Temperature dependence of the x - ray photoemission line shape and of the hopping rate in a marginal Fermi liquid

AbslraeL We study the spectral properties of a localized particle (a deep core level, or a heavy particle hopping in a solid), coupled to conduction electrons that are described by a marginal Fermi liquid hypotheris. Our main result is that, in lhis model, the core lwel line shape in an x-ray photoemission experiment shifls with temperature. m e spestmm we find is consistent with the decrease of the hopping rate with decreasing lemperature obtained by Zhaug CI al. In the presence of a distribution of energy levels for the hopping panicle, the temperature dependence of the hopping rate is found to be l ess pronounced. The observability of both the shifl in the x-ray photoemission s p e c t ~ m and the decrease of the hopping rale depends on the strength of the interaction. Our mugh estimate of the value of the interaction parameter indicates that lhe effect might be obsenrable in x-ray photoemission experiments As is well known, the normal-state properties of high-temperature superconductors differ in many ways from those of classical superconductors. To describe these merences empirically, Varma et a1 [I,?.] recently introduced the marginal Fermi liquid (MFL) hypothesis, a phenomenological unsutz for the electronic polarizability. From this umutz, they can reproduce a large number of the characteristic features of the high-temperature superconductors. At present, though, a microscopic basis for this MFL hypothesis is lacking, nor is it clear to what extent the umutz can really be self-consistent. In the absence of a theory, it is important to try to assess the range of validity of the MFL hypothesis as much as possible, by comparing its predictions with experiments. Recently, Zhang et uf [3] pointed out that the hopping of a localized particle that interacts with an MFL differs significantly from that of a particle interacting with an ordinary Fermi liquid (FL): in an ~ n , the hopping rate U goes down as the temperature is lowered, whereas in an FL it goes up with decreasing temperature. This is due to the vanishing of the quasi-particle spectral weight at the Fermi surface in the MFL umu~z, or, equivalently, due to the logarithmic divergence of the effective mass as T + 0 in an MFL In a metal, the probability of a particle hopping to a neighbouring site is lowered because of the interaction with the conduction electrons. The overlap of the many-electron wave functions with …