A temperature behavior of the frustrated translational mode of adsorbate and the nature of the "adsorbate-substrate" interaction

TL;DR

This paper investigates how the frustrated translational mode of adsorbates varies with temperature, revealing different behaviors based on the ohmicity of the system and providing analytical expressions for shifts and broadening.

Contribution

It introduces a formalism for analyzing the temperature dependence of the T-mode considering memory effects and derives analytical expressions for weak coupling in specific regimes.

Findings

T-mode shift and broadening are linear in temperature for Ohmic and super-Ohmic systems.

Nonlinear temperature dependence of T-mode observed in strongly sub-Ohmic systems.

Explanation of experimental blue- or red-shifts based on system evolution times.

Abstract

A temperature behavior of the frustrated translational mode (T-mode) of a light particle, coupled by different regimes of ohmicity to the surface, is studied within a formalism of the generalized diffusion coefficients. The memory effects of the adsorbate motion are considered to be the main reason of the T-mode origin. Numerical calculations yield a thermally induced shift and broadening of the T-mode, which is found to be linear in temperature for Ohmic and super-Ohmic systems and nonlinear for strongly sub-Ohmic ones. We obtain analytical expressions for the T-mode shift and width at weak coupling for the systems with integer "ohmicity" indexes n=0-2 in zero temperature and high temperature limits. We provide an explanation of the experimentally observed blue- or red-shifts of the T-mode on the basis of a comparative analysis of two typical times of the system evolution: a time of decay of the "velocity-velocity" autocorrelation function, and a correlation time of the thermal bath random forces. A relation of the T-mode to the multiple jumps of the adsorbate is discussed, and generalization of conditions of the multiple hopping to the case of quantum surface diffusion is performed.