Magnetoresistance measurements on fractal wire networks

Measurements of the magnetoresistance have been carried out on aluminum Sierpinski gasket wire networks fabricated using submicrometer E-beam lithography. The results are in agreement with the predictions of recent calculations of the localization contribution to the magnetoresistance in the fractal regime where the phase-breaking length, L, is greater than L0, the minimum gasket dimension. All details of the theory are observed, including periodic corrections to scaling due to the discrete dilational invariance of the gasket. Over the temperature range from Tc=1.192 to 4.0 K we have quantitatively analyzed the magnetiresistance and determined the phase-breaking length, L(T). The predominant phase-breaking mechanism inferred from such analysis is found to be one-dimensional electron-electron scattering with small (quasielastic) energy transfers.