Phonon Softening and Weak Temperature-dependent Lorenz Number for   Bio-supported Ultra-thin Ir Film
  This work reports on the first-time study of the temperature-dependent behavior of the Lorenz number of bio-supported average 3.2 nm-thin Ir film down to 10 K. Due to the strong imperfection-electron scattering, a very large residual resistivity is observed for the film that dominates the overall electron transport. The Debye temperature (221 K)of the film is found much smaller than that of bulk (308 K). This phonon softening strongly confirms the extensive surface and grain boundary electron scatterings. More than one order of magnitude reduction is observed for the thermal conductivity of the film. We find the Wiedemann-Franz Law still applies to our film even at low temperatures. The overall Lorenz number and that of imperfection structure are close to the Sommerfeld value and shows little temperature dependence. This is contrast to other studied low dimensional metallic structures that have a much larger Lorenz number. Electron tunneling and hopping in the biomaterial substrate are speculated responsible for the observed Lorenz number. 
Zhe Cheng, Zaoli Xu, Shen Xu, Xinwei Wang, Yuanyuan Wang
cond-mat.mes-hall