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The temperature-dependent damping of quantum-mechanical interference patterns from surface-state electrons scattering off steps on Ag(111) and Cu(111) has been studied using scanning tunneling microscopy (STM) and spectroscopy in the temperature range 3,5-178 K. The thermal damping of the electron standing waves is described quantitatively within a simple plane-wave model accounting for thermal broadening due to the broadening of the Fermi-Dirac distributions of sample and tip, for beating effects between electrons with different kll vectors, and for inelastic collisions of the electrons, e.g., with phonons. Our measurements reveal that Fermi-Dirac broadening fully explains the observed damping for Ag and Cu. From the analysis of our data, lower limits of the phase-relaxation lengths at the Fermi energy EF Of the two-dimensional electron gas of L-phi(E-F)greater than or similar to 600 Angstrom at 3.5 K and greater than or similar to 250 Angstrom at 77 K for Ag(111), and of L-phi(E-F)greater than or similar to 660 Angstrom at 77 K and greater than or similar to 160 Angstrom at 178 K for Cu(111) are deduced. In contrast to integral measurements such as photoemission we measure L-phi close to EF and also locally. The latter eliminates residual line widths due to surface defect scattering found in the integrating techniques. Our STM results, therefore, currently provide a very good absolute estimate of L-phi and the inelastic lifetime tau=L-phi/v(F), respectively. Our values can be combined with photoemission results on dL(phi)/dT to derive the inelastic lifetime of surface state electrons at any T.
Fabrizio Carbone, Alexey Sapozhnik, Phoebe Marie Tengdin, Giovanni Maria Vanacore, Ivan Madan, Ido Kaminer, Simone Gargiulo, Francesco Barantani, Veronica Leccese
Javier García Hernández, Mikhail Maslov, Samuele Mazzi