Phonon Contribution to quasiparticle lifetimes in Cu measured by angle-resolved photoemission PRB 51, (1995)‏

Experiment Line shape of photoelectron spectrum emitted from sp-derived surface state at on Cu(111) is investigated Line shape is Lorentzian, linear T dependence of width (30 30 K, K)‏ Less than 5 meV variation with binding energy Temperature dependence explained as phonon contribution to inverse hole lifetime

Experiment electron-phonon mass enhancement parameter Looking at bulk holes in copper near to the Fermi energy, comparable to determinations based on low-energy techniques (Fermi surface probes, conductivity, specific heat measurements)‏ There exist three processes which (linearly, because of theory) contribute to valence hole decay at T=0 in metals

Experiment* Aim: quantitative understanding of temperature dependence of linewidth of a Cu(111) surface state based on phonon contribution to hole lifetime and to describe a surface sensitive method of determining

Theory Spectral function (indicates how line looks)‏ Self energy (zero for noninteracting situation)‏ change in - energy - lifetime

Theory If self energy is only weekly dependent on energy and its imaginary component is small compared to binding energy, then : and therefore the lineshape is Lorentzian with FWHM: the contributions add linearly.

Contributions* Auger decay (one hole decays into two less tightly bound holes and an electron via electron- electron interaction (electron hole pair creation))‏ Phonon scattering (hole decays into less tightly bound hole plus a phonon via electron-phonon interaction (phonon creation))‏ Scattering by an impurity/defect (changed momentum at fixed energy)‏

Contributions Auger decay (5 meV, T contribution <1 meV)‏ Phonon Scattering (valid at T<<300 K, near Fermi energy, see width vs temperature plot)‏

width vs temperature

Contributions Dependence of phonon contribution on energy requires assumption about the form of phonon spectrum, very little energy dependence on width until hole energies in the phonon band are reached Inverse lifetime

Contributions* f=Fermi-, n=Bose-Einstein-Distribution alpha^2 F= Eliashberg coupling function, in the Debye-model it will become lambda*(omega/omega_d)^2 for omega<omega_d and 0 for all other cases Impurity scattering contribution is proportional to the impurity concentration (independent of T and binding energy) [for bulk, effect is about 10 meV/%]

width vs binding energy*

Results Auger Contribution small, its temperature dependence even smaller Impurity and defect contribution is independent of temperature and binding energy (expected to be important for typical degrees of surface cleanliness)‏ Phonon contribution is dominant at room temperature (nearly all of T dependence)

Results T dependence is linear (slope )‏ Experimental determination of through width vs temperature plot is possible (see width vs temperature plot)‏

peak width vs temperature

data plot of normal emission* Representative data at normal emission (2 peak structure from ArI doublet), foregoing plot made of these plots Off normal slightly wider (<5 meV), but same temperature dependence

Problems* Closer Analysis shows dependence of on position on the Fermi surface Experiment cyclotron masses: M.J.G. Lee, PRB 2,250(1970): =0.085(belly) to =0.023(neck) Theory: F.S. Khan et al., PRB 26,1538(1982) =0.08(belly) to =0.16(neck)‏ (belly,neck) – orbit perpendicular to (111) direction

Problem + Solution* Bulk Fermi surface states are those at the neck, therefore comparison leads to substantial disagreement between photoemission and clyclotron masses experiment, but good agreement with theory Possible solution: Lee Experiment wrong, while it uses =m_obs/m_0 – 1, where m_obs is observed mass and m is the calculated bare mass

Possible solution* While is relatively small, uncertainites of 10% in measurement and bare mass calculation can be maginified to near 100% in determination of Photoemission is more direct and sensitive, therefore it is more likely to be correct.

Conclusion Valence photoemission linewidths can be quantitatively understood as inverse hole lifetimes using known bulk parameters Dominant contribution to hole lifetime typically comes from phonons Surface value for can be derived from temperature dependence of observed linewidth