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, $L_{\phi }$, is greater than $L_0$, 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 $T_c$=1.192 to 4.0 K we have quantitatively analyzed the magnetiresistance and determined the phase-breaking length, $L_{\phi }$(T). The predominant phase-breaking mechanism inferred from such analysis is found to be one-dimensional electron-electron scattering with small (quasielastic) energy transfers.