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.
Highlights
Ultrathin metallic films grown on semiconductor substrates have attracted much attention due to their two-dimensional (2D) physical properties [1,2,3,4]
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
As for the strength of e-ph interaction averaged over electron momentum, it was mainly studied at the Fermi level (EF) of freestanding Pb(111) films using both scalar relativistic [9,19,21] and including spin-orbit coupling (SOC) calculations [22]
Summary
Ultrathin metallic films grown on semiconductor substrates have attracted much attention due to their two-dimensional (2D) physical properties [1,2,3,4]. We intend to show that SOC is very important for an accurate quantitative description of the e-ph interaction in Si-supported Pb films too and the perfect coincidence between the theoretical and experimental values of Tc looks accidental because of the overestimation of the e-ph coupling strength in the scalar relativistic calculations [20,21]. Another question is whether the positions of EF in the experiment [3] and in the calculations coincide with respect to the substrate valence band edge because the critical temperature, Tc is measured (and calculated) at the Fermi level. We analyze the state-dependent strength of electron-phonon interaction in occupied Pb electronic bands
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