The electron-phonon coupling strength at metal surfaces directly determined from the Helium atom scattering Debye-Waller factor

TL;DR

This paper presents a quantum-theoretical method to determine the electron-phonon coupling strength at metal surfaces directly from Helium atom scattering data, linking the Debye-Waller factor to the coupling constant.

Contribution

It introduces a new derivation showing the Debye-Waller exponent's direct proportionality to the electron-phonon coupling constant, enabling direct measurement from scattering data.

Findings

The Debye-Waller exponent is proportional to the electron-phonon coupling constant λ.

Comparison with literature shows substantial agreement in λ values.

Method allows extraction of λ from temperature or energy dependence of scattering intensities.

Abstract

A new quantum-theoretical derivation of the elastic and inelastic scattering probability of He atoms from a metal surface, where the energy and momentum exchange with the phonon gas can only occur through the mediation of the surface free-electron density, shows that the Debye-Waller exponent is directly proportional to the electron-phonon mass coupling constant $\lambda$. The comparison between the values of $\lambda$ extracted from existing data on the Debye-Waller factor for various metal surfaces and the $\lambda$ values known from literature indicates a substantial agreement, which opens the possibility of directly extracting the electron-phonon coupling strength in quasi-2D conducting systems from the temperature or incident energy dependence of the elastic Helium atom scattering intensities.