofilms grown on Si(111) up to a single wetting layer − raises the question of the origin and strength of the electron–phonon (e–ph) interaction. With a decrease in the film thickness, the influence of the substrate and the interface on the interaction of electrons and phonons manifests itself more strongly and extra decay channels toward the substrate can be opened .…”

“…In this paper, the strength of e–ph interaction λ is obtained both for the low-temperature (low- T ) 4/3 ML and high-temperature (high- T ) 1 × 1 phases ,, of Pb on the Si(111) surface using a theoretical analysis of the experimental HAS data obtained during cooling from the annealing temperature of 700–120 K. We show that the DFPT calculation of the dense low-temperature phase, including self-consistently the spin–orbit coupling (SOC), yields both phonon dispersion curves and mass enhancement parameter λ in good agreement with the data measured with HAS for the wetting Pb layer at low temperature. To take into account the influence of the substrate on the electronic and vibrational properties of the wetting layer, the theoretical ab initio study considers a combined film-substrate system which obviously should be important for such small thicknesses.…”

Electron–phonon coupling and superconductivity in a 2D Tl–Pb compound on Si(111)

“…The discovery of superconductivity was followed by a number of theoretical works which focused on the strength of the electron–phonon (e–ph) interaction and the critical temperature of superconductivity in Pb/Si(111) and In/Si(111) systems. 9,14–17…”