# Phonon-induced electronic relaxation in a strongly correlated system: the Sn/Si(111) $(\sqrt 3 \times \sqrt 3)$ adlayer revisited

## TL;DR

This study combines first-principles calculations and modeling to reveal that electron-hole pair excitations in the Sn/Si(111) surface are long-lived due to non-linear phonon decay processes, highlighting strong electronic correlations.

## Contribution

The paper demonstrates the long-lived nature of electron-hole excitations in a strongly correlated surface system using a hybrid functional and Mott-Hubbard model, linking electronic correlations with phonon spectra.

## Key findings

- Electron-hole pairs can last hundreds of nanoseconds.
- Electronic correlations stiffen specific surface phonon modes.
- Decay into phonons is highly non-linear, prolonging excitation lifetimes.

## Abstract

The ordered adsorbate layer Sn/Si(111) $(\sqrt 3 \times \sqrt 3)$ with coverage of one third of a monolayer is considered as a realization of strong electronic correlation in surface physics. Our theoretical analysis shows that electron-hole pair excitations in this system can be long-lived, up to several hundred nanoseconds, since the decay into surface phonons is found to be a highly non-linear process. We combine first-principles calculations with help of a hybrid functional (HSE06) with modeling by a Mott-Hubbard Hamiltonian coupled to phononic degrees of freedom. The calculations show that the Sn/Si(111) $(\sqrt 3 \times \sqrt 3)$ surface is insulating and the two Sn-derived bands inside the substrate band gap can be described as the lower and upper Hubbard band in a Mott-Hubbard model with $U=0.75$eV. Furthermore, phonon spectra are calculated with particular emphasis on the Sn-related surface phonon modes. The calculations demonstrate that the adequate treatment of electronic correlations leads to a stiffening of the wagging mode of neighboring Sn atoms; thus, we predict that the onset of electronic correlations at low temperature should be observable in the phonon spectrum, too. The deformation potential for electron-phonon coupling is calculated for selected vibrational modes and the decay rate of an electron-hole excitation into multiple phonons is estimated, substantiating the very long lifetime of these excitations.