Experimental study of localization in thin wires

Abstract

The electrical properties of wires with cross-sectional areas in the range 1 × ${10}^{-11\mathrm{}}$ to 3 × ${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^2$ have been studied. At temperatures below about 10 K, the resistance of the wires increases as the temperature is lowered. The magnitude of the resistance rise increases both as the cross-sectional area of the wire is made smaller and as the amount of randomness is increased. This behavior is in qualitative agreement with the recent predictions by Thouless concerning localization in thin wires. However, the magnitude of the resistance rise is much smaller than originally predicted, and to obtain quantitative agreement with the experimental results it is necessary to assume that the rate at which electrons are inelastically scattered is proportional to the temperature and independent of the size of the wire. This is not consistent with the usual electron-phonon or electron-electron scattering process, and suggests that either the sample geometry affects these processes or that scattering from some other source, such as the tunneling levels believed to be present in all highly disordered systems, is the dominant inelastic scattering process. Experiments on thin films with resistances per square in the range 15 to 100 $\Omega$ are also reported. The behavior of the films is similar to that of the wires; they exhibit a resistance rise at low temperatures, and the magnitude of the rise becomes larger as the resistance per square is increased. These results are in good agreement with the predictions of Abrahams et al. for localization in two dimensions and correlate well with recent experimental results of Dolan and Osheroff. The effect of a magnetic field has also been investigated. It is found that a field of 75 kOe has no significant effect on the behavior of the wires. However, a field of this size appears to change the behavior of the films markedly. While our results are all consistent with theoretical predictions based on localization, they are also consistent with recent theories based on electron-electron interaction effects in disordered systems.