Nonmonotonic temperature dependence of the thermopower of atomic-size gold contacts
We report measurements of the thermopower of atomic-size gold contacts realized by the mechanically controllable break junction (MCBJ) technique over a temperature range from 18 K to 295 K. A thermometer included in the lithographic structure close to the constriction provides a direct measurement of the temperature increase generated by heating one side of the contact with a focused laser beam. While the conductance histograms confirm the quantum nature of the transport, we observe a nonmonotonic temperature dependence of the ensemble-averaged thermopower with a minimum of $-2\,\mu$VK$^{-1}$ at about 150 K. The values for the thermopower obtained at the lowest and the high temperature are compatible with values reported in the literature, but the nonmonotonic behavior in between disagrees with the expected linear dependence for quantum coherent conductors described by the Landauer formula. We develop a theoretical model based on an energy dependent transmission function that qualitatively reproduces the nonmonotonic behavior, but fails quantitatively. We therefore interpret our data as a result of phonon contributions to the thermopower beyond the Landauer model and with opposite sign than the classical phonon drag known from bulk systems. Our findings show that, firstly, the thermopower gives important insight into the transport properties of atomic-size structures and second that the linear approximation of the Landauer model has to be used with caution when studying more complex transport properties even for atomic contacts from free-electron metals.