Electron-Mediated Phonon-Phonon Coupling Drives the Vibrational Relaxation of CO on Cu(100)

We bring forth a consistent theory for the electron-mediated vibrational intermode coupling that clarifies the microscopic mechanism behind the vibrational relaxation of adsorbates on metal surfaces. Our analysis points out the inability of state-of-the-art nonadiabatic theories to quantitatively reproduce the experimental linewidth of the CO internal stretch mode on Cu(100) and it emphasizes the crucial role of the electron-mediated phonon-phonon coupling in this regard. The results demonstrate a strong electron-mediated coupling between the internal stretch and low-energy CO modes, but also a significant role of surface motion. Our nonadiabatic theory is also able to explain the temperature dependence of the internal stretch phonon linewidth, thus far considered a sign of the direct anharmonic coupling.

Figure 1

(a) Schematic of the EMPP coupling process of the IS mode of CO on Cu(100). The IS mode (red) couples to low-energy FR and FT modes, as well as to the modes consisting of the joint motion of CO and Cu surface atoms (blue). (b) Indirect phonon-assisted electronic transitions involved in the EMPP process at $T=0\mathrm{K}$ (phonon emission) and $T>0\mathrm{K}$ (phonon absorption). In each case, both intraband and interband scattering are allowed.

Figure 2

(a) Different contributions to the IS phonon linewidth ${\gamma }_{0\lambda }$ coming from direct interband transitions (dark blue), interband transitions with phenomenological broadening $\mathrm{\Gamma }=60\mathrm{meV}$ (light blue), and the EMPP coupling at $T=10\mathrm{K}$ (orange). The experimental total linewidths obtained in Refs. [2, 4] are shown with blue and brown dashed lines, respectively. The inelastic contribution obtained in Ref. [4] is shown with a red dashed line. Gray shaded area represents all the other experimental values, including experimental error bars [6]. (b) Temperature dependence of the IS phonon linewidth as obtained from the EMPP coupling term (blue dots) and the corresponding experimental values [5] (orange diamonds).